Patent Publication Number: US-2023155149-A1

Title: Pi control partial derivative based i-term for wind-up prevention

Description:
TECHNICAL FIELD 
     The present disclosure is directed to a systems, devices, and methods for providing control for a proportional-integral-derivative (PID or PI) Controller. More specifically, the present disclosure is directed to calculating and controlling the saturation limits of the I-term of the PID controller to reduce integral wind-up. 
     BACKGROUND OF THE DISCLOSURE 
     The advent of new fuel cell technologies has produced new advances in vehicle design. These advances include new 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 vehicles employ multiple fuel cells in a fuel cell stack. These 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. Some existing fuel cell systems rely on proportional-integral-derivative (PID or PI) controllers to maintain the temperature of fuel cell within an optimal temperature range. However, these systems are not optimized for highly non-linear conditions, such as those commonly occurring in fuel cell systems. In particular, Integral (I-term) Wind-up poses a serious challenge for these systems. 
     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 using a PID controller, and in particular, a need for preventing Integral Wind-up. 
     SUMMARY 
     In some example aspects, the present disclosure introduces a system for heating or cooling a fuel cell stack of a vehicle, which may include: a fuel cell stack having a plurality of fuel cells; an actuator having an actuator position and configured to increase or decrease a fluid temperature of a fluid in the plurality of fuel cells; and an electronic control unit (ECU) coupled to the actuator, the ECU including a proportional-integral-derivative (PID) controller; wherein the ECU is configured to: determine a temperature control signal corresponding to a target temperature of the fluid; perform a feedforward control of the actuator to cause the actuator to increase or decrease the fluid temperature toward the target temperature of the fluid; receive a feedback control signal from the PID controller, the feedback control signal based on an error signal that corresponds to an additional change in the actuator position to cause the fluid temperature to increase or decrease to reduce a temperature difference, wherein the feedback control signal applies an I-term saturation limit; and control the actuator based on a sum of the feedforward control and the feedback control signal. 
     In some implementations, the PID controller is configured to generate the feedback control signal by accounting for present error values, past error values, and potential future errors of the error signal. The PID controller may be configured to apply the I-term saturation limit according to the equations: 
     
       
         
           
             
               
                 
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                     max 
                   
                 
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                       Controlled 
                       
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                         allowed 
                       
                     
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                           state 
                         
                       
                     
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               ; 
             
             ⁢ 
             
 
             
               
                 
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                         allowed 
                       
                     
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             ⁢ 
             
 
             
               
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                 . 
               
             
           
         
       
     
     The PID controller may be configured to apply the I-term saturation limit to a final PI combined feedback term according to the equations: 
     
       
         
           
             
               
                 PI 
                 - 
                 
                   term 
                   unlimited 
                 
               
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                         ∂ 
                         PIControl 
                       
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             ; 
           
         
       
       
         
           
             
               
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                         term 
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             ; 
             and 
           
         
       
       
         
           
             
               PI 
               - 
               
                 term 
                 limited 
               
             
             = 
             
               
                 min 
                 ⁡ 
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                     max 
                     ⁡ 
                     ( 
                     
                       
                         PI 
                         - 
                         
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                           unlimited 
                         
                       
                       , 
                       
                         PI 
                         - 
                         
                           term 
                           min 
                         
                       
                     
                     ) 
                   
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                       max 
                     
                   
                 
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               . 
             
           
         
       
     
     The actuator may be a three-way valve. The target temperature of the fluid and the fluid temperature correspond to the fluid at an inlet of the fuel cell stack. 
     Example methods for heating or cooling a fuel cell stack of a vehicle are also provided, which may include: providing a fuel cell stack having a plurality of fuel cells; providing an actuator having an actuator position and configured to increase or decrease a fluid temperature of a fluid in the plurality of fuel cells; and providing an electronic control unit (ECU) coupled to the actuator, the ECU including a proportional-integral-derivative (PID) controller; with the ECU, determining a temperature control signal corresponding to a target temperature of the fluid; with the ECU, performing a feedforward control of the actuator to cause the actuator to increase or decrease the fluid temperature toward the target temperature of the fluid; with the ECU, receiving a feedback control signal from the PID controller, the feedback control signal based on an error signal that corresponds to an additional change in the actuator position to cause the fluid temperature to increase or decrease to reduce a temperature difference, wherein the feedback control signal applies a I-term saturation limit; and controlling the actuator based on a sum of the feedforward control and the feedback control signal. 
     In some implementations, the method further comprises generating the feedback control signal with the PID controller by accounting for present error values, past error values, and potential future errors of the error signal. The method may include applying the I-term saturation limit with the PID controller according to the equations: 
                 I   -     term   max       =     Δ   ⁢       Controlled     state   ⁢         allowed       (         ∂   I     -     term   state         ∂     Controlled   state         )         ;                   I   -     term   min       =     -   Δ   ⁢       Controlled     state   ⁢         allowed       (         ∂   I     -     term   state         ∂     Controlled   state         )         ;         and 
         I −term limited =min(max( I −term unlimited   ,I −term min ), I −term max ).
 
     The method may include applying the I-term saturation limit to a final PI combined feedback term with the PID controller according to the equations: 
     
       
         
           
             
               
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             ; 
           
         
       
       
         
           
             
               
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                         state 
                       
                     
                   
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             ; 
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               PI 
               - 
               
                 term 
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             = 
             
               
                 min 
                 ⁡ 
                 ( 
                 
                   
                     max 
                     ⁡ 
                     ( 
                     
                       
                         PI 
                         - 
                         
                           term 
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                         PI 
                         - 
                         
                           term 
                           min 
                         
                       
                     
                     ) 
                   
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               . 
             
           
         
       
     
     In some implementations, the actuator is a three-way valve. The target temperature of the fluid and the fluid temperature may correspond to the fluid at an inlet of the fuel cell stack. 
     Example systems for heating or cooling a fuel cell circuit of a vehicle are also provided, which may include: a fuel cell stack having a plurality of fuel cells and configured to receive a fluid and to heat the fluid; an actuator having an actuator position and configured to increase or decrease a fluid temperature of the fluid; and an electronic control unit (ECU) coupled to the actuator, the ECU configured to: determine a temperature control signal corresponding to a target temperature of the fluid; perform a feedforward control of the actuator to cause the actuator to increase or decrease the fluid temperature towards the target temperature of the fluid; determine a temperature difference between the fluid temperature of the fluid and the target temperature of the fluid; determine a sensitivity that corresponds a change in a parameter value or the actuator position to a change in the fluid temperature; apply the sensitivity to the temperature difference to determine an error signal that corresponds to an additional change in the actuator position to cause the fluid temperature to increase or decrease to reduce the temperature difference; receive a feedback control signal from a PID controller, the feedback control signal based on the error signal, wherein the feedback control signal applies a I-term saturation limit; and control the actuator based on the error signal. 
     In some implementations, the PID controller is part of the ECU. The PID controller may be configured to generate the feedback control signal by accounting for present error values, past error values, and potential future errors of the error signal. The PID controller may be configured to apply the I-term saturation limit according to the equations: 
     
       
         
           
             
               
                 I 
                 - 
                 
                   term 
                   max 
                 
               
               = 
               
                 Δ 
                 ⁢ 
                 
                   
                     Controlled 
                     
                       state 
                       ⁢ 
                           
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                         I 
                       
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                         term 
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                         Controlled 
                         state 
                       
                     
                   
                   ) 
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 I 
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                   term 
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                     allowed 
                   
                 
                 ⁢ 
                 
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                         Controlled 
                         state 
                       
                     
                   
                   ) 
                 
               
             
             ; 
             and 
           
         
       
       
         
           
             
               I 
               - 
               
                 term 
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             = 
             
               
                 min 
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                     max 
                     ⁡ 
                     ( 
                     
                       
                         I 
                         - 
                         
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                       , 
                       
                         I 
                         - 
                         
                           term 
                           min 
                         
                       
                     
                     ) 
                   
                   , 
                   
                     I 
                     - 
                     
                       term 
                       max 
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     The PID controller may be configured to apply the I-term saturation limit to a final PI combined feedback term according to the equations: 
     
       
         
           
             
               
                 PI 
                 - 
                 
                   term 
                   unlimited 
                 
               
               = 
               
                 P 
                 - 
                 
                   term 
                   unlimited 
                 
                 + 
                 I 
                 - 
                 
                   term 
                   limited 
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 PI 
                 - 
                 
                   term 
                   max 
                 
               
               = 
               
                 Δ 
                 ⁢ 
                 
                   
                     Controlled 
                     
                       state 
                       ⁢ 
                           
                       allowed 
                     
                   
                   ( 
                   
                     
                       
                         ∂ 
                         PIControl 
                       
                       - 
                       
                         term 
                         state 
                       
                     
                     
                       ∂ 
                       
                         Controlled 
                         state 
                       
                     
                   
                   ) 
                 
               
             
             ; 
           
         
       
       
         
           
             
               
                 PI 
                 - 
                 
                   term 
                   min 
                 
               
               = 
               
                 - 
                 Δ 
                 ⁢ 
                 
                   
                     Controlled 
                     
                       state 
                       ⁢ 
                           
                       allowed 
                     
                   
                   ( 
                   
                     
                       
                         ∂ 
                         PIControl 
                       
                       - 
                       
                         term 
                         state 
                       
                     
                     
                       ∂ 
                       
                         Controlled 
                         state 
                       
                     
                   
                   ) 
                 
               
             
             ; 
             and 
           
         
       
       
         
           
             
               PI 
               - 
               
                 term 
                 limited 
               
             
             = 
             
               
                 min 
                 ⁡ 
                 ( 
                 
                   
                     max 
                     ⁡ 
                     ( 
                     
                       
                         PI 
                         - 
                         
                           term 
                           unlimited 
                         
                       
                       , 
                       
                         PI 
                         - 
                         
                           term 
                           min 
                         
                       
                     
                     ) 
                   
                   , 
                   
                     PI 
                     - 
                     
                       term 
                       max 
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     In some implementations, the actuator is a three-way valve. The target temperature of the fluid and the fluid temperature may correspond to the fluid at an inlet of the fuel cell stack. The ECU may be further configured to control the actuator based on a sum of the feedforward control and the feedback control signal. 
    
    
     
       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 heating or cooling a fuel cell circuit according to an embodiment of the present invention. 
         FIG.  5    is a block diagram illustrating a three-way valve controller for feedback-based control of a three-valve of a fuel cell circuit according to an embodiment of the present invention. 
         FIGS.  6 - 9    are block diagrams illustrating control logic for heating or cooling 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 providing feedback control of actuators of the fuel cell circuit to increase or decrease a fluid temperature. The systems provide various benefits and advantages such as adjusting control of different actuators based on temperature discrepancies at different locations, which results in more accurate control of the actuators. The systems further advantageously prevent I-term wind-up by calculating and controlling the I-term as discussed herein. In particular, I-term saturation may be based on the system sensitivity (partial derivative), allowing the limits to increase/decrease proportionally to the system response. An allowed learning limit based on the state being controlled can be defined and the partial derivative coverts the controlled state limit to the PI control state. Beyond just the I-term saturation, the partial derivative scaling method may be applied to the final PI combined feedback term as well. 
     An exemplary system includes a fuel cell stack and an actuator that can increase or decrease a fluid temperature of a fluid flowing through the fuel cell stack. The system further includes an electronic control unit (ECU). The ECU may include a PID controller. The ECU can determine a desired temperature of the fluid as well as a feedforward control signal for controlling the actuator to cause the fluid temperature to move towards the desired temperature. The ECU can also determine a temperature difference between the fluid temperature at a location and the desired temperature at the location, as well as a sensitivity. The ECU then applies the sensitivity to the temperature difference to determine an error signal corresponding to an error in the actuator position, and then controls the actuator based on the error signal to cause the fluid temperature to become closer in value to the desired temperature. The ECU may also receive feedback from the PID controller, including an I-term based on a partial derivative to prevent integral wind-up. Feedback controls for a PID are discussed at length in U.S. Pat. No. 10,720,655, which is incorporated by reference herein in its entirety. Further methods for heating and cooling a fuel cell circuit of a vehicle are discussed in U.S. Pat. No. 10,777,831, which is incorporated by reference herein in its entirety. 
       FIG.  1    shows a diagram of a vehicle  100  including components of a system  101  for controlling a temperature of fuel cells of the vehicle  100 . In some implementations, the vehicle  100  and 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 that regard, the ECU  102  may control various aspects of the system  101  as well as well as aspects of the vehicle itself (such as steering, braking, accelerating, or the like). 
     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  106  may include a GPS sensor or an IMU sensor. The speed sensor  106  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 implementations, the battery  116  includes one or more energy storage devices including a battery, a fly-wheel, a super-capacitor, a thermal storage device, or other energy storage devices. 
     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. The motor/generator  114  may further convert mechanical power received from the engine  112  or wheels of the vehicle into electricity, which may be stored in the battery  116  as energy and/or used by other components of the vehicle. In some embodiments, the motor-generator  114  may also or instead include a turbine or other device capable of generating thrust. 
     Additional details of the fuel cell circuit  118  are illustrated in  FIG.  2   . In some implementations, 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 an actuator which may be 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% 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 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. 
     In some implementations, the three-way valve is driven by the ECU  102 , and in particular, may be driven according to one or more of a feedforward signal and feedback signal. The feedback signal may be calculated by a PID controller implementing a partial derivative I-term to reduce or prevent integral windup during a heating or cooling process, as shown more particular with reference to  FIG.  3   . 
     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 . 
       FIG.  4    shows a method  400  for feedback-based heating or cooling of a fuel cell circuit. The fuel cell circuit may be the fuel cell circuit shown in  FIGS.  1  and  2   . In some implementations, the method  400  is performed by a feedback control, such as the feedback control  316  of  FIG.  3   . 
     The method  400  may include step  402  in which the ECU determines 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, such as at the inlet of the fuel cell stack. The temperature control signal may be determined using a state governor such as the state governor  308  of  FIG.  3   . 
     The method  400  may include step  404  in which the ECU performs 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 (such as state estimator  320  of  FIG.  3   ). In some implementations, the ECU directly controls one or more actuators of the fuel cell circuit using the feedforward control. In some implementations, the ECU directly controls one or more actuator using a combination of the feedforward control and feedback control. 
     The method  400  may include step  406  in which the fluid temperature of the fluid at one or more location is detected by a temperature sensor or calculated by the ECU, such as in a state estimator. 
     The method  400  may include step  408  in which the ECU determines 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. 
     The method  400  may include step  410  in which the ECU determines or calculates 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. 
     The method  400  may include optional step  412  in which the ECU divides 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, step  412  may be skipped. 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 step  408  may correspond to a temperature error. In other words, 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 step  414 , 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. 
     The method  400  may include step  416  in which the ECU passes 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 these values. In particular, the PID controller may analyze a proportional term (P-term) which may be proportional to a current value of the error signal, an integral term (I-term) which may account for past values of the error signal and integrate them over time, and a derivative term (D-term) which may provide potential future errors of the error signal based on its current rate of change. The controller may balance the effect of the P, I, and D terms to optimize their control function. 
     Integral Wind-up is an issue that presents challenges for many PID controllers, especially in highly non-linear systems such as temperature control for fuel cells. These systems may have highly non-linear behavior that is not captured adequately by traditional methods. Existing systems to manage temperature using a PID controller generally set static upper and lower limits without including learning values, which may worsen problems with Integral Wind-up. In particular, this phenomenon may be caused by large changes in setpoints, causing the I-term to accumulate a significant error over time, which can cause significant overshooting or undershooting. 
     In some implementations, the I-term and total PI feedback amount (including the sum of the P-term and I-term) are saturated using a partial derivative calculation to capture the system sensitivity and non-linearity. In these implementations, the I-term of the PID controller may be calculated by traditional methods and/or by a partial derivative method. This may result in scaling the I-term saturation based on the system sensitivity and allowing the upper and lower limits to increase or decrease proportionally to the system response. Defining the I-term saturation limits may have the effect of optimizing the system for non-linear systems and may help to prevent Integral Wind-up in the fuel cell control systems as discussed herein. Setting the I-term saturation limits may be accomplished through the use of the following equations: 
     
       
         
           
             
               
                 
                   
                     I 
                     - 
                     
                       term 
                       max 
                     
                   
                   = 
                   
                     Δ 
                     ⁢ 
                     
                       
                         Controlled 
                         
                           state 
                           ⁢ 
                               
                           allowed 
                         
                       
                       ( 
                       
                         
                           
                             ∂ 
                             I 
                           
                           - 
                           
                             term 
                             state 
                           
                         
                         
                           ∂ 
                           
                             Controlled 
                             state 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
                     . 
                         
                     1 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     - 
                     
                       term 
                       min 
                     
                   
                   = 
                   
                     - 
                     Δ 
                     ⁢ 
                     
                       
                         Controlled 
                         
                           state 
                           ⁢ 
                               
                           allowed 
                         
                       
                       ( 
                       
                         
                           
                             ∂ 
                             I 
                           
                           - 
                           
                             term 
                             state 
                           
                         
                         
                           ∂ 
                           
                             Controlled 
                             state 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
                     . 
                         
                     2 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     I 
                     - 
                     
                       term 
                       limited 
                     
                   
                   = 
                   
                     min 
                     ⁡ 
                     ( 
                     
                       
                         max 
                         ⁡ 
                         ( 
                         
                           
                             I 
                             - 
                             
                               term 
                               unlimited 
                             
                           
                           , 
                           
                             I 
                             - 
                             
                               term 
                               min 
                             
                           
                         
                         ) 
                       
                       , 
                       
                         I 
                         - 
                         
                           term 
                           max 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
                     . 
                         
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     The partial derivative term in Equations 1-3 above 
     
       
         
           
             ( 
             
               
                 
                   ∂ 
                   I 
                 
                 - 
                 
                   term 
                   state 
                 
               
               
                 ∂ 
                 
                   Controlled 
                   state 
                 
               
             
             ) 
           
         
       
     
     may be calculated in real time based on the system states. The partial derivative term may represent the system sensitivity at the current system states and may capture non-linearity of the system. 
     The ΔControlled state allowed  term in Equations 1-2 above may represent how much the I-term can contribute to closing the controlled state error. This may help to prevent Integral Wind-up by limiting the accumulation of errors in the I-term during a calculation process. For example, if the controlled stated is fuel cell (FC) inlet temperature, setting ΔControlled state allowed =10 means that the I-term can only grow enough to close a FC inlet temperature error of ±10 degrees C. In this example, the partial derivative term 
     
       
         
           
             ( 
             
               
                 
                   ∂ 
                   I 
                 
                 - 
                 
                   term 
                   state 
                 
               
               
                 ∂ 
                 
                   Controlled 
                   state 
                 
               
             
             ) 
           
         
       
     
     will dynamically scale the I-term limits so that the I-term can only accumulate the equivalent of a ±10 degrees C. error in the controlled state. 
     In some implementations, the same method of scaling the I-term (e.g., according to Eqs. 1-3) can be applied to the final total PI combined feedback term (also referred to as the PI control value which may include the sum of the P-term and the I-term), such as through the use of the following equations: 
     
       
         
           
             
               
                 
                   
                     PI 
                     - 
                     
                       term 
                       unlimited 
                     
                   
                   = 
                   
                     P 
                     - 
                     
                       term 
                       unlimited 
                     
                     + 
                     I 
                     - 
                     
                       term 
                       limited 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
                     . 
                         
                     4 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     PI 
                     - 
                     
                       term 
                       max 
                     
                   
                   = 
                   
                     Δ 
                     ⁢ 
                     
                       
                         Controlled 
                         
                           state 
                           ⁢ 
                               
                           allowed 
                         
                       
                       ( 
                       
                         
                           
                             ∂ 
                             PIControl 
                           
                           - 
                           
                             term 
                             state 
                           
                         
                         
                           ∂ 
                           
                             Controlled 
                             state 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   
                     [ 
                     
                       Eq 
                       . 
                           
                       5 
                     
                     ] 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     PI 
                     - 
                     
                       term 
                       min 
                     
                   
                   = 
                   
                     - 
                     Δ 
                     ⁢ 
                     
                       
                         Controlled 
                         
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                           ⁢ 
                               
                           allowed 
                         
                       
                       ( 
                       
                         
                           
                             ∂ 
                             PIControl 
                           
                           - 
                           
                             term 
                             state 
                           
                         
                         
                           ∂ 
                           
                             Controlled 
                             state 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
                     . 
                         
                     6 
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     PI 
                     - 
                     
                       term 
                       limited 
                     
                   
                   = 
                   
                     min 
                     ⁡ 
                     ( 
                     
                       
                         max 
                         ⁡ 
                         ( 
                         
                           
                             PI 
                             - 
                             
                               term 
                               unlimited 
                             
                           
                           , 
                           
                             PI 
                             - 
                             
                               term 
                               min 
                             
                           
                         
                         ) 
                       
                       , 
                       
                         PI 
                         - 
                         
                           term 
                           max 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   
                     Eq 
                     . 
                         
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     The method  400  may include step  418  in which the ECU controls the actuator based on the feedback control signal. For example, the ECU may generate a sum of the feedforward control signal and the feedback control signal and control the actuator based on the sum. In some implementations, the ECU controls the actuator based on the feedback control signal alone. In some exemplary implementations, the method  400  may include returning to step  402  after the completion of step  418  to proceed through the steps again. 
     Referring to  FIG.  5   , a three-way controller  500  is shown. In some implementations, the three-way controller  500  is included in the ECU  102  of  FIG.  2   , and in particular, may carry out the feedback control  316 . The three-way valve controller  500  may include logic or dedicated hardware designed to perform a method similar to the method  400  of  FIG.  4    to perform feedback control of the three-way valve. 
     The three-way valve controller  500  may include a number of calculation blocks  502 ,  510 ,  524 ,  532  that receive various inputs and output signals. These may include difference block  502  which may receive a fluid temperature (T F C u)  504  measured or calculated at the inlet of a fuel cell stack, such as fuel cell stack  200  in  FIG.  2   . For example, the fluid temperature  504  may be calculated by a state estimator of the ECU  102 . The difference block  502  may further receive a desired temperature (T FC in_cmd )  506  corresponding to a desired temperature of the fluid at the inlet of the fuel cell stack. The difference block  502  may output a temperature difference (ΔT FC in error )  508  corresponding to a difference between the fluid temperature  504  and the desired temperature  506 . In some implementations, the temperature difference  502  represents an amount of error compared to an expected fluid temperature. 
     The three-way valve controller  500  may further include a second difference block  510 . The second difference block  510  may receive a radiator temperature (T rad out )  512  corresponding to a temperature of the fluid at an outlet of a radiator. The second difference block  510  may further receive a bypass fluid temperature (T bypass )  514  corresponding to a temperature of the fluid at a location along a bypass branch of the fuel cell circuit. In some implementations, the second difference block  510  outputs a difference  516  between the radiator temperature  512  and the bypass fluid temperature  514 . 
     The three-way valve controller  500  may further include a sensitivity block  518 . The sensitivity block  518  may receive the difference  516  between the radiator temperature  512  and the bypass fluid temperature  514  along with a pump fluid temperature (T pump in )  520  corresponding to a temperature of the fluid at an inlet of the pump. The sensitivity block  518  may determine a sensitivity  522  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  522  may indicate how much of a change in valve position (Z) results in a 1 degree (C.) change of the fluid temperature at the inlet of the fuel cell stack. The sensitivity  522  may be calculated using a partial derivative I-term as discussed above, and in particular, may be based on Equations 1-3 as set forth above. The implementation of this sensitivity  522  may allow the upper and lower limits to increase or decrease proportionally to the system response, which in turn may help prevent I-term wind-up. Control logic  600  associated with the sensitivity block  518  is shown in  FIG.  6   . 
     The three-way valve controller  500  may further include a multiplication block  524 . The multiplication block  524  may apply the sensitivity  522  to the temperature difference  508 . For example, the multiplication block  524  may multiply the temperature difference  508  by the sensitivity  522 . The result of the multiplication block  524  may be an error signal  526 , 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  500  may further include a proportional-integral-derivative (PID) controller  528 . The PID controller  528  may receive the error signal  526  and may generate a feedback control signal  530  by accounting for present error values, past error values, and potential future errors of the error signal  526 . In some implementations, the PID controller  528  is configured to apply the steps of method  400  to prevent I-term wind-up by limiting the total allowed contribution of state error. The PID controller  528  may apply Equations 4-7 as set forth above to the error signal  526  to produce a feedback control signal (ΔZ FB )  530 . Control logic  700  associated with the PID controller  528  is shown in  FIG.  7   . 
     The ECU  102  may further include a combination block  532  that receives the feedback control signal  530  along with a feedforward control signal  534 . The feedforward control signal  534  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  532  may generate a sum of the feedback control signal  530  and the feedforward control signal  534 . The combination block  532  may output a combined control signal  536  that corresponds to a final desired valve position of the three-way valve  500  based on feedforward and feedback control. The ECU  102  may control the three-way valve based on the final desired valve position. 
     Referring to  FIG.  6   , control logic  600  for the sensitivity block  518  of  FIG.  5    is shown. In this example, equations are given representing the correction of bypass path flow resistance (Z). The flow resistance (Z) is then used to calculate the valve flow resistance. From there, the valve resistance is converted to the equivalent valve position. Other associated inputs  602 ,  604 ,  606 ,  614 ,  616 ,  618 , outputs  617 ,  624 , and comparison blocks  610 ,  612  are also shown in the control logic  600 . 
     Referring to  FIG.  7   , control logic  700  for the PID controller  528  of  FIG.  5    is shown. This control logic  700  includes the partial derivative feedback term produced by control logic  600  as inputs  702 . The control logic also includes inputs  704  that represent the ΔControlled state allowed  term in Equations 5 and 6 above, as well as inputs  706 ,  708 ,  713 ,  714 ,  724 ,  726 ,  728  and comparison blocks  710 , multiplication blocks  712 , and calculation blocks  711 . In some implementations, calculation block  720  represents the partial derivative-based I-term wind-up prevention and calculation block  730  represents the PI-term maximum and minimum limits based on the partial derivative term. 
     Referring to  FIGS.  8  and  9   , control logic  800  related to Feedback Prohibit, Hold, and Reset functions and control logic  900  related to passing through the Feedforward value is shown. In some implementations, the control logic  800  determines the feedforward block  312  and the control logic  900  determines the feedback block  316  in  FIG.  3   . 
     The foregoing outlines features of several implementations so that a person of ordinary skill in the art may better understand the aspects of the present disclosure. Such features may be replaced by any one of numerous equivalent alternatives, only some of which are disclosed herein. One of ordinary skill in the art should appreciate that they may readily use the present disclosure as a basis for designing or modifying other processes and structures for carrying out the same purposes and/or achieving the same advantages of the implementations introduced herein. One of ordinary skill in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the present disclosure, and that they may make various changes, substitutions and alterations herein without departing from the spirit and scope of the present disclosure. 
     The Abstract at the end of this disclosure is provided to comply with 37 C.F.R. § 1.72(b) to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. 
     Moreover, it is the express intention of the applicant not to invoke 35 U.S.C. § 112(f) for any limitations of any of the claims herein, except for those in which the claim expressly uses the word “means” together with an associated function.