Patent Publication Number: US-10777831-B2

Title: Equation based cooling system control strategy/method

Description:
BACKGROUND 
     1. Field 
     The present disclosure relates to systems and methods for controlling a temperature of a fluid that flows through a fuel cell stack of a fuel cell circuit based on feedforward and feedback control of multiple actuators of the fuel cell circuit. 
     2. Description of the Related Art 
     As the push for conservation of natural resources and reduced pollution advances, various concepts have been discovered to achieve such goals. These concepts range from harvesting wind and sun-based energy to various improvements in vehicle design. The vehicle improvements include new engines designed to improve fuel economy, hybrid vehicles that operate using a combination of an engine and a motor-generator to further improve fuel economy, fully electric vehicles that operate based on power stored in a battery, and fuel cell vehicles that generate electricity by facilitating a chemical reaction. 
     Many fuel cell vehicles include a fuel cell stack that includes multiple fuel cells. The fuel cells may receive a fuel, which typically includes hydrogen, along with oxygen or another oxidizing agent. The fuel cell stack may facilitate a chemical reaction between the hydrogen and oxygen. This chemical reaction generates electricity and water as a byproduct. The electricity generated by the fuel cell stack may be stored in a battery or directly provided to a motor-generator to generate mechanical power to propel the vehicle. While fuel cell vehicles are an exciting advance in the automobile industry, the technology is relatively new, providing space for improvements to the technology. 
     It is desirable for fuel cells to operate within a predetermined temperature range. If the temperature is too low then the power output by the fuel cells may likewise be relatively low. If the temperature is too high then the fuel cells may dry out, damaging or destroying the fuel cells. 
     Thus, there is a need in the art for systems and methods for accurately controlling a temperature of a fuel cell stack use in a vehicle. 
     SUMMARY 
     Described herein is a system for heating or cooling a fuel cell circuit of a vehicle. The system includes a fuel cell stack having a plurality of fuel cells and designed to receive a fluid and to heat the fluid. The system also includes a temperature sensor designed to detect a fluid temperature of the fluid. The system also includes a pump designed to pump the fluid through the fuel cell circuit. The system also includes an electronic control unit (ECU) coupled to the temperature sensor and the pump. The ECU is designed to determine a temperature control signal based on the fluid temperature of the fluid. The ECU is also designed to calculate a desired mass flow rate of the fluid through the fuel cell stack based on the temperature control signal. The ECU is also designed to calculate a desired pump speed of the pump based on the desired mass flow rate of the fluid through the fuel cell stack. The ECU is also designed to control the pump to pump the fluid at the desired pump speed to increase or decrease the fluid temperature of the fluid. 
     Also described is a system for heating or cooling a fuel cell circuit of a vehicle. The system includes a fuel cell stack having a plurality of fuel cells and designed to receive a fluid and to heat the fluid. The system also includes a temperature sensor designed to detect a fluid temperature of the fluid. The system also includes a radiator designed to remove thermal energy from at least some of the fluid. The system also includes a fan designed to force a gas towards the radiator to increase heat transfer from the fluid to the gas. The system also includes an electronic control unit (ECU) coupled to the temperature sensor and the pump. The ECU is designed to determine a temperature control signal based on the fluid temperature of the fluid. The ECU is also designed to calculate a desired amount of thermal energy to be removed from the radiator by the fan based on the temperature control signal. The ECU is also designed to calculate a desired fan speed of the fan to achieve the desired amount of thermal energy to be removed from the radiator by the fan based on the desired amount of thermal energy to be removed from the radiator by the fan. The ECU is also designed to control the fan to operate at the desired fan speed. 
     Also described is a method for heating or cooling a fuel cell circuit of a vehicle. The method includes receiving and heating, by a fuel cell stack having a plurality of fuel cells, a fluid. The method also includes detecting, by a temperature sensor, a fluid temperature of the fluid. The method also includes determining, by an electronic control unit (ECU), a temperature control signal based on the fluid temperature of the fluid. The method also includes calculating, by the ECU, a desired fluid ratio corresponding to a desired percentage of a flow of the fluid that is received by a radiator of the fuel cell circuit to a total flow of the fluid through the radiator and through a bypass branch that bypasses the radiator based on the temperature control signal. The method also includes determining, by the ECU, a desired valve position of a three-way valve based on the desired fluid ratio. The method also includes controlling, by the ECU, the three-way valve to have the desired valve position such that the three-way valve achieves the desired fluid ratio. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other systems, methods, features, and advantages of the present invention will be or will become apparent to one of ordinary skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present invention, and be protected by the accompanying claims. Component parts shown in the drawings are not necessarily to scale, and may be exaggerated to better illustrate the important features of the present invention. In the drawings, like reference numerals designate like parts throughout the different views, wherein: 
         FIG. 1  is a block diagram illustrating various components of a vehicle having a fuel cell circuit capable of generating electricity based on a chemical reaction according to an embodiment of the present invention; 
         FIG. 2  is a block diagram illustrating various features of the fuel cell circuit of  FIG. 1  according to an embodiment of the present invention; 
         FIG. 3  is a block diagram illustrating various logic components of an electronic control unit (ECU) of the vehicle of  FIG. 1  for increasing or decreasing a temperature of fluid in the fuel cell circuit according to an embodiment of the present invention; 
         FIG. 4  is a flowchart illustrating a method for determining a desired temperature rate of change of a fuel cell circuit in order to cause a temperature of fluid to reach a desired temperature of the fluid according to an embodiment of the present invention; 
         FIG. 5  is a graph illustrating an exemplary implementation of the method of  FIG. 4  according to an embodiment of the present invention; 
         FIG. 6  illustrates a lookup table that maps target fuel cell outlet temperatures to temperature differentials according to an embodiment of the present invention; 
         FIG. 7  is a graph illustrating requested and actual temperatures of fluid of a fuel cell circuit controlled using a method similar to the method of  FIG. 4  according to an embodiment of the present invention; 
         FIGS. 8A and 8B  are flowcharts illustrating a method feedforward control of one or more actuator of a fuel cell circuit to heat or cool the fuel cell circuit using according to an embodiment of the present invention; 
         FIGS. 9A and 9B  are flowcharts illustrating a method for estimating parameters usable to control one or more actuator of a fuel cell circuit according to an embodiment of the present invention; 
         FIG. 10  is a block diagram illustrating a model of a fuel cell circuit used by the method of  FIGS. 9A and 9B  to estimate the parameters according to an embodiment of the present invention; 
         FIG. 11  is a block diagram illustrating an exemplary flow splitting element of a fuel cell circuit according to an embodiment of the present invention; 
         FIGS. 12A and 12B  are flowcharts illustrating a method for feedback based heating or cooling of a fuel cell circuit according to an embodiment of the present invention; 
         FIG. 13  is a block diagram illustrating a three-way valve controller for feedback based control of a three-way valve of a fuel cell circuit according to an embodiment of the present invention; 
         FIG. 14  is a block diagram illustrating a pump controller for feedback based control of a pump of a fuel cell circuit according to an embodiment of the present invention; 
         FIGS. 15A and 15B  are flowcharts illustrating a method for correcting an estimated parameter that is used to control an actuator of a fuel cell circuit according to an embodiment of the present invention; and 
         FIG. 16  is a block diagram illustrating an estimated parameter controller for correcting an estimated parameter that is used to control a fan of a fuel cell circuit according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure describes systems and methods for heating and cooling fuel cells of a fuel cell circuit. In particular, the present disclosure describes systems and methods for feedforward control of actuators to increase or decrease a fluid temperature of fluid within the fuel cell circuit. The system advantageously includes multiple actuators, the inclusion of which facilitates relatively fine tuning of the fluid temperature. The actuators are controlled based on modeled temperature and pressure values which are beneficially updated in near real-time, providing the benefit of higher accuracy relative to sensors that have delayed readings. Furthermore, use of the modeled temperature and pressure values reduces the cost of the fuel cell circuit because less sensor hardware is required for accurate temperature control. 
     An exemplary system includes a fuel cell stack having multiple fuel cells that receive a fluid. The system also includes a temperature sensor to detect a fluid temperature. The system further includes a pump to pump the fluid, a radiator to cool the fluid, a radiator fan to increase radiator cooling, and a three-way valve that directs the fluid through either the radiator or a bypass branch that bypasses the radiator. The system further includes an electronic control unit (ECU) that receives the detected fluid temperature and determines a temperature control signal based on the detected fluid temperature. The ECU also calculates pressure, temperature, and other values at various locations along the fuel cell circuit and controls the actuators based on the fluid temperature and the calculated values. 
     Turning to  FIG. 1 , a vehicle  100  includes components of a system  101  for controlling a temperature of fuel cells of the vehicle. In particular, the vehicle  100  and the system  101  include an ECU  102 , a memory  104 , a speed sensor  106 , and a temperature sensor  108 . The vehicle  100  further includes a power source  110  which may include at least one of an engine  112 , a motor-generator  114 , a battery  116 , or a fuel cell circuit  118 . 
     The ECU  102  may be coupled to each of the components of the vehicle  100  and may include one or more processors or controllers, which may be specifically designed for automotive systems. The functions of the ECU  102  may be implemented in a single ECU or in multiple ECUs. The ECU  102  may receive data from components of the vehicle  100 , may make determinations based on the received data, and may control the operation of components based on the determinations. 
     In some embodiments, the vehicle  100  may be fully autonomous or semi-autonomous. In that regard, the ECU  102  may control various aspects of the vehicle  100  (such as steering, braking, accelerating, or the like) to maneuver the vehicle  100  from a starting location to a destination. 
     The memory  104  may include any non-transitory memory known in the art. In that regard, the memory  104  may store machine-readable instructions usable by the ECU  102  and may store other data as requested by the ECU  102 . 
     The speed sensor  106  may be any speed sensor capable of detecting data usable to determine a speed of the vehicle  100 . For example, the speed sensor  128  may include a GPS sensor or an IMU sensor. The speed sensor  128  may also or instead include an angular velocity sensor configured to detect an angular velocity of the wheels of the vehicle  100  or the engine, a speedometer, or the like. 
     The temperature sensor  108  may include one or more temperature sensor capable of detecting data usable to determine an ambient temperature within a portion of the vehicle  100  or outside of the vehicle  100 . For example, the temperature sensor  108  may include a thermocouple, a thermometer, an infrared temperature sensor, a thermistor, or the like. 
     The engine  112  may convert a fuel into mechanical power. In that regard, the engine  112  may be a gasoline engine, a diesel engine, or the like. 
     The battery  116  may store electrical energy. In some embodiments, the battery  116  may include any one or more energy storage device including a battery, a fly-wheel, a super-capacitor, a thermal storage device, or the like. 
     The fuel cell circuit  118  may include a plurality of fuel cells that facilitate a chemical reaction to generate electrical energy. In that regard, the electrical energy generated by the fuel cell circuit  118  may be stored in the battery  116 . In some embodiments, the vehicle  100  may include multiple fuel cell circuits including the fuel cell circuit  118 . 
     The motor-generator  114  may convert the electrical energy stored in the battery (or electrical energy received directly from the fuel cell circuit  118 ) into mechanical power usable to propel the vehicle  100 . The motor-generator  114  may further convert mechanical power received from the engine  112  or wheels of the vehicle  100  into electricity, which may be stored in the battery  116  as energy and/or used by other components of the vehicle  100 . In some embodiments, the motor-generator  114  may also or instead include a turbine or other device capable of generating thrust. 
     The body of the vehicle  100  may include a grill  120  located at a front of the vehicle. The grill  120  may receive an airflow  122 . The speed of the airflow  122  may directly correspond to the speed of the vehicle  100 . For example, if a headwind of 5 miles per hour (mph) exists outside of the vehicle  100  and the vehicle is traveling at 50 mph then the speed of the airflow  122  will be approximately 55 mph. 
     Turning now to  FIG. 2 , additional details of the fuel cell circuit  118  are illustrated. The fuel cell circuit  118  includes a fuel cell stack  200  having a plurality of fuel cells. The fuel cells may each facilitate a chemical reaction to generate electricity. The reaction may generate heat. Furthermore, a fluid may flow through the fuel cell stack  200  and may transfer at least some of the heat away from the fuel cell stack  200 . In that regard, the fuel cell stack  200  may include an inlet  228  for receiving the fluid and an outlet  230  through which the fluid exits the fuel cell stack  200 . 
     It may be desirable for the fuel cell stack  200  to operate within a predetermined temperature range. For example, it may be desirable for the fuel cells of the fuel cell stack  200  to operate between 50 degrees Celsius (50 degrees C., 122 degrees Fahrenheit (122 degrees F.)) and 80 degrees C. (176 degrees F.). 
     The fuel cell stack  200  may generate more electrical energy at relatively high temperatures (i.e., when the temperature is closer to 80 degrees C. than 50 degrees C.). However, the fuel cell stack  200  may undesirably lose moisture (i.e., may dry out) when operated at these relatively high temperatures. In that regard, it may be desirable for the fuel cell stack  200  to operate closer to 80 degrees C. when a relatively large amount of electrical energy is requested, and closer to 50 degrees C. when a relatively small amount of electrical energy is requested. The fuel cell circuit  118  includes various features for increasing or decreasing the temperature of the fuel cell stack  200 . 
     The fuel cell circuit  118  may further include an intercooler  202 . The intercooler  202  may be oriented in parallel with the fuel cell stack  200 . The intercooler  202  may receive a hot airflow  203  (i.e., an airflow having a greater temperature than the temperature of the fluid within the intercooler  202 ) and may transfer heat from the hot airflow  203  to the fluid. Accordingly, the fuel cell stack  200  and the intercooler  202  may be considered heating elements of the fuel cell circuit  118  as they both increase the temperature of the fluid. All of the fluid within the fuel cell circuit  118  eventually flows through the combination of the fuel cell stack  200  and the intercooler  202  as shown by an arrow  205 . 
     The fuel cell circuit  118  may further include a three-way valve  204 . The fuel cell circuit  118  may also include one or more radiator  210  along with a bypass branch  206  that bypasses the one or more radiator  210 . The three-way valve  204  may divide the fluid between the radiators  210  and the bypass branch  206  based on a valve position of the three-way valve  204 . The three-way valve  204  may have multiple valve positions each dividing the flow between the bypass branch  206  and the radiators  210  at different ratios. 
     For example, the three-way valve  204  may have a first position in which 80 percent (80%) of the fluid flows through the bypass branch  206  (as shown by an arrow  207 ) and 20% of the fluid flows through the radiators  210  (as shown by an arrow  209 ). The three-way valve  204  may further have a second position in which 70% of the fluid flows through the bypass branch  206  and 30% of the fluid flows through the radiators  210 . The three-way valve  204  may have multiple discrete valve positions or may have infinite continuous valve positions (i.e., may direct any value between 0% and 100% of the fluid through each of the bypass branch  206  or the radiators  210 ). 
     The fluid that flows through the bypass branch  206  may avoid the radiators  210 , thus allowing a majority of heat within the fluid to remain in the fluid. An ionizer  208  may receive some of the fluid that flows through the bypass branch  206 . The ionizer  208  may function as an ion exchanger and may remove ions from the fluid to reduce conductivity. In that regard, the ionizer may be referred to as a de-ionizer. 
     The radiators  210  may transfer heat away from the fluid to a gas (such as air) flowing over or past the radiators  210 . In that regard, the radiators  210  may be referred to as cooling elements of the fuel cell circuit  118 . 
     In some embodiments, the radiators  210  may include a main radiator  212  and two secondary radiators  214 ,  216 . A fan  218  may be oriented in such a manner as to direct a flow of gas  219  over the radiators  210 . In some embodiments, the fan  218  may only direct the flow of gas  219  over the main radiator  212 . The main radiator  212  has a fluid inlet  232  in which the fluid flows into the main radiator  212  and a fluid outlet  234  in which the fluid flows out of the main radiator  212 . The main radiator  212  may further include an air inlet  236  that receives the gas  219  (i.e., airflow) from the fan  218  as well as an air outlet  238  in which the airflow exits the main radiator  212 . 
     Referring briefly to  FIGS. 1 and 2 , one or more of the radiators  210  may further receive the airflow  122  received via the grill  120  of the vehicle  100 . As mentioned above, the velocity of the airflow  122  corresponds to a speed of the vehicle  100 . As the speed of the vehicle  100  increases, the velocity of the airflow  122  further increases, thus increasing the transfer of heat away from the fluid. 
     Returning reference to  FIG. 2 , the fuel cell circuit  118  may further include a pump  220 . The pump  220  may include any pump capable of forcing the fluid through the fuel cell circuit  118 . For example, the pump  220  may include a hydraulic pump, a diaphragm pump, a piston pump, a rotary gear pump, or the like. 
     The fuel cell circuit  118  may further include a reservoir  240 . The reservoir may include a volume in which the fluid, such as a coolant, is stored. The fluid may be provided to the fuel cell circuit  118  from the reservoir  240 . In some embodiments, the reservoir  240  may include a port through which a user of the vehicle may provide the fluid to the reservoir  240 . 
     The fuel cell circuit  118  may further include two temperature sensors including a first temperature sensor  224  and a second temperature sensor  226 . The first temperature sensor  224  may detect the temperature of the fluid exiting the fuel cell stack  200  at the outlet  230 . The second temperature sensor  226  may detect the temperature of the combined fluid exiting the radiators  210 . In some embodiments, greater or fewer temperature sensors may be used, and the temperature sensors may be positioned at additional or alternative locations. 
     Referring again to  FIGS. 1 and 2 , the ECU  102  may determine a target temperature of the fuel cell stack  200  based on a received power request of the vehicle  100 . As described above, it may be desirable for the temperature of the fuel cell stack  200  to increase when a relatively large amount of power is requested from the fuel cell stack  200 . This is because the increased temperature corresponds to an increased power output of the fuel cell stack  200 . Likewise, it may be desirable for the temperature of the fuel cell stack  200  to decrease when a relatively small amount of power is requested from the fuel cell stack  200  in order to retain moisture in the fuel cell stack  200 . 
     The ECU  102  may also receive the detected temperatures from the first temperature sensor  224  and the second temperature sensor  226 . The ECU  102  may then control the actuators of the fuel cell circuit  118  (the three-way valve  204 , the fan  218 , and the pump  220 ) to cause the temperature of the fuel cell stack  200  (such as the temperature of the fluid at the outlet  230 ) to increase or decrease. The ECU  102  may cause the temperature to increase or decrease towards the target temperature based on the target temperature and the detected temperatures. 
     The three-way valve  204  may be used to adjust the temperature of the fluid by directing more of the fluid through the bypass branch  206  or through the radiators  210 . For example, if the three-way valve  204  increases a flow of the fluid through the bypass branch  206  then the overall temperature of the fluid may increase because it is directed back towards the heating elements without significant loss of heat. Similarly, if the three-way valve  204  increases a flow of the fluid through the radiators  210  then the overall temperature of the fluid may decrease because more fluid is directed through the radiators  210  where thermal energy may be removed from the fluid. 
     The fan  218  may likewise be used to adjust the temperature of the fluid by increasing or decreasing the flow of gas  219  over the main radiator  212 . For example, if the speed of the fan  218  is increased (resulting in a greater quantity of gas  219  flowing over the main radiator  212 ) then the temperature of the fluid may decrease as more thermal energy is transferred out of the fluid. Similarly, if the speed of the fan  218  is decreased then the temperature of the fluid may increase as less thermal energy is transferred out of the fluid. 
     The pump  220  may also be used to indirectly adjust the temperature of the fluid by increasing or decreasing a flow rate, such as a mass flow rate, of the fluid through the fuel cell circuit  118 . As the flow rate increases, heat transfer between the fluid and the various components increases, which may result in an increase or decrease in temperature based on how much of the fluid flows through the bypass branch  206  or the radiators  210 , and based on a temperature of the fuel cell stack  200 . Thus, the temperature of the fluid may correspond to the flow rate of the fluid. 
     Referring now to  FIGS. 2 and 3 , the ECU  102  may include a temperature control system  303  that controls the temperature of the fuel cell circuit  118 . The temperature control system  303  may be implemented using specifically designated hardware of the ECU  102 , or may be implemented using general hardware of the ECU  102 . 
     The temperature control system  303  may include an upper controller  300 , a state mediator  304 , a state governor  308 , a feedforward control  312 , a feedback control  316 , a state estimator  320 , an observer  322 , and an actuator control  330 . The temperature control system  303  may receive an input, such as a power request  301 , and may generate an output, such as an actuator control signal  334 . 
     The upper controller  300  may receive the power request  301 . The upper controller  300  may then identify a target temperature of the fuel cell stack  200  based on the power request  301 . For example, if the power request is relatively large then the upper controller  300  may set a target temperature to be relatively high, such as 75 degrees C. (167 degrees F.). Likewise, if the power request is relatively small then the upper controller  300  may set a target temperature to be relatively low, such as 55 degrees C. (131 degrees F.). The upper controller  300  may then output an unfiltered target fuel cell temperature  302 . 
     The state mediator  304  may receive the unfiltered target fuel cell temperature  302 . The state mediator  304  may filter the received signal and output a target fuel cell temperature  306 . The state mediator  304  may filter the unfiltered target fuel cell temperature  302  for various reasons. For example, the filtering may remove noise on the signal, may act as a bandpass filter to ensure that the target fuel cell temperature  306  is within a safe temperature range, or the like. The safe temperature range may correspond to a temperature range at which the temperature is unlikely to damage components of the fuel cell circuit  118  (i.e., such as by overheating or drying out) and at which the fuel cell circuit  118  is capable of generating power. 
     The state governor  308  may receive the target fuel cell temperature  306 . The state governor  308  may generally dictate how fast the temperature of the fluid in the fuel cell circuit  118  should respond to the temperature change request (i.e., how fast the temperature should increase or decrease). The state governor  308  may output a temperature rate of change  310  corresponding to a desired rate of temperature change of the fluid (such as at the inlet  228  or the outlet  230  of the fuel cell stack  200 ). For example, the temperature rate of change  310  may be measured in degrees (e.g., degrees C.) per second. 
     The state estimator  320  may receive inputs including sensor values  326  and current actuator positions  328  (or commanded actuator positions) and may estimate conditions at various locations of the fuel cell circuit  118 . The sensor values may include, for example, temperatures detected from the first temperature sensor  224  and the second temperature sensor  226 . The actuator positions  328  may be received from the actuators  332  themselves (the pump  220 , the three-way valve  204 , and the fan  218 ) or from the actuator control signal  334 . 
     The fuel cell circuit  118  includes relatively few sensors. Additional data is desirable in order to provide optimal control of the actuators  332 . In that regard, the state estimator  320  may calculate or predict the additional data (i.e., current conditions) based on the sensor values  326  and the actuator positions  328 . For example, the state estimator  320  may calculate or predict temperatures at locations of the fuel cell circuit  118  in which temperature sensors are not present. As another example, the state estimator  320  may calculate or predict pressure of the fluid at various locations of the fuel cell circuit  118 . As yet another example, the state estimator  320  may further calculate or predict quantities of heat added to or subtracted from the fluid by the various elements of the fuel cell circuit  118 . The state estimator  320  may output calculated or predicted values  324  corresponding to current conditions of the fuel cell circuit  118 . 
     The feedforward control  312  may receive the temperature rate of change  310  from the state governor  308  along with the calculated or predicted values  324  from the state estimator  320 . In some embodiments, the feedforward control  312  may further receive the detected temperatures from the temperature sensors. The feedforward control  312  may determine desired positions of the actuators  332  to achieve the desired temperature rate of change  310  of the fluid of the fuel cell circuit  118 . The feedforward control  312  may determine these desired positions based on the received temperature rate of change  310  and the calculated or predicted values  324 . The feedforward control  312  may output feedforward control signals  314  corresponding to the determined desired positions of the actuators  332 . 
     The feedback control  316  may also receive the temperature rate of change  310  from the state governor  308  along with the calculated or predicted values  324  from the state estimator  320 . In some embodiments, the feedback control  316  may further receive the detected temperatures from the temperature sensors. The feedback control  316  may identify whether the actuators  332  are achieving the desired temperature rate of change  310 . The feedback control  316  may further generate feedback control signals  318  that correspond to adjustments to the actuators  332  to close the gap between a measured temperature rate of change and the desired temperature rate of change  310 . 
     The observer  322  may operate as feedback control for the radiators  210 . In that regard, the observer may determine a difference between a detected temperature at the outlet  227  of the radiators  210  and an estimated temperature at the outlet  227  as determined by the state estimator  320 . The observer  322  may then change values determined by the state estimator  320  to cause the estimated temperature to be closer in value to the detected temperature. 
     The actuator control  330  may receive the feedforward control signals  314  and the feedback control signals  318  and generate actuator control signals  334  based on the combination of the feedforward control signals  314  and the feedback control signals  318 . One or more of the actuator control signals  334  may be transmitted to each of the actuators  332 . For example, the actuator control signals  334  may include a first signal that controls a valve position of the three-way valve  204 , a second signal that controls a fan speed of the fan  218 , and a third signal that controls a pump speed of the pump  220 . In some embodiments, the actuator control  330  may generate the actuator control signals  334  by adding the feedforward control signals  314  and the feedback control signals  318 . 
     Referring now to  FIG. 4 , a method  400  for determining a desired temperature rate of change of a fuel cell circuit, such as the fuel cell circuit  118  of  FIG. 2 , is shown. The method  400  may be performed by a state governor, such as the state governor  308  of  FIG. 3 . 
     In block  402 , one or more temperature sensor of a fuel cell circuit may detect a current temperature corresponding to a temperature of fluid within the fuel cell circuit. For example, the first temperature sensor  224  may detect a temperature of the fluid at the outlet  230  of the fuel cell stack  200 , and the second temperature sensor  226  may detect a temperature of the fluid at the outlet  227  of the radiators. 
     In block  404 , the ECU of the vehicle may estimate or calculate additional values corresponding to the fuel cell circuit. For example, the state estimator  320  of  FIG. 3  may estimate or calculate values based on the detected temperatures and the current actuator positions. The additional values may include, for example, temperatures of the fuel cell circuit at locations other than the locations of the temperature sensors, pressures at various locations along the fuel cell circuit, or the like. 
     In block  406 , if the vehicle or fuel cell stack is warming up from a cold start (i.e., such as when the vehicle is initially turned on) then the ECU may determine a fuel cell inlet temperature command value. The ECU may determine the target fuel cell inlet temperature based on the temperatures detected in block  402  and the values calculated in block  404 . For example, the target fuel cell inlet temperature may be determined using equation 1 below. 
     
       
         
           
             
               
                 
                   
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     In equation 1, 
             T     FC     in   cmd             
corresponds to the target fuel cell inlet temperature. T FC     cmd    corresponds to the target fuel cell outlet temperature, which is set to be equal to the detected fuel cell outlet temperature of the fuel cell stack during the warm-up. ΔT FC     tgt    corresponds to a target temperature difference between the fuel cell inlet temperature and the fuel cell outlet temperature, and is determined by the upper controller. T FC     in cmd previous    corresponds to the target fuel cell inlet temperature determined during a previous calculation of equation 1. T FC     in tgt    corresponds to a final target fuel cell inlet temperature, which is the final desired operating temperature of the fluid at the inlet.
 
     After the fuel cell circuit has warmed up, the final target fuel cell inlet temperature remains relatively constant, and thus is a stable (i.e., unchanging) value during operation of the fuel cell circuit. Stated differently, the final target fuel cell inlet temperature remains relatively unchanged throughout operation of the vehicle after the initial warmup. 
     Referring briefly to  FIG. 5 , a graph  500  illustrates implementation of equation 1 by the ECU to set the target fuel cell inlet temperature. In particular, the graph  500  illustrates the current fuel cell outlet temperature  502 , the target fuel cell outlet temperature  504 , the current fuel cell inlet temperature  506 , and the target fuel cell inlet temperature  508 . The graph  500  further illustrates the target temperature difference  510  between the fuel cell inlet temperature and the fuel cell outlet temperature, and the current temperature difference  512 . 
     During a first segment  514  of an initial warm-up, the target fuel cell inlet temperature  508  increases simultaneously with the current fuel cell outlet temperature  502 . The target fuel cell inlet temperature  508  is calculated as the difference between the current fuel cell outlet temperature  502  and the target temperature difference  510 . 
     At the beginning of a second segment  516 , the upper controller has increased the target temperature difference  510 . Because the target fuel cell inlet temperature  508  is calculated as the difference between the current fuel cell outlet temperature  502  and the target temperature difference  510 , the target fuel cell inlet temperature  508  remains constant for a period of time  518  until the current temperature difference  512  is equal to the target temperature difference  510 . The target fuel cell inlet temperature  508  begins increasing again when the current temperature difference  512  is equal to or exceeds the target temperature difference  510 . 
     The target temperature difference  510  decreases at the beginning of a third segment  520  of the warm-up. Accordingly, the target fuel cell inlet temperature  508  increases to again be equal to the difference between the current fuel cell outlet temperature  502  and the reduced target temperature difference  510 . 
     By setting the target fuel cell inlet temperature  508  to be equal to the minimum of the calculated value or the final target fuel cell inlet temperature, equation 1 ensures that the target fuel cell inlet temperature  508  fails to exceed the final target fuel cell inlet temperature. 
     Referring now to  FIGS. 4 and 5  and in block  408 , the ECU may control one or more actuator of the fuel cell circuit to increase a temperature of the fluid to cause the current fuel cell inlet temperature to be equal to the target fuel cell inlet temperature. For example, the ECU may control one or more of a three-way valve, a radiator fan, or a pump to increase the temperature of the fluid. As shown in the graph  500 , the current fuel cell inlet temperature  506  remains relatively similar to the target fuel cell inlet temperature  508  during the entire warm-up. 
     Returning reference to  FIG. 4 , the ECU may receive or calculate a target fuel cell outlet temperature in block  410 . The target fuel cell outlet temperature may correspond to a desired temperature of the fluid at the outlet of the fuel cell stack and may be determined by one or more of an upper controller or a state mediator of the ECU. As shown, the ECU may control the temperature of the fluid of the fuel cell circuit using a target fuel cell inlet temperature during the initial warm-up, and may control the temperature of the fluid of the fuel cell circuit using a target fuel cell outlet temperature during normal operation after the initial warm-up. 
     In block  412 , the ECU may calculate a temperature differential. The temperature differential may correspond to a difference between the target fuel cell outlet temperature and the current fuel cell outlet temperature. 
     In block  414 , the ECU may determine a temperature rate of change. The temperature rate of change may correspond to a desired rate of increase or decrease of the temperature of the fluid at a particular location, such as at the outlet of the fuel cell stack. The temperature rate of change may be represented as dT/dt (“T” representing temperature and “t” representing time), and may have units of degrees per second (such as degrees C./second). 
     The ECU may determine the temperature rate of change based on the target fuel cell outlet temperature received from the upper controller, the temperature differential calculated in block  412 , and a desire to conserve energy. For example, if the temperature differential is relatively low it may be desirable to use relatively little energy to warm-up the fuel cell stack in order to increase energy efficiency of the vehicle. 
     In some embodiments, the ECU may determine the temperature rate of change by comparing the target fuel cell outlet temperature and the temperature differential to a lookup table stored in a memory. 
     Referring now to  FIG. 6 , an exemplary lookup table  600  is shown. The Y axis of the lookup table  600  corresponds to the target fuel cell outlet temperature and the X axis corresponds to the temperature differential. A negative temperature differential indicates that it is desirable for the current fuel cell outlet temperature to decrease and a positive temperature differential indicates that it is desirable for the current fuel cell outlet temperature to increase. Likewise, a negative temperature rate of change corresponds to a decreasing temperature rate, and a positive temperature rate of change corresponds to an increasing temperature rate. 
     As shown, the lookup table  600  includes a plurality of regions. The regions include a rapid temperature decrease region  602 , a reduced energy temperature decrease region  604 , an error correction region  606 , a reduced energy temperature increase region  610 , and a rapid temperature increase region  610 . The rapid temperature decrease region  602  and the rapid temperature increase region  612  each correspond to a relatively high temperature rate of change. 
     The relatively high temperature rates of change may be selected based on capabilities of the system. For example, the rapid temperature decrease region  602  may have a temperature rate of change of 1 degree C. per second, which may be a maximum temperature decrease rate that the fuel cell circuit is capable of achieving. Likewise, the rapid temperature increase region  612  may have a maximum temperature rate of change of 4.3 degrees C. per second, which may be a maximum temperature increase rate that the fuel cell circuit is capable of achieving. 
     The temperature rates of change in the rapid temperature decrease region  602  may be desirable when the fuel cell outlet temperature is to be decreased significantly. In that regard, the relatively high rate of temperature decrease in the rapid temperature decrease region  602  may reduce the likelihood of the fuel cell stack drying out. Likewise, the temperature rate of change in the rapid temperature increase region  610  may be desirable when the fuel cell outlet temperature is to be increased significantly. In that regard, the relatively high rate of temperature increase in the rapid temperature increase region  610  may allow the fuel cell stack to provide a relatively large amount of power when a relatively large power request is received. 
     The relatively high temperature rates of change may be relatively energy inefficient and thus may be undesirable for relatively small temperature changes. In that regard, the reduced energy rates of change may correspond to temperature increase and decrease rates that are relatively energy efficient. Accordingly, the reduced energy rates of change may be less than the relatively high temperature rates of change, but may also be more energy-efficient than the relatively high temperature rates of change. 
     The error correction rates of change may be less than the reduced energy rates of change, and may be more energy efficient than the reduced energy rates of change. In that regard, the error correction rates of change may be utilized to correct relatively small differences between the target fuel cell outlet temperature and the actual fuel cell outlet temperature. 
     Returning reference to  FIG. 4 , the ECU may control the one or more actuator of the fuel cell circuit to increase or decrease the temperature of the fluid based on the temperature rate of change that was determined in block  414 . 
     Referring now to  FIG. 7 , a graph  700  illustrates a power request signal  702  corresponding to a power request of the vehicle. The graph  700  further illustrates a current fuel cell outlet temperature  704  and a target fuel cell outlet temperature  706 , along with a current fuel cell inlet temperature  708  and a target fuel cell inlet temperature  710 . As described above and shown in  FIG. 7 , the target fuel cell inlet temperature  710  remains constant throughout operation of the vehicle. In that regard, the current fuel cell inlet temperature  708  also remains relatively constant. 
     The ECU may control the current fuel cell outlet temperature based on the previously determined temperature rate of change. During a first time window  712  the power request signal  702  is low, corresponding to a lack of power request. Accordingly, the target fuel cell outlet temperature  706  remains at a relatively low value throughout the first time window  712 , and the current fuel cell outlet temperature  704  remains relatively the same as the target fuel cell outlet temperature  706 . 
     At the beginning of a second time window  714 , the power request signal  702  increases to a relatively low value, corresponding to a relatively low amount of energy being requested from the fuel cell stack. Accordingly, the target fuel cell outlet temperature  706  increases by a relatively small amount. Accordingly, the temperature differential may be relatively small such that the temperature rate of change falls within the reduced energy temperature increase region as a rapid temperature increase is unnecessary. Because the ECU controls the actuators to increase the temperature at the reduced energy temperature rate of change, the current fuel cell outlet temperature  704  may increase gradually during the second time window  714 . 
     At the beginning of a third time window  716 , the power request signal  702  increases to a wide open throttle (WOT) power request which corresponds to a relatively large amount of energy being requested from the fuel cell stack. Accordingly, the target fuel cell outlet temperature  706  increases by a relatively large amount. As a result, the temperature differential may be relatively large such that the temperature rate of change falls within the rapid temperature increase region to facilitate the relatively large amount of energy requested of the fuel cell stack. 
     Because the ECU controls the actuators to increase the temperature at the rapid temperature rate of change, the current fuel cell outlet temperature  704  may increase relatively rapidly at the beginning of the third time window  716 . Accordingly, the current fuel cell outlet temperature  704  may reach the target fuel cell outlet temperature  706  relatively quickly. 
     At the beginning of a fourth time window  718 , the power request signal  702  decreases to a low power request which corresponds to a relatively small amount of energy being requested from the fuel cell stack. Accordingly, the target fuel cell outlet temperature  706  decreases by a relatively large amount. The temperature differential corresponding to this rapid decrease of the target fuel cell outlet temperature  706  may be relatively large such that the temperature rate of change falls within the rapid temperature decrease region to prevent dry out of the fuel cell stack. Because the ECU controls the actuators to decrease the temperature at the rapid temperature rate of change, the current fuel cell outlet temperature  704  may decrease relatively rapidly at the beginning of the fourth time window  718 . 
     After a relatively short period of time  720  the ECU may determine that the current fuel cell outlet temperature  704  is sufficiently small that dry out of the fuel cell stack is unlikely to occur. Furthermore, the temperature differential has decreased after the period of time  720  due to the decreased current fuel cell outlet temperature  704 . Thus, the temperature rate of change may change to the reduced energy temperature decrease region in order to conserve energy. Thus, after the period of time  720  has elapsed, the current fuel cell outlet temperature  704  may decrease more gradually due to the newly reduced temperature rate of change. 
     Referring now to  FIGS. 8A and 8B , a method  800  for feedforward control of one or more actuator of the fuel cell circuit to heat or cool the fuel cell circuit is shown. The method  800  may be performed, for example, by a feedforward control of an ECU such as the feedforward control  312  of the ECU  102  of  FIG. 3 . 
     In block  802 , the ECU may determine a temperature rate of change. The temperature rate of change may be determined using a method similar to the method  400  of  FIG. 4 . In some embodiments, the ECU may also or instead determine or receive another temperature control signal corresponding to a desired pressure(s) at various locations along the fuel cell circuit, or the like. 
     In block  806 , the ECU may calculate a desired mass flow rate of the fluid that corresponds to the temperature rate of change. The ECU may calculate the desired mass flow rate based on the temperature rate of change determined in block  802  as well as the estimated or calculated values determined in block  804 . For example, the ECU may calculate the desired mass flow rate using an equation similar to equation 2 below: 
     
       
         
           
             
               
                 
                   
                     
                       m 
                       . 
                     
                     FF 
                   
                   = 
                   
                     
                       
                         
                           v 
                           eq 
                         
                         ⁢ 
                         
                           ρ 
                           eq 
                         
                         ⁢ 
                         
                           c 
                           eq 
                         
                         ⁢ 
                         
                           dT 
                           dt 
                         
                       
                       - 
                       
                         Q 
                         FC 
                       
                     
                     
                       ( 
                       
                         
                           c 
                           ⁡ 
                           
                             ( 
                             
                               Δ 
                               ⁢ 
                               T 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             1 
                             ρ 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 P 
                                 
                                   FC 
                                   in 
                                 
                               
                               - 
                               
                                 P 
                                 
                                   FC 
                                   out 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     In equation 2, {dot over (m)} FF  represents the desired mass flow rate of the fluid through a fuel cell stack, such as the fuel cell stack  200  of  FIG. 2 . V eq  represents an equivalent volume of the fluid (including a coolant and water) and the fuel cell stack, and is a physical property of the fluid and fuel cell stack. ρ eq  represents an equivalent density of the fluid and the fuel cell stack and may be received from the state estimator in block  804 . c eq  represents an equivalent specific heat of the fluid in the fuel cell stack and may also be received from the state estimator in block  804 . 
             dT   dt         
represents the temperature rate of change calculated in block  802 . Q FC  represents an amount of heat generated by the fuel cell stack and may be received from the state estimator in block  804 . c represents the specific heat of the fluid and may be received from the state estimator in block  804 . ΔT represents a difference between the target fuel cell inlet temperature and the target fuel cell outlet temperature (T FC     in cmd   −T FC     cmd   ) and may be received from a state governor, such as the state governor  308  of  FIG. 3 , or from a state estimator in block  804 . ρ represents the density of the fluid and may be received from the state estimator in block  804 . P FC     in    represents a current pressure of the fluid at an inlet of the fuel cell stack and P FC     out    represents a current pressure of the fluid at an outlet of the fuel cell stack, both of which may be received from the state estimator in block  804 .
 
     Referring to  FIG. 2  and as described above, {dot over (m)} FF  represents the desired mass flow rate of the fluid through the fuel cell stack  200 . However, the fluid output by the pump  220  is received by both the fuel cell stack  200  and the intercooler  202 . In that regard, it is desirable for the ECU to further calculate the desired mass flow rate of the fluid through the pump  220  (i.e., a sum of the mass flow rate through the fuel cell stack  200  and the intercooler  202 ), also referred to as a total desired mass flow rate. The ECU may utilize a state estimator, such as the state estimator  320  of  FIG. 3 , to calculate the total desired mass flow rate through the pump  220 . 
     Returning reference to  FIGS. 8A and 8B , the ECU may determine a desired pump speed of the pump based on the total desired mass flow rate calculated in block  808 . In some embodiments, the memory of the vehicle may store a lookup table that maps desired mass flow rates to corresponding pumps speeds. In these embodiments, the ECU may compare the desired mass flow rate calculated in block  806  to the lookup table and retrieve the pump speed that corresponds to the desired mass flow rate. 
     In some embodiments, the ECU may determine the desired pump speed based on a sum of the total desired mass flow rate calculated in block  806  and an adjustment to the total desired mass flow rate calculated by a feedback control, such as the feedback control  316  of  FIG. 3 . In that regard, the desired pump speed may be a function of the total desired mass flow rate, the adjustment to the total desired mass flow rate, and a difference in pressure between an outlet of the pump and an inlet of the pump. The difference in pressure between the outlet of the pump and the inlet of the pump may correspond to a total pressure drop over the fuel cell circuit. The ECU may compare the results of the function to a lookup table and retrieve the desired pump speed from the lookup table based on the comparison. 
     In block  810 , the ECU may control the pump to pump the fluid through the fuel cell circuit at the desired pump speed determined in block  808 . 
     In block  812 , the ECU may calculate a desired fluid split ratio of the fluid that is output by a three-way valve, such as the three-way valve  204  of  FIG. 2 . Referring briefly to  FIG. 2 , the desired fluid split ratio may correspond to a ratio of fluid that is directed towards the radiators  210  to fluid that is directed through the bypass branch  206 . In some embodiments, the desired fluid split ratio may represent a percentage of the total fluid output by the three-way valve  204  that is directed towards the radiators  210 , or may represent a percentage of the total fluid output by the three-way valve  204  that is directed through the bypass branch  206 . 
     Returning reference to  FIGS. 8A and 8B , the ECU may calculate the desired fluid split ratio using an equation similar to equation 3 below. 
     
       
         
           
             
               
                 
                   
                     → 
                     
                       Z 
                       FF 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           T 
                           
                             pump 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             in 
                           
                         
                         - 
                         
                           T 
                           bypass 
                         
                       
                       ) 
                     
                     
                       ( 
                       
                         
                           T 
                           
                             rad 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             out 
                           
                         
                         - 
                         
                           T 
                           bypass 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     In equation 3, Z FF  represents the desired fluid split ratio calculated by the feedforward control and corresponds to a percentage of the total fluid output by the three-way pump that is directed through the radiators. T pump in  represents a temperature of an inlet of the pump and may be calculated by the state estimator in block  804 . T bypass  represents a temperature of the fluid directed through the bypass branch, which may be calculated at an outlet of the three-way valve that outputs fluid to the bypass branch, and may be calculated by the state estimator in block  804 . T rad out  corresponds to a temperature of the fluid at an outlet of the radiators and may be detected using a temperature sensor, such as the second temperature sensor  226  of  FIG. 2 . 
     In block  814 , the ECU may determine a desired valve position of the three-way valve based on the desired fluid split ratio calculated in block  812 . In some embodiments, the memory of the vehicle may store a lookup table that maps desired fluid split ratios to corresponding valve positions. In these embodiments, the ECU may compare the desired fluid split ratio calculated in block  812  to the lookup table and retrieve the desired valve position that corresponds to the desired fluid split ratio. 
     In some embodiments, the ECU may determine the desired valve position based on a sum of the desired fluid split ratio calculated in block  812  and an adjustment to the desired fluid split ratio calculated by the feedback control. In that regard, the desired valve position may be a function of the desired fluid split ratio and the adjustment to the desired fluid split ratio. The ECU may compare the results of the function to a lookup table and retrieve the desired valve position based on the comparison. 
     In block  816 , the ECU may control the three-way valve to have the desired valve position that was determined in block  814 . 
     In block  818 , the ECU may calculate a desired amount of thermal energy (i.e., heat) to be removed by radiators of the fuel cell circuit (including main and secondary radiators such as the main radiator  216  and the secondary radiators  214  and  216  of  FIG. 2 ). The ECU may calculate the desired amount of thermal energy to be removed by the radiators using an equation similar to equation 4 below. 
     
       
         
           
             
               
                 
                   
                     Q 
                     
                       rad 
                       total 
                     
                   
                   = 
                   
                     
                       
                         V 
                         eq 
                       
                       ⁢ 
                       
                         ρ 
                         eq 
                       
                       ⁢ 
                       
                         c 
                         eq 
                       
                       ⁢ 
                       
                         dT 
                         dt 
                       
                     
                     - 
                     
                       Q 
                       FC 
                     
                     - 
                     
                       Q 
                       IC 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     In equation 4, Q rad     total    represents the desired amount of thermal energy (i.e., heat) to be removed by all radiators of the fuel cell circuit. V eq  represents an equivalent volume of the fluid (including a coolant and water) and the fuel cell stack, and is a physical property of the fluid and fuel cell stack. ρ eq  represents an equivalent density of the fluid and the fuel cell stack and may be received from the state estimator in block  804 . c eq  represents an equivalent specific heat of the fluid and the fuel cell stack and may also be received from the state estimator in block  804 . 
             dT   dt         
represents the temperature rate of change calculated in block  802 . Q FC  represents an amount of heat generated by the fuel cell stack (i.e., a stack heating amount) and may be received from the state estimator in block  804 . Q IC  represents an amount of heat generated by the intercooler (i.e., an intercooler heating amount) and may be received from the state estimator in block  804 .
 
     In block  820 , the ECU may calculate a desired amount of thermal energy to be removed from the main radiator by the fan. The ECU may make this calculation using the desired amount of thermal energy to be removed by all radiators that was calculated in block  818 . The ECU may calculate the desired amount of thermal energy to be removed from the main radiator by the fan using an equation similar to equation 5 below.
 
 Q rad main     fan     =Q   rad     total     −Q   rad     sub1     −Q rad sub2   −Q rad main     amb     Equation 5
 
     In equation 5, Qrad main     fan    represents the desired amount of thermal energy to be removed from the main radiator by the fan. Q rad     total    represents the desired amount of thermal energy to be removed by all radiators that was calculated in block  818 . Q rad     sub1    represents an amount of thermal energy dissipated by the first secondary radiator and Qrad sub2  represents an amount of thermal energy dissipated by the second secondary radiator (i.e., a secondary amount of thermal energy). Q rad     sub1    and Qrad sub2  may be received from the state estimator in block  804 , and may be calculated using an equation that is based on a temperature and velocity of ambient air that flows over the secondary radiators. Qrad main     amb    represents an amount of thermal energy dissipated by the main radiator due to the ambient air (i.e., airflow other than that generated by the fan). 
     Because the fan does not blow the air over the secondary radiators, the secondary radiators may reject heat into an air flow received through a grill of the vehicle, which may vary based on a speed of the vehicle. Furthermore, the main radiator may receive the airflow through the grill which may affect the value of Qrad main     amb   . In that regard, the values of Q rad     sub1   , Qrad sub2 , and Qrad main     amb    may be based on an amount of airflow received via the grill (which is based on a speed of the vehicle), a temperature of the airflow, and an amount of the fluid that flows through each of the radiators. Therefore, the ECU may receive the vehicle speed and may calculate the values of Q rad     sub1   , Qrad sub2 , and Qrad main     amb    based on the received vehicle speed. The ECU may further estimate the temperature of the ambient air based on a temperature sensor located in or on the vehicle. 
     In block  822 , the ECU may calculate a desired fan speed of the fan to achieve the desired amount of thermal energy to be removed from the main radiator by the fan. The ECU may calculate the desired fan speed using an equation similar to equation 6 below. 
     
       
         
           
             
               
                 
                   
                     kf 
                     
                       rad 
                       
                         main 
                         fan 
                       
                     
                   
                   = 
                   
                     
                       Qrad 
                       
                         main 
                         fan 
                       
                     
                     
                       ( 
                       
                         
                           Trad 
                           main 
                         
                         - 
                         
                           Tair 
                           ⁢ 
                           _ 
                           ⁢ 
                           in 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     In equation 6, 
                   kf     ra   ⁢           ⁢     d     main   fan                                 
represents a radiator heat transfer coefficient. This coefficient is a function of the flow rate of the fluid and a speed of the air through the radiator, and may be determined experimentally. This coefficient may be used (along with a current flow rate of the fluid) to solve for an angular velocity of the fan (i.e., fan speed), which corresponds to a desirable voltage level of the fan. Qrad main     fan    represents the desired amount of thermal energy to be removed from the main radiator by the fan that was calculated in block  820 . Trad main  represents a temperature of the fluid at a fluid inlet of the main radiator and may be received from the state estimator in block  804 . Tair_in represents a temperature of the air at an air inlet of the main radiator and may likewise be received from the state estimator in block  804 .
 
     After calculating the radiator heat transfer coefficient, the ECU may then determine a desired fan speed. The ECU may determine the desired fan speed using a lookup table. In particular, the ECU may compare the radiator heat transfer coefficient to a lookup table and retrieve a corresponding desired fan speed. 
     In some embodiments, the ECU may determine the desired fan speed based on a function of the radiator heat transfer coefficient and a volumetric flow rate of the fluid through an inlet of the main radiator. In some embodiments, the ECU may compare the result of the function to a lookup table and retrieve the desired fan speed based on the comparison. 
     In block  824 , the ECU may determine a desirable power signal to provide to the fan. The desirable power signal may be based on one or both of the radiator heat transfer coefficient or the desired fan speed. For example, the ECU may compare the desired fan speed to a lookup table and retrieve a corresponding desirable power signal to provide to the fan. In some embodiments, the desirable power signal may correspond to a direct current (DC) power signal having a specific voltage. In some embodiments, the desirable power signal may correspond to an alternating current (AC) power signal having a specific root mean square (RMS) voltage or a specific duty cycle. In that regard, the desirable power signal may include one or more of a specific voltage (DC or RMS) or a specific duty cycle of the power signal. 
     In block  826 , the ECU may provide the desirable power signal to the fan to cause the fan to operate at the desired speed to blow air towards the main radiator at the desirable speed of the air. 
     In some embodiments, the ECU may control the fan of the radiator in a different manner than that shown in blocks  818  to  826 . In particular, the ECU may compare a radiator outlet temperature, corresponding to the temperature of the fluid at the outlet of the radiator, to a target fuel cell inlet temperature. For example, the ECU may determine whether the radiator outlet temperature is greater than or equal to a sum of the target fuel cell inlet temperature and a threshold temperature, such as 3 degrees C., 5 degrees C., 7 degrees C., or the like. If the radiator outlet temperature is greater than or equal to the sum, then the ECU may initiate a fan-on event. When the radiator outlet temperature becomes less than the sum, then the ECU may cancel the fan-on event. The ECU may control the fan to turn on when the fan-on event is initialized, and to turn off when the fan-on event is cancelled. 
     In some embodiments, the ECU may latch the fan-on event. For example, the ECU may control the fan-on event to remain in place for a predetermined period of time after initiating the fan-on event and before cancelling the fan-on event. The predetermined period of time may correspond to a sufficient time period to reduce the likelihood of the fan oscillating between an “on” state and an “off” state frequently enough to irritate a driver. In that regard, the latching may reduce the likelihood of the fan oscillating between “on” and “off,” which may be undesirable. 
     In some embodiments, the ECU may latch the fan-on event by adjusting the threshold temperature based on whether the ECU is initiating the fan-on event or is cancelling the fan-on event. For example, the ECU may set the threshold temperature to be 6 degrees C. when initiating the fan-on event, and may set the threshold temperature to be 8 degrees C. when cancelling the fan-on event. In that regard, the ECU may initiate the fan-on event when the temperature reaches a first value, such as 48 degrees C., and may cancel the fan-on event when the temperature reaches a second value, such as 46 degrees C. 
     Referring now to  FIGS. 9A and 9B , a method  900  for heating or cooling a fuel cell circuit by estimating current conditions of the fuel cell circuit is shown. The method may be performed, for example, by a state estimator of an ECU such as the state estimator  320  of the ECU  102  of  FIG. 3 . 
     In block  902 , a model of the fuel cell circuit may be created and stored. The model may be created by designers of the fuel cell circuit and may be stored in a memory of the vehicle that is accessible by the ECU. The ECU may use the model of the fuel cell circuit to estimate various temperatures, pressures, and the like throughout the various components of the fuel cell circuit. 
     Referring briefly to  FIG. 10 , a model  1000  of a fuel cell circuit, such as the fuel cell circuit  118  of  FIG. 2 , is shown. The model  1000  may include representations of the main components  1002  (represented by large squares), representations of pipes  1004  (represented by small squares) that connect the main components  1002 , and representation of flow splitters  1006  (represented by triangles) in which the flow of fluid is split into two or more flows. 
     Returning reference to  FIGS. 9A and 9B , the ECU may receive a plurality of inputs in block  904 . The inputs may include detected temperature values including temperatures detected by temperature sensors along with actuator control signals. The actuator control signals may correspond to commanded actuator values of the actuators (including a pump, a three-way valve, and a radiator fan). 
     In block  906 , the ECU may determine a temperature control signal that corresponds to a desired temperature of the fluid. For example, the temperature control signal may correspond to a temperature rate of change determined by a state governor. 
     In block  908 , the ECU may calculate flow resistance values of components of the fuel cell circuit, and in block  910  the ECU may calculate mass flow values of the fluid through the components of the fuel cell circuit. The flow resistance values and the mass flow values may be calculated for each component including the main components and pipes. 
     The flow resistance value for each component may be calculated using an equation similar to equation 7 below. 
     
       
         
           
             
               
                 
                   Z 
                   = 
                   
                     
                       Fd 
                       ⁡ 
                       
                         ( 
                         
                           Length 
                           + 
                           
                             Length 
                             Add 
                           
                         
                         ) 
                       
                     
                     
                       4 
                       ⁢ 
                       
                         DA 
                         2 
                       
                       ⁢ 
                       ρ 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
           
         
       
     
     In equation 7, Z represents the flow resistance. Fd corresponds to a Darcy friction factor of the component, which may be calculated from experimental correlations corresponding to the relevant flow regime (such as whether the flow is turbulent, laminar, etc.), which may be dictated by a corresponding Reynolds number. The Darcy friction factor may indicate an amount of friction loss through the component. Length represents a length of the component. Length add  corresponds to a tuning parameter which may be adjusted by the ECU during operation of the fuel cell circuit, or by designers of the ECU, to increase in accuracy of the calculation for the flow resistance. The Length add  parameter may be adjusted until the flow resistance curve is substantially equal to an empirical curve. D represents a hydraulic diameter of the component, and A represents a cross-sectional area of the component. ρ represents density of the fluid within the component. In equation 7, Fd and ρ are variable parameters, and the remaining parameters remain constant over time. 
     The mass flow for a given component may be calculated using an equation similar to equation 2 described above. 
     Referring again to  FIG. 10 , due to the law of conservation of mass, mass flow of the fluid through components connected adjacently in series will be the same. For example, a fuel cell stack  1008  and a pipe  1010  are connected in series. Thus, all of the fluid that flows through the fuel cell stack  1008  will subsequently flow through the pipe  1010  without becoming separated. In that regard, the mass flow of the fluid through the fuel cell stack  1008  will be equal to the mass flow of the fluid through the pipe  1010 . Similarly, the mass flow of the fluid through an intercooler  1012  will be equal to the mass flow of the fluid through another pipe  1014 . 
     When fluid from multiple components join together, such as at a junction  1016 , the mass flow after the junction (i.e., through a subsequent component, such as a pipe  1018 ) will be equal to a sum of the mass flow through the components. In that regard, the mass flow of the fluid through the pipe  1018  will be equal to a sum of the mass flow through the first pipe  1010  and the mass flow through the second pipe  1014 . 
     The calculation for mass flow, however, becomes more challenging for locations in which the flow of the fluid is split (i.e., where components are connected in parallel). For example and referring to  FIGS. 10 and 11 , a diagram  1100  illustrates an exemplary flow splitting situation. The diagram  1100  includes a main flow path  1102  that splits into a first flow path  1104  and a second flow path  1106  at a flow splitter  1108 . The first flow path  1104  flows through a first component  1110  and a second component  1112  before rejoining with the second flow path  1106  at a junction  1114 . The second flow path  1106  flows through a third component  1116  and a fourth component  1118  before rejoining with the first flow path  1104  at the junction  1114 . 
     The diagram  1100  may loosely represent a portion of the model  1000  including a flow splitter  1020  (represented by the flow splitter  1108 ), a first flow path  1022  and a second flow path  1024 . The first flow path  1022  includes two pipes  1026 ,  1028  and a main radiator  1030 , and the second flow path  1024  includes two pipes  1032 ,  1034  and a secondary radiator  1036 . As shown, the model  1000  of the fuel cell circuit includes multiple compound flow splits and parallel branches that include multiple components connected in series. 
     When solving for the mass flows and flow resistances of the model  1000 , the flow resistances of one or more component may be known, and the mass flow may be known for at least one component (such as a pump  1038 ). Because the mass flow is known for one component the mass flow will remain the same for each subsequent component before reaching a flow splitter. In that regard, the mass flow of the fluid through another pipe  1040  will be equal to the mass flow of the fluid through the pump  1038 . 
     When the fluid reaches a flow splitter, additional calculations may be performed to calculate equivalent flow resistances of combinations of components as well as mass flows through each branch. The mass flow ({dot over (m)} total ) of the main flow path  1102  may be known (i.e., it may be set to be equal to the mass flow through a previous series component). Likewise, flow resistances of the components  1110 ,  1112 ,  1116 ,  1118  may be known. 
     In order to calculate equivalent flow resistances, equations 8 and 9 below may be used. 
     
       
         
           
             
               
                 
                   
                     Z 
                     
                       eq 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       series 
                     
                   
                   = 
                   
                     
                       Z 
                       1 
                     
                     + 
                     
                       Z 
                       2 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
             
               
                 
                   
                     Z 
                     
                       eq 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       parallel 
                     
                   
                   = 
                   
                     
                       Z 
                       4 
                     
                     
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               
                                 Z 
                                 3 
                               
                               
                                 Z 
                                 4 
                               
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
     
     Equation 8 may be used to calculate equivalent flow resistance for components connected in series. In that regard, an equivalent flow resistance through the first flow path  1104  may be equal to a sum of the flow resistance (Z 1 ) of the first component  1110  and the flow resistance (Z 2 ) of the second component  1112 . 
     Equation 9 may be used to calculate equivalent flow resistance for components connected in parallel. For example, the equivalent flow resistance through the first flow path  1104  (Z 3 ) and through the second flow path  1106  (Z 4 ) may be known. In that regard, an equivalent flow resistance corresponding to a flow resistance through all of the components  1110 ,  1112 ,  1116 ,  1118  may be calculated using equation 9. 
     In order to calculate mass flow ({dot over (m)} 1 ) through the first flow path  1104  and mass flow ({dot over (m)} 2 ) through the second flow path  1106 , equations 10 and 11 below may be used. 
     
       
         
           
             
               
                 
                   
                     
                       m 
                       . 
                     
                     1 
                   
                   = 
                   
                     
                       
                         m 
                         . 
                       
                       total 
                     
                     
                       1 
                       + 
                       
                         
                           
                             Z 
                             3 
                           
                           
                             Z 
                             4 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
               
             
             
               
                 
                   
                     
                       m 
                       . 
                     
                     2 
                   
                   = 
                   
                     
                       
                         m 
                         . 
                       
                       total 
                     
                     - 
                     
                       
                         m 
                         . 
                       
                       1 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   11 
                 
               
             
           
         
       
     
     Equation 10 may be calculated to determine the mass flow ({dot over (m)} 1 ) of the fluid through the first flow path  1104 . Z 3  represents the equivalent flow resistance of the components  1110 ,  1112  of the first flow path  1104 , and Z 4  represents the equivalent flow resistance of the components  1116 ,  1118  of the second flow path  1106 . However, Z 3  and Z 4  are unknown values at the current timestep. In that regard, equation 10 is to be solved using Z 3  and Z 4  from a previous time period. Because calculations are performed at relatively short intervals (such as between 1 millisecond (ms) and 1 second, or between 5 ms and 50 ms, or about 16 ms), the equivalent flow resistances are unlikely to significantly vary between subsequent time periods. In that regard, solving equation 10 using the equivalent flow resistances from a previous time period is likely to provide a relatively accurate mass flow value. It is desirable to use the equivalent flow resistances from the previous timestep due to the fact that neither the current flow resistances nor the current mass flow values are known, and the fact that a mass flow value is necessary to solve for equivalent flow resistance (and vice versa, per Equation 7). Using the equivalent flow resistances from the previous timestep provides the advantage of allowing the ECU to dynamically solve for the flow split in any branch in real time. In some embodiments, a tool called a “real time iterative solver” may be used to solve the set of equations in real time. 
     Once the mass flow ({dot over (m)} 1 ) through the first flow path  1104  is calculated using equation 10, the mass flow ({dot over (m)} 2 ) through the second flow path  1106  may be calculated using equation 11 by subtracting the mass flow ({dot over (m)} 1 ) through the first flow path  1104  from the total mass flow ({dot over (m)} total ). 
     After calculating the mass flow values, equations 8 through 11 may be calculated again to determine flow resistances for the current time period. These calculations may be made using the mass flow values calculated based on the flow resistances of the previous time period. 
     Returning reference to  FIGS. 9A, 9B, and 10 , the ECU may determine a reservoir pressure of fluid within a reservoir  1042  of the fuel cell circuit in block  912 . The reservoir  1042  may be a reservoir that contains fluid to be added to the fuel cell circuit. In some embodiments, the reservoir  1042  may include a port that allows a user of a corresponding vehicle to provide the fluid, such as a coolant. The reservoir pressure may be determined based on sensor data or may be calculated by the ECU. 
     In block  914 , the ECU may calculate pressure values for each of the components of the fuel cell circuit based on the reservoir pressure and the mass flow values calculated in block  910 . In particular, a pressure drop across each component of the fuel cell circuit may be calculated using equation 12 below.
 
Δ P={dot over (m)}   2   Z   Equation 12
 
     In equation 12, ΔP represents the pressure drop over a given component, such as the pipe  1040 . {dot over (m)} represents the mass flow of the fluid through the given component, and Z represents the flow resistance of the component. In that regard, equation 12 may be used to calculate the pressure drop over each component of the fuel cell circuit. 
     The pump  1038  may operate as both a pressure source and a mass flow source. In some embodiments, the pump  1038  may be a turbo style pump, meaning that the pump speed, mass flow through the pump  1038 , and pressure values are coupled. Thus, a previous timestep total system pressure drop value may be used, along with a current timestep pump speed, to calculate or estimate a current timestep total mass flow (i.e., mass flow through the pump  1038 ). 
     After the reservoir pressure and the pressure drop over each component of the fuel cell circuit are known, the pressures at the inlets and outlets of each component may be calculated. For example, the pressure at an outlet of a pipe  1044  is equal to the reservoir pressure because the outlet of the pipe  1044  and the reservoir  1042  are directly connected. Because the pressure drop over the pipe  1044  is known, the pressure at the inlet of the pipe  1044  may be calculated by adding the pressure drop over the pipe  1044  to the reservoir pressure. This calculation may continue around the fuel cell circuit until the pressure at each node of the fuel cell circuit is determined. 
     In block  916 , density values of the fluid through each of the components may be calculated. For example, the density values may be calculated using an equation similar to equation 7 above. 
     In block  918 , specific heat values may be calculated for the fluid in each of the components. For example, the specific heat values may be calculated using an equation similar to equation 2 above. 
     In block  920 , heat transfer values may be calculated for each of the components of the fuel cell circuit. The heat transfer values may correspond to an amount of heat that is added to, or subtracted from, the fluid by the given component. As described above, the intercooler  1012  and the fuel cell stack  1008  are the two components which add heat to the fluid. The heat transfer value (Q FC ) of the fuel cell stack  1008  may be calculated or estimated using an equation, such as equation 2 above. The heat transfer value of the intercooler  1012  may be calculated using a similar or other equation. 
     The radiators  1046  and each of the pipes  1004  may each remove heat from the fluid. The heat transfer value of each of the radiators  1046  of the fuel cell circuit may be calculated using equations, such as equations 3 through 6 described above. The heat transfer value of each of the pipes  1004  may be estimated based on the convection properties of the pipes  1004 , the temperature of the fluid, and the ambient temperature outside of the pipes  1004 . 
     In block  922 , the ECU may calculate a plurality of temperature values corresponding to the components of the fuel cell circuit. For example, the ECU may calculate temperature values at the outlets of the components. Due to the conservation of energy laws, a temperature at an outlet of the first component will be equal to a temperature at an inlet of an adjacent downstream component. The temperature values may be calculated using a temperature value from a previous time period. The temperature values may be calculated using an equation similar to equation 13 below. 
     
       
         
           
             
               
                 
                   
                     T 
                     
                       k 
                       + 
                       1 
                     
                   
                   = 
                   
                     
                       x 
                       
                         k 
                         + 
                         1 
                       
                     
                     - 
                     
                       
                         e 
                         
                           
                             
                               - 
                               Δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           τ 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             x 
                             
                               k 
                               + 
                               1 
                             
                           
                           - 
                           
                             T 
                             k 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
               
             
           
         
       
     
     In equation 13, T k+1  represents the temperature of the fluid at an outlet of the corresponding component at a current time period. T k  represents the temperature of the fluid at a previous time period which may have been previously calculated. Δt represents a length of the time period (such as between 1 ms and 1 second, or between 5 ms and 50 ms, or about 16 ms). τ represents a time constant and is equal to 
                 ρ   ⁢           ⁢   V       m   .       ,         
where ρ represents density of the fluid within the component, V represents volume of the fluid within the component, and {dot over (m)} represents mass flow of the fluid through the component. x k+1  represents an independent variable, the value of which is calculated for the current time period.
 
     In particular, x k+1  may be provided as 
               [       T   1     +       1     ρ   ⁢           ⁢   C       ⁢     (       P   1     -     P   2       )       -       1     c   ⁢     m   .         ⁢     (   Q   )         ]     .         
T 1  represents a temperature at an inlet of the component. ρ represents density of the fluid within the component, and c represents specific heat of the fluid within the component. P 1  represents a pressure of the fluid at an inlet of the component, and P 2  represents a pressure of the fluid at an outlet of the component. {dot over (m)} represents mass flow of the fluid through the component. Q represents the heat transfer value of the component and may be obtained from the calculation performed in block  920 .
 
     Equation 13 may be performed by the ECU at each time period for each of the components. Because the temperature is known (from temperature sensors) for at least one component of the fuel cell circuit (such as an outlet of the fuel cell stack  1008 ), this temperature may be used as an input for solving an outlet temperature of an adjacent downstream component (such as an inlet temperature of the pipe  1010 ). Once the outlet temperature of the adjacent downstream component is calculated, the outlet temperature may be computed or calculated for the next component, and so forth, until the outlet temperature is known for each component of the fuel cell circuit. 
     In block  924 , the ECU may calculate a desired actuator position of each actuator of the fuel cell circuit. As described above, the actuators may include a radiator fan, a pump, and a three-way valve. For example, a feedforward control or a feedback control of the ECU may calculate the desired actuator positions based on the temperature control signal and the values calculated by the state estimator, such as the mass flow values, the pressure values, and the temperature values. 
     In block  926 , the ECU may control the actuators to have the desired actuator position. 
     Referring now to  FIGS. 12A and 12B , a method  1200  for feedback based heating or cooling of a fuel cell circuit is shown. The method  1200  may be performed by a feedback control, such as the feedback control  316  of  FIG. 3 . 
     In block  1202 , the ECU may determine a temperature control signal corresponding to a desired temperature of the fluid in the fuel cell circuit. For example, the temperature control signal may correspond to a desired temperature of the fluid and may include, for example, a temperature rate of change. In some embodiments, the temperature control signal may be determined based on a desired temperature of the fluid at one or more location. The temperature control signal may be determined using a state governor such as the state governor  308  of  FIG. 3 . 
     In block  1204 , the ECU may perform a feedforward control of the actuator in order to increase or decrease the fluid temperature based on the temperature control signal. For example, the ECU may determine a feedforward control signal using a feedforward control such as the feedforward control  312  of  FIG. 3 . The feedforward control may be based on the temperature control signal and estimated values that were calculated using a state estimator. In some embodiments, the ECU may directly control one or more actuator of the fuel cell circuit using the feedforward control. In some embodiments, the ECU may directly control one or more actuator using a combination of the feedforward control and feedback control. 
     In block  1206 , the fluid temperature of the fluid at one or more location may be detected by a temperature sensor or calculated by the ECU, such as in a state estimator. 
     In block  1208 , the ECU may, determine a temperature difference between the detected or calculated fluid temperature and a desired temperature of the fluid at one or more location. For example, the ECU may determine a temperature difference between a detected or calculated temperature at an outlet of the fuel cell stack and a desired temperature of the fluid at the outlet of the fuel cell stack. 
     In block  1210 , the ECU may determine or calculate a sensitivity. The sensitivity may correspond or associate a change in actuator position (including a physical change in actuator position, a change in an actuator control signal, or a change in parameter value used to determine the actuator control signal) to a change in the fluid temperature. For example, the sensitivity may indicate how much change in an actuator position of an actuator changes the fluid temperature of the fluid by 1 degree. As another example, the sensitivity may indicate how much a change in mass flow changes the fluid temperature of the fluid by 1 degree. 
     In some embodiments and in block  1212 , the ECU may divide the sensitivity by a time delay. This may be especially useful if the fluid temperature of the fluid is detected by a sensor. This is because the fluid temperature detected by a sensor may be delayed by one or more seconds, such as 1 to 5 seconds. In that regard, if control of the actuator is based on a time delayed sensor reading, the actuator control may oscillate due to the delayed reading. Dividing the sensitivity by the time delay results in a more gradual change in the actuator control, thus reducing the likelihood of oscillation of the actuator control. 
     In some embodiments, especially if the fluid temperature is calculated by the ECU rather than detected by a sensor having a time delay, block  1212  may be avoided. This is because the calculation of the fluid temperature may have a relatively small delay, if any delay at all. Therefore, the actuator control may be based on a more current reading such that the time delay operation is unnecessary. 
     The temperature difference determined in block  1208  may correspond to a temperature error. Stated differently, the temperature difference corresponds to an error because it is the difference between a desired temperature at the location and the actual temperature at the location. In that regard and in block  1214 , the sensitivity may be applied to the temperature difference in order to determine an error signal. The error signal may correspond to, or indicate, an error in the actuator position or an error in the parameter used to calculate the actuator position that caused the temperature difference. For example, the error signal may indicate that a pump is pumping the fluid through the fuel cell circuit at a mass flow rate that is either too low or too high. The error signal may further indicate or correspond to a difference in mass flow that will cause the actual temperature of the fluid to be relatively equal to the desired temperature of the fluid. 
     In block  1216 , the ECU may pass the error signal through a proportional-integral-derivative (PID, or PI) controller to generate a feedback control signal. The PID controller may analyze past and present values of the error signal and generate the feedback control signal based on present error values, past error values, and potential future errors of the error signal. 
     In block  1218 , the ECU may control the actuator based on the feedback control signal. For example, the ECU may generate a sum of the feedforward control signal (such as a control signal generated using the method  800  of  FIGS. 8A and 8B ) and the feedback control signal and control the actuator based on the sum. In some embodiments, the ECU may control the actuator based on the feedback control signal alone. 
     Referring now to  FIG. 13 , the ECU  102  of  FIG. 2 , and in particular the feedback control  316 , may include a three-way valve controller  1300 . The three-way valve controller  1300  may include logic or dedicated hardware designed to perform a method similar to the method  1200  of  FIGS. 12A and 12B  to perform feedback control of the three-way valve. 
     The three-way valve controller  1300  may include a difference block  1302 . The difference block  1302  may receive a fluid temperature  1304  measured or calculated at the inlet of the fuel cell stack. For example, the fluid temperature  1304  may be calculated by a state estimator of the ECU  102 . The difference block  1302  may further receive a desired temperature  1306  corresponding to a desired temperature of the fluid at the inlet of the fuel cell stack. The difference block  1302  may output a temperature difference  1308  corresponding to a difference between the fluid temperature  1304  and the desired temperature  1306 . 
     The three-way valve controller  1300  may further include a second difference block  1310 . The second difference block  1310  may receive a radiator temperature  1312  corresponding to a temperature of the fluid at the outlet of the radiator. The second difference block  1310  may further receive a bypass fluid temperature  1314  corresponding to a temperature of the fluid at a location along a bypass branch of the fuel cell circuit. The second difference block  1310  may output a difference  1316  between the radiator temperature  1312  and the bypass fluid temperature  1314 . 
     The three-way valve controller  1300  may further include a sensitivity block  1318 . The sensitivity block  1318  may receive the difference  1316  between the radiator temperature  1312  and the bypass fluid temperature  1314  along with a pump fluid temperature  1320  corresponding to a temperature of the fluid at an inlet of the pump. The sensitivity block  1318  may determine a sensitivity  1322  that corresponds a change in valve position of the three-way valve to a change in fluid temperature of the fluid, such as a fluid temperature at the inlet of the fuel cell stack. For example, the sensitivity  1322  may indicate how much of a change in valve position (Z) results in a 1 degree change of the fluid temperature at the inlet of the fuel cell stack. 
     The sensitivity  1322  may be calculated using an equation similar to equation 14 below. In some embodiments, the sensitivity may be provided as a lookup table or lookup map that is populated using an equation similar to equation 14. In some embodiments, the sensitivity may be provided as the equation such that the sensitivity block  1318  calculates the sensitivity based on the received inputs. 
     
       
         
           
             
               
                 
                   
                     dZ 
                     dT 
                   
                   = 
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   ( 
                                   
                                     
                                       ( 
                                       
                                         
                                           T 
                                           
                                             pump 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             in 
                                           
                                         
                                         + 
                                         
                                           Δ 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             T 
                                             
                                               ( 
                                               
                                                 1 
                                                 ⁢ 
                                                 C 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                     - 
                                     
                                       T 
                                       bypass 
                                     
                                   
                                   ) 
                                 
                                 
                                   ( 
                                   
                                     
                                       T 
                                       
                                         rad 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         out 
                                       
                                     
                                     - 
                                     
                                       T 
                                       bypass 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             - 
                           
                         
                       
                       
                         
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     T 
                                     
                                       pump 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       in 
                                     
                                   
                                   - 
                                   
                                     T 
                                     bypass 
                                   
                                 
                                 ) 
                               
                               
                                 ( 
                                 
                                   
                                     T 
                                     
                                       rad 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       out 
                                     
                                   
                                   - 
                                   
                                     T 
                                     bypass 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         T 
                         
                           ( 
                           
                             1 
                             ⁢ 
                             C 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   14 
                 
               
             
           
         
       
     
     In equation 14, 
             dZ   dT         
represents me sensitivity  1322  that is determined or calculated by the sensitivity block  1318 . T pump in  represents the pump fluid temperature  1320 . ΔT represents a set change in the fluid temperature at the inlet of the fuel cell stack. In some embodiments, ΔT is set to be equal to 1 degree C. T bypass  represents the bypass fluid temperature  1314 , and T rad out  represents the radiator temperature  1312  at the outlet of the radiator. The sensitivity
 
             dZ   dT         
indicates how much the fluid split ratio of the three-way valve must change in order to achieve a predefined temperature change (such as 1 degree C.) of the fluid at the inlet of the fuel cell stack.
 
     As described above with reference to  FIGS. 8A and 8B , the fluid split ratio may correspond to a ratio of an amount of fluid (e.g., measured using mass flow) that is directed towards the radiators to a total amount of fluid (e.g., measured using mass flow) flowing through the entire fuel cell circuit. Thus, a fluid split ratio of 1 may indicate that all of the fluid is flowing through the radiators and none through the bypass branch. Furthermore and also as described above with reference to  FIGS. 8A and 8B , the fluid split ratio of the three-way valve (Z) is a function of a difference between the radiator temperature  1312  at the outlet of the radiator and the bypass fluid temperature  1314 . 
     The three-way valve controller  1300  may further include a multiplication block  1324 . The multiplication block  1324  may apply the sensitivity  1322  to the temperature difference  1308 . For example, the multiplication block  1324  may multiply the temperature difference  1308  by the sensitivity  1322 . The result of the multiplication block  1324  may be an error signal  1326 , and may indicate an error in the three-way valve position (measured, for example, in values corresponding to the fluid split ratio). 
     The three-way valve controller  1300  may further include a proportional integral derivative (PID) controller  1328 . The PID controller  1328  may receive the error signal  1326  and may generate a feedback control signal  1330  by accounting for present error values, past error values, and potential future errors of the error signal  1326 . 
     The ECU  102  may further include a combination block  1332  that receives the feedback control signal  1330  along with a feedforward control signal  1334 . The feedforward control signal  1334  may correspond to a feedforward control of the three-way valve as determined or calculated by a feedforward control such as the feedforward control  312  of  FIG. 3 . 
     The combination block  1332  may generate a sum of the feedback control signal  1330  and the feedforward control signal  1334 . The combination block  1332  may output a combined control signal  1336  that corresponds to a final desired valve position based on feedforward and feedback control. In particular, the combined control signal  1336  may correspond to a final desired fluid split ratio. 
     The combined control signal  1336  may be received by a lookup table  1338 . In some embodiments, the lookup table  1338  may instead include a calculation or other method or apparatus for converting a fluid split ratio to a desired valve position. In that regard, the lookup table  1338  may receive the combined control signal  1336 , and may convert the combined control signal  1336  into a final desired valve position  1340 , and may output the final desired valve position  1340 . The ECU may control the three-way valve based on the final desired valve position  1340 . 
     Referring now to  FIG. 14 , the ECU  102  of  FIG. 2 , and in particular the feedback control  316 , may include a pump controller  1400 . The pump controller  1400  may be implemented as logic or dedicated hardware and designed to perform a method similar to the method  1200  of  FIGS. 12A and 12B  to perform feedback control of the pump. 
     The pump controller  1400  may include a difference block  1402 . The difference block  1402  may receive a fluid temperature  1404  measured or calculated at the outlet of the fuel cell stack. For example, the fluid temperature  1404  may be measured by a temperature sensor, such as the temperature sensor  224  of  FIG. 2 , or may be calculated by a state estimator of the ECU  102 . The difference block  1402  may further receive a desired temperature  1406  corresponding to a desired temperature of the fluid at the outlet of the fuel cell stack. For example, the desired temperature  1406  may correspond to a commanded temperature of the fluid at the outlet of the fuel cell stack and may be determined by an upper controller of the ECU  102 . The difference block  1402  may output a temperature difference  1408  corresponding to a difference between the fluid temperature  1404  and the desired temperature  1406 . 
     The pump controller  1400  may further include a second difference block  1410 . The second difference block  1410  may receive the fluid temperature  1404  and a fuel cell inlet temperature  1414  corresponding to a temperature of the fluid at the inlet of the fuel cell stack. The fuel cell inlet temperature  1414  may be measured or calculated by a state estimator of the ECU  102 . The second difference block  1410  may output a difference  1416  between the fluid temperature  1404  and the fuel cell inlet temperature  1414 . The difference  1416  may also be referred to as a temperature gradient of the fuel cell stack as it corresponds to a temperature difference between the inlet and the outlet of the fuel cell stack. 
     The pump controller  1400  may further include a sensitivity block  1418 . The sensitivity block  1418  may receive the difference  1416  along with an amount of heat  1420  output by the fuel cell stack (corresponding to an amount of heat transferred from the fuel cell stack to the fluid) and an equivalent specific heat  1412  of the fluid in the fuel cell stack. The sensitivity block  1418  may determine a sensitivity  1422  that corresponds a change in pump output (such as a change in mass flow of the fluid) of the pump to a change in fluid temperature of the fluid, such as a fluid temperature at the outlet of the fuel cell stack. For example, the sensitivity  1322  may indicate how much of a change in mass flow output by the pump corresponds to a 1 degree change of the fluid temperature at the outlet of the fuel cell stack. 
     The sensitivity  1422  may be calculated using an equation similar to equation 15 below. In some embodiments, the sensitivity may be provided as a lookup table or lookup map that is populated using an equation similar to equation 15. In some embodiments, the sensitivity may be provided as the equation such that the sensitivity block  1418  calculates the sensitivity based on the received inputs. 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         m 
                         . 
                       
                     
                     
                       dT 
                       
                         FC 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         out 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           - 
                           
                             Q 
                             FC 
                           
                         
                         
                           
                             
                               
                                 c 
                                 
                                   eq 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         - 
                                         
                                           ( 
                                           
                                             
                                               T 
                                               
                                                 FC 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 out 
                                               
                                             
                                             - 
                                             
                                               T 
                                               
                                                 FC 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 in 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                       + 
                                       
                                         dT 
                                         
                                           FC 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           out 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   - 
                                   
                                     Q 
                                     FC 
                                   
                                 
                                 
                                   c 
                                   
                                     eq 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         - 
                                         
                                           ( 
                                           
                                             
                                               T 
                                               
                                                 FC 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 out 
                                               
                                             
                                             - 
                                             
                                               T 
                                               
                                                 FC 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 in 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       - 
                     
                     
                       dT 
                       
                         FC 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         out 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   15 
                 
               
             
           
         
       
     
     In equation 15, 
               Δ   ⁢           ⁢     m   .         dT     FC   ⁢           ⁢   out             
represents the sensitivity  1422  that is determined or calculated by the sensitivity block  1418 . As shown, the sensitivity  1422  corresponds a change in mass flow output by the pump (Δ{dot over (m)}) to a change of the fluid temperature at the outlet of the fuel cell stack (dT FC out ). In particular, the sensitivity
 
               Δ   ⁢           ⁢     m   .         dT     FC   ⁢           ⁢   out             
indicates an amount of change of the mass flow output by the pump required to achieve a predefined temperature change (such as 1 degree C.). In some embodiments, dT FC out  is set to be equal to 1 degree C. c eq  represents an equivalent specific heat  1412  of the fluid in the fuel cell stack. Q FC  represents the amount of heat  1420  output by the fuel cell stack. T FC out  represents the fluid temperature  1404  of the fluid at the outlet of the fuel cell stack, and T FC in  represents the fuel cell inlet temperature  1414  at the inlet of the fuel cell stack.
 
     The pump controller  1400  may further include a division block  1426 . The division block  1426  may receive the sensitivity  1422  along with a time delay  1424 . The division block  1426  may divide the sensitivity  1422  by the time delay  1424 . By performing this division, the division block  1426  reduces the sensitivity  1422  to cause a more gradual change in the pump control. In that regard, the division block  1426  may reduce oscillation of the pump control. This may be useful if the fluid temperature  1406  is detected by a temperature sensor due to the delayed reading of the temperature sensor. In some embodiments, the division block  1426  may be excluded, particularly if the fluid temperature  1406  is calculated by a state estimator of the ECU  102 . The division block  1426  may output an adjusted sensitivity  1428 . In some embodiments, the three-way valve controller  1300  of  FIG. 13  may likewise include a similar division block. 
     The pump controller  1400  may further include a multiplication block  1430 . The multiplication block  1430  may apply the adjusted sensitivity  1428  to the temperature difference  1408 . For example, the multiplication block  1430  may multiply the temperature difference  1408  by the adjusted sensitivity  1428 . The result of the multiplication block  1430  may be an error signal  1432 , indicating an error in the desired mass flow to be output by the pump. In that regard, the error signal may include a mass flow value. 
     The pump controller  1400  may further include a PID controller  1434 . The PID controller  1434  may receive the error signal  1432  and may generate a feedback control signal  1436  by accounting for present error values, past error values, and potential future errors of the error signal  1432 . 
     The ECU  102  may further include a combination block  1438  that receives the feedback control signal  1436  along with a feedforward control signal  1440 . The feedforward control signal  1448  may correspond to a feedforward control of the pump as determined or calculated by a feedforward control such as the feedforward control  312  of  FIG. 3 . 
     The combination block  1438  may generate a sum of the feedback control signal  1436  and the feedforward control signal  1440 . The combination block  1438  may output a combined control signal  1442  that corresponds to a final desired mass flow to be output by the pump based on feedforward and feedback control. 
     The combined control signal  1442  may be received by a lookup table  1444 . In some embodiments, the lookup table  1444  may instead include a calculation or other method or apparatus for converting a mass flow rate to a pump control signal. In that regard, the lookup table  1444  may receive the combined control signal  1442 , and may convert the combined control signal  1442  into a final pump control signal  1446 . The ECU may control the pump based on the final pump control signal  1446 . 
     Referring now to  FIGS. 15A and 15B , a method  1500  for correcting an estimated parameter is shown. The method  1500  may be performed by components of a fuel cell circuit such as the fuel cell circuit  118  of  FIG. 2 . For example, the method  1500  may be performed by an observer of an ECU, such as the observer  322  of  FIG. 3 . The estimated parameter may include an estimated or calculated parameter generated by a state estimator. Correction of the estimated parameter may cause multiple calculations by the state estimator to improve in accuracy due to a trickle-down effect. 
     In block  1502 , the ECU may estimate an estimated parameter that affects an amount of heat removed by a radiator. As described above, a velocity of the ambient air that passes over the radiators may be included in a calculation for the amount of heat removed by the radiator. In that regard, the estimated parameter may include the velocity of the ambient air that flows over one or more radiator. In some embodiments, the estimated parameter may include another value such as a temperature of the ambient air or the like. 
     In block  1504 , the ECU may determine an actuator control signal used to control the actuator. For example, the actuator may include the fan such that the control signal corresponds to a fan speed of the fan or a power signal for powering the fan. The ECU may determine the actuator control signal in a feedforward control such as the feedforward control  312  of  FIG. 3 . 
     In block  1506 , a temperature sensor may detect a fluid temperature of the fluid within the fuel cell circuit. For example, the fluid temperature may be detected at an outlet of one or more radiator, such as by the temperature sensor  226  of the fuel cell circuit  118  of  FIG. 2 . 
     In block  1508 , the ECU may estimate an estimated fluid temperature of the fluid. For example, the estimated fluid temperature may be estimated for the same location at which the fluid temperature was detected in block  1506  (i.e., the outlet of the radiators). The ECU may estimate the estimated fluid temperature using a state estimator, such as the state estimator  320  of  FIG. 3 . 
     In block  1510 , the ECU may calculate or determine a temperature difference between the fluid temperature that was detected in block  1506  and the estimated fluid temperature that was calculated in block  1508 . In that regard, the temperature difference may indicate an error or a miscalculation by the state estimator as it represents a difference between the measured temperature and the temperature estimated by the state estimator. 
     In block  1512 , the ECU may determine or calculate a sensitivity. The sensitivity may correspond or associate a change in the estimated parameter to a change in the fluid temperature. Because the estimated parameter is used to determine the control signal for the fan, a change in the estimated parameter ultimately affects an amount of heat removed from the fluid by the radiators. For example, the sensitivity may indicate how much change in the estimated parameter is needed to cause the fluid temperature to change by 1 degree C. In some embodiments, the fluid temperature may be measured or calculated at the outlet of the radiators. 
     In block  1514 , the ECU may apply the sensitivity to the temperature difference in order to determine an error signal. The error signal may indicate, or correspond to, an error in the estimated parameter that caused the temperature difference. For example, the error signal may indicate that the value of the estimated parameter (e.g., ambient air velocity) calculated by the state estimator is too low or too high. The error signal may further indicate or correspond to a difference in the value of the estimated parameter that will cause the estimated fluid temperature to be substantially equal to the actual fluid temperature of the fluid. 
     In block  1516 , the ECU may pass the error signal through a PID controller to generate an updated estimated parameter. The PID controller may analyze past and present values of the error signal and generate the updated estimated parameter based on present error values, past error values, and potential future error values of the error signal. 
     In block  1518 , the ECU may determine an updated actuator control signal based on the updated estimated parameter. For example, the feedforward control may generate a new fan control signal using the updated estimated parameter rather than the original estimated parameter generated by the state estimator. In that regard, use of the updated estimated parameter is likely to cause the actual temperature of the fluid to be closer in value to a desired temperature of the fluid. 
     In block  1520 , the ECU may control the actuator based on the updated actuator control signal generated in block  1518 . 
     Referring now to  FIG. 16 , the ECU  102  of  FIG. 2 , and in particular the observer  322 , may include an estimated parameter controller  1600 . The estimated parameter controller  1600  may be implemented using logic or dedicated hardware and designed to perform a method similar to the method  1500  of  FIGS. 15A and 15B  to update a parameter estimated by the state estimator. 
     The estimated parameter controller  1600  may include a difference block  1602 . The difference block  1602  may receive a fluid temperature  1604  measured at the outlet of the radiators (such as by the temperature sensor  226  of  FIG. 2 ). The difference block  1602  may further receive an estimated fluid temperature  1606  corresponding to a fluid temperature of the fluid at the outlet of the radiators that was calculated by a state estimator. The difference block  1602  may output a temperature difference  1608  corresponding to a difference between the measured fluid temperature  1604  and the estimated fluid temperature  1606 . In that regard, the temperature difference  1608  may indicate an error in the calculation of the estimated fluid temperature  1606 . 
     The estimated parameter controller  1600  may further include a sensitivity block  1614 . The sensitivity block  1614  may receive the fluid temperature  1604 , a temperature  1610  of the ambient air flowing over the radiators, and a specific volumetric flowrate  1612  (e.g., measured in liters per minute) of the coolant (i.e., ambient air) flowing over the radiators. The temperature  1610  and the specific volumetric flowrate  1612  may be estimated or calculated by a state estimator. The sensitivity block  1614  may determine a sensitivity  1618  that corresponds a change in the velocity of the ambient air to a change in fluid temperature of the fluid, such as the fluid temperature  1604  measured at the outlet of the radiators. For example, the sensitivity  1618  may indicate how much change in velocity will result in a 1 degree C. change of the fluid temperature  1604 . 
     The sensitivity  1618  may be calculated using an equation similar to equation 16 below. In some embodiments, the sensitivity may be provided as a lookup table or lookup map that is populated using an equation similar to equation 16. In some embodiments, the sensitivity may be provided as the equation such that the sensitivity block  1614  calculates the sensitivity based on the received inputs. 
     
       
         
           
             
               
                 
                   
                     dT 
                     dv 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           Var 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         - 
                         
                           Var 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       ) 
                     
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         v 
                         
                           ( 
                           
                             1 
                             ⁢ 
                             
                               m 
                               / 
                               s 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   16 
                 
               
             
           
         
       
     
     In equation 16, 
             dT   dv         
represents the sensitivity  1618 . As mentioned above, the sensitivity  1618  may correspond a change in the velocity of ambient air to a predetermined change in temperature (such as 1 degree C.). Δv represents a predetermined change in the velocity, such as 1 meter per second (1 m/s). Equation 1 illustrates that the sensitivity  1618  is a function of a temperature of the fluid at the inlet of all radiators (Trad in ), the temperature  1610  of the ambient air flowing over all radiators (Tair_in), and the specific volumetric flowrate  1612  of the coolant (i.e., air) that flows over the corresponding radiator ( ).
 
     
       
         
           
             Var 
             ⁢ 
             
                 
             
             ⁢ 
             1 
             ⁢ 
             
                 
             
             ⁢ 
             may 
             ⁢ 
             
                 
             
             ⁢ 
             be 
             ⁢ 
             
                 
             
             ⁢ 
             represented 
             ⁢ 
             
                 
             
             ⁢ 
             as 
             ⁢ 
             
                 
             
             ⁢ 
             
               ( 
               
                 
                   Trad 
                   in 
                 
                 - 
                 
                   ( 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kf_MAP 
                                     main 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         ( 
                                         
                                           v 
                                           
                                             
                                               amb 
                                               air 
                                             
                                             + 
                                             
                                               Δ 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               
                                                 v 
                                                 
                                                   ( 
                                                   
                                                     1 
                                                     ⁢ 
                                                     
                                                       m 
                                                       / 
                                                       s 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         V 
                                         
                                           
                                             coolant 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               rad 
                                               main 
                                             
                                           
                                           . 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Trad 
                                       
                                         main 
                                         in 
                                       
                                     
                                     - 
                                     
                                       Tair_in 
                                       main 
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                       
                         
                           
                             m 
                             . 
                           
                           main 
                         
                         ⁢ 
                         
                           c 
                           main 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   kf_MAP 
                                   
                                     sub 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     
                                       ( 
                                       
                                         v 
                                         
                                           
                                             amb 
                                             air 
                                           
                                           + 
                                           
                                             Δ 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               v 
                                               
                                                 ( 
                                                 
                                                   1 
                                                   ⁢ 
                                                   
                                                     m 
                                                     / 
                                                     s 
                                                   
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                     , 
                                     
                                       V 
                                       
                                         
                                           coolant 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             rad 
                                             
                                               sub 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               1 
                                             
                                           
                                         
                                         . 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     Trad 
                                     
                                       sub 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         1 
                                         in 
                                       
                                     
                                   
                                   - 
                                   
                                     Tair_in 
                                     
                                       sub 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             m 
                             . 
                           
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁢ 
                         
                           c 
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                     
                     + 
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kf_MAP 
                                     
                                       sub 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         ( 
                                         
                                           v 
                                           
                                             
                                               amb 
                                               air 
                                             
                                             + 
                                             
                                               Δ 
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               
                                                 v 
                                                 
                                                   ( 
                                                   
                                                     1 
                                                     ⁢ 
                                                     
                                                       m 
                                                       / 
                                                       s 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                         
                                         ) 
                                       
                                       , 
                                       
                                         V 
                                         
                                           
                                             coolant 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               rad 
                                               
                                                 sub 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 2 
                                               
                                             
                                           
                                           . 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Trad 
                                       
                                         sub 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           2 
                                           in 
                                         
                                       
                                     
                                     - 
                                     
                                       Tair_in 
                                       
                                         sub 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                       
                         
                           
                             m 
                             . 
                           
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁢ 
                         
                           c 
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                     
                   
                   ) 
                 
               
               ) 
             
           
         
       
     
     In Var1, Trad in  represents the fluid temperature at the inlet of all radiators. kf_MAP xx  represents a lookup table value that is determined using a corresponding kf factor for each of the radiators (one main radiator (main) and two secondary radiators (sub1 and sub2)). v amb     air    represents the velocity of the ambient air.   represents a specific volumetric flowrate of the coolant (i.e., air) that flows over the corresponding radiator. Trad xx     in    represents a temperature of the fluid at the inlet of each corresponding radiator. Tair_in xx  represents a temperature of the air flowing over each corresponding radiator. {dot over (m)} xx  represents the mass flow of the fluid flowing through the corresponding radiator. c xx  represents a specific heat of the fluid flowing through the corresponding radiator. 
     
       
         
           
             Var 
             ⁢ 
             
                 
             
             ⁢ 
             2 
             ⁢ 
             
                 
             
             ⁢ 
             may 
             ⁢ 
             
                 
             
             ⁢ 
             be 
             ⁢ 
             
                 
             
             ⁢ 
             represented 
             ⁢ 
             
                 
             
             ⁢ 
             as 
             ⁢ 
             
                 
             
             ⁢ 
             
               ( 
               
                 
                   Trad 
                   in 
                 
                 - 
                 
                   ( 
                   
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kf_MAP 
                                     main 
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         v 
                                         
                                           amb 
                                           air 
                                         
                                       
                                       , 
                                       
                                         V 
                                         
                                           
                                             coolant 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               rad 
                                               main 
                                             
                                           
                                           . 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Trad 
                                       
                                         main 
                                         in 
                                       
                                     
                                     - 
                                     
                                       Tair_in 
                                       main 
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                       
                         
                           
                             m 
                             . 
                           
                           main 
                         
                         ⁢ 
                         
                           c 
                           main 
                         
                       
                     
                     + 
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kf_MAP 
                                     
                                       sub 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         v 
                                         
                                           amb 
                                           air 
                                         
                                       
                                       , 
                                       
                                         V 
                                         
                                           
                                             coolant 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               rad 
                                               
                                                 sub 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 1 
                                               
                                             
                                           
                                           . 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Trad 
                                       
                                         sub 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           1 
                                           in 
                                         
                                       
                                     
                                     - 
                                     
                                       Tair_in 
                                       
                                         sub 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         1 
                                       
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                       
                         
                           
                             m 
                             . 
                           
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁢ 
                         
                           c 
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                     
                     + 
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     kf_MAP 
                                     
                                       sub 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       
                                         v 
                                         
                                           amb 
                                           air 
                                         
                                       
                                       , 
                                       
                                         V 
                                         
                                           
                                             coolant 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               rad 
                                               
                                                 sub 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 2 
                                               
                                             
                                           
                                           . 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       Trad 
                                       
                                         sub 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           2 
                                           in 
                                         
                                       
                                     
                                     - 
                                     
                                       Tair_in 
                                       
                                         sub 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                       
                         
                           
                             m 
                             . 
                           
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁢ 
                         
                           c 
                           
                             sub 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                     
                   
                   ) 
                 
               
               ) 
             
           
         
       
     
     The estimated parameter controller  1600  may further include a multiplication block  1620 . The multiplication block  1620  may receive the sensitivity  1618  and the temperature difference  1608 , and may apply the sensitivity  1618  to the temperature difference  1608 . For example, the multiplication block  1620  may multiply or divide the temperature difference  1608  by the sensitivity  1618 . The result of the multiplication block  1620  may be an error signal  1622 , such as an error in the estimated parameter (i.e., the velocity of the ambient air). 
     The estimated parameter controller  1600  may further include a PID controller  1624 . The PID controller  1624  may receive the error signal  1622  and may generate an updated estimated parameter  1626 . The PID controller  1624  may generate the updated estimated parameter  1626  by accounting for present error values, past error values, and potential future errors of the error signal  1622 . The ECU  102  may then transfer the updated estimated parameter  1626  to a feedforward control for controlling the fan of the fuel cell circuit. 
     Where used throughout the specification and the claims, “at least one of A or B” includes “A” only, “B” only, or “A and B.” Exemplary embodiments of the methods/systems have been disclosed in an illustrative style. Accordingly, the terminology employed throughout should be read in a non-limiting manner. Although minor modifications to the teachings herein will occur to those well versed in the art, it shall be understood that what is intended to be circumscribed within the scope of the patent warranted hereon are all such embodiments that reasonably fall within the scope of the advancement to the art hereby contributed, and that that scope shall not be restricted, except in light of the appended claims and their equivalents.