Abstract:
A method of estimating temperature in an engine including estimating metal temperatures at each of a plurality of nodes and estimating a coolant temperature. The method further includes detecting a measured coolant temperature and determining a gain based on a difference between the estimated coolant temperature and the measured coolant temperature. The method adjusts the metal temperatures at each of the plurality of nodes based on the gain. The method estimates the metal temperatures of engine components without temperature sensors.

Description:
FIELD 
     The present invention relates to engine control, and more particularly to an engine temperature estimator. 
     BACKGROUND 
     Internal combustion engines create heat through combustion, friction and various component inefficiencies. A cooling system regulates the temperature of the engine to protect the engine from excessive heat and to promote efficient combustion. A cold engine may be less efficient and may produce increased emissions. An overly hot engine increases stress on engine components and may cause mechanical failures. 
     The internal combustion engine typically operates more efficiently when regions within the engine are maintained at different temperatures. For example, the engine may benefit from a lower temperature in the bottom of the engine relative to the top of the engine. To maintain different temperatures in the regions of the engine, traditional cooling systems typically employ multiple sensors that measure and track metal temperatures in the engine. It can be appreciated that measuring metal temperatures in a mass production engine can be complex and costly. For example, any additional sensors increase production costs, add to engine complexity and increase vehicle warranty costs. 
     SUMMARY 
     A method of estimating temperature in an engine including estimating metal temperatures at each of a plurality of nodes and estimating a coolant temperature. The method further includes detecting a measured coolant temperature and determining a gain based on a difference between the estimated coolant temperature and the measured coolant temperature. The method adjusts the metal temperatures at each of the plurality of nodes based on the gain. The method estimates the current metal temperatures without temperature sensors. 
     In one feature, the method distributes an amount of engine coolant to a plurality of engine locations based on said temperatures. 
     Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the various embodiments of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will become more fully understood from the detailed description, the appended claims and the accompanying drawings, wherein: 
         FIG. 1  is a schematic diagram illustrating a vehicle including a control module constructed in accordance with the teachings of the present invention; 
         FIG. 2  is a flow chart illustrating a methodology for designing an engine component temperature estimator in accordance with the teachings of the present invention; 
         FIG. 3  is a flow chart illustrating an engine component temperature estimator control in accordance with the teachings of the present invention; and 
         FIG. 4  is a schematic diagram illustrating the control module and the engine of  FIG. 1  including a metal and coolant temperature detection module and a gain adjustment module. 
     
    
    
     DETAILED DESCRIPTION 
     The following description of the various embodiments is merely exemplary in nature and is in no way intended to limit the invention, its application or uses. As used herein, the term module refers to an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that executes one or more software or firmware programs, a combinational logic circuit, or other suitable components that provide the described functionality. Moreover, vehicle controllers may communicate with various vehicle systems using digital or analog inputs and outputs and/or an automotive communications network including, but not limited to, the following commonly used vehicle communications network standards: CAN, SAE J1850, and GMLAN. 
     Referring now to  FIG. 1 , a portion of a vehicle  10  includes an engine  12  that produces a torque output to drive the vehicle  10  through a powertrain  14  in a manner known in the art. The engine  12  can be an internal combustion engine. It can be appreciated that the engine  12  could also be configured with a variety of powerplant configurations, such as, but not limited to, fuel cell and/or battery powered electric machines, internal combustion engines such as diesel, biomass, gasoline, and natural gas consuming engines, and hybrid combinations thereof. 
     The engine  12  includes an intake manifold  16  and a throttle  18 . Airflow into the intake manifold  16  is regulated by the throttle  18 . The airflow from the intake manifold  16  and fuel from a fuel pump  20  is ignited in a plurality of cylinders  22  by an ignition system  24 , in a manner known in the art. Combustion in each of the cylinders  22  pushes a piston  26  toward a crankshaft  28 , to which the piston  26  is attached by a connecting rod  30 . An up and down motion of the piston  26  is transmitted to the crankshaft  28  resulting in rotational power being delivered to the powertrain  14 . It is appreciated that while the illustrated engine utilizes a spark ignition, the present invention applies to diesel and other sparkless compression ignition engines. 
     Each of the cylinders  22  includes a cylinder head  32 , a valve bridge  34  and a cylinder liner  36 . The cylinders  22  are located in an engine block  38 . It is appreciated that the components of the engine  12  can produce, and retain heat. Moreover, the components of the engine  12  can transfer heat between and amongst the components through conduction, convection, radiation and/or advection. As such, a cooling system  40 , which is connected to the engine  12 , provides cooling to the components and regions of the engine  12 . 
     The cooling system  40  directs coolant through a plurality of cooling channels  42  to cool the various components and regions of the engine  12 . The cooling system  40  includes a water pump  44 , which propels coolant throughout the plurality of cooling channels  42 . The water pump  44  can be an electric water pump with a variable flow rate. It can be appreciated that a mechanical water pump can also be used that is otherwise mechanically driven off the engine  12 . The cooling system  40  also includes a radiator  46  and a heater  48 . The radiator  46  reduces the temperature of the coolant by transferring heat from the coolant to the outside of the vehicle  10 . The heater  48  can also reduce the temperature of the coolant by transferring heat from the coolant to the inside of the vehicle  10 . A thermostat  50  can prevent delivery of coolant to the radiator  46  during engine warm-up in a manner known in the art. 
     The cooling system  40  includes the water pump  44  and a valve  52 , both of which can communicate with a control module  54 . The control module  54  can control a variable flow rate of the water pump  44 . The control module  54  can communicate with the valve  52  to distribute coolant between various components and regions of the engine  12 . More specifically, the cylinder head  32  and the engine block  38 , which can be referred to as a top of the engine and a bottom of the engine, respectively, can operate more efficiently at different respective temperatures. Moreover, the cooling system  40  can more efficiently cool the engine  12  by controlling distribution of coolant. As such, the water pump  44  and the valve  52  can be controlled by the control module  54  to direct varying coolant volumes to the top of the engine and the bottom of the engine to maintain optimum temperatures in the various regions of the engine. 
     The control module  54  can also control operations of the vehicle  10  based on vehicle operating parameters  56  that can include environmental indicators such as humidity, temperature or air pressure. The vehicle operating parameters  56  can also include a powerplant profile and a powerplant status that indicates, for example, a cold engine signal or engine controller faults. It is appreciated that a cold engine refers to the temperatures of the respective components of the engine  12  being approximately equal to the ambient temperature conditions. As such, the cold engine temperature can refer to an engine temperature in the range of about 0° C. (32° F.) to about 32° C. (90° F.). The powerplant profile can include lookup data that indicates, for example, a torque output based on spark retardation, torque output based on engine speed and effects of the environmental indicators on engine power. A telematic module  58 , such as OnStar® can also provide input to and receive output from the control module  54 . 
     The control module  54  can generate a throttle control signal  60  that is sent to a throttle actuator  62  that regulates the throttle  18 . An engine speed sensor  64  generates an engine speed signal  66  for engine  12 , which is also communicated to the control module  54 . A powertrain speed sensor  68  generates a power train speed signal  70 , which is also communicated to the control module  54 . An entrance coolant temperature sensor  72  transmits an entrance coolant temperature signal  74  to the control module  54 . Similarly, an exit coolant temperature sensor  76  transmits an entrance coolant temperature signal  78  to the control module  54 . It is appreciated that while a single entrance coolant temperature sensor  72  is illustrated adjacent to the valve  52 , two entrance coolant temperature sensors can be used and located at the locations of the engine  12  that correspond to the top and bottom of the engine respectively. 
     With reference to  FIG. 2 , a methodology is shown that develops an engine temperature estimator model from which an engine temperature estimator control system can be derived and implemented in a vehicle. To develop the engine temperature estimator model, the methodology can include, for example, a first portion  102  and a second portion  104 , as shown in  FIG. 2 . In the first portion  102 , a detailed multi-cylinder engine temperature model is created that models heat transfer and heat generation throughout an engine. In the second portion  104 , the detailed multi-cylinder engine temperature model is simplified and linearized to develop an exemplary engine temperature estimator control system. 
     In step  106 , a plurality of node locations are determined for the detailed multi-cylinder engine temperature model. For example, the detailed model locates five nodes per each cylinder in the engine block, the cylinder head, the valvebridge, the cylinder liner and the engine coolant. It is appreciated that the nodes can be located in various other locations in the engine such as, but not limited to, the piston, an oil reservoir, a camshaft or a piston ring. Moreover, the methodology can be applied to engines with various configurations having, for example, a varying numbers of cylinders. The nodes, for example, can represent physical location that corresponds to a position on the engine component. By way of example, the node can represent a portion of cylinder liner in one cylinder. 
     In step  108 , a thermal capacitance is determined at each of the nodes. The thermal capacitance is based on, for example, the geometry, material properties and temperature of the engine components or portion thereof that each node represents. In step  110 , a heat source is determined at each of the nodes to account for heat generation from the engine component in which the node is located. The heat generation or heat loss can be produced by friction, combustion or other losses within the engine. As such, values are computed for these heat sources using, for example, vehicle operating parameters including, but not limited to, engine speed, engine load, manifold pressure and fuel flow rate. 
     In step  112 , heat transfer paths are determined between each of the nodes. It can be appreciated that in the internal combustion engine all of the nodes can exchange heat. In other examples, the nodes may be located such that no heat transfer occurs between two or more of the nodes because one node may be thermally insulated from another node. It is appreciated that one or more of the appropriate equations for heat transfer (i.e. conduction, convection, radiation and/or advection) are used to determine the heat transfer paths. In step  114 , resistances are determined along each of the heat transfer paths. The resistances are based on, for example, geometry of the engine component, flow rate to and from the engine component and material properties of the engine components or portions thereof. 
     In step  116 , engine temperatures and heat transfer rates are determined using the detailed multi-cylinder engine temperature model as constructed in the first portion  102  of the methodology. To determine the temperatures and heat transfer rates, the engine is operated through a plurality of engine operating points selected from a standardized engine test. The test includes, for example, a plurality of test points that can correspond to a certain load on the engine at a certain engine speed for predetermined time periods. The detailed multi-cylinder model, which is a detailed heat transfer model of the engine, determines the engine temperatures and heat transfer rates based on how heat is created and transferred around the engine during the test over a plurality of engine operating points. It can be appreciated that the detailed model can be adjusted to better predict engine temperatures and heat transfer paths by confirming estimated temperatures with measured temperatures and iterating the design of the detailed model as produced in the first portion  102  of the methodology. 
     It can also be appreciated that the detailed model can accurately estimate metal temperatures of various engine components and portions thereof relative to physically installed temperature sensors. The detailed model can provide accurate estimated engine temperatures and heat transfer rates, but the detailed model can be complex and costly to implement into an engine control system because of, for example, modifications and additional computational power required. The detailed model, however, can be simplified and still provide accurate control. In step  118 , the detailed model created in the first portion  102  of the methodology is simplified. The simplified model retains all of the parameters needed to predict engine temperatures such as, for example, coolant flow rate, engine speed and fuel flow rate, but is less complex and therefore easier to implement on the vehicle. In simplifying the detailed model, different configurations and resolutions can be used so that temperatures estimated by the simplified model match those obtained with the detailed model over a sufficient range of engine operating scenarios. 
     The simplified model includes a system of first-order differential equations generated for a plurality of engine nodal lumps. It is appreciated that the number of engine nodal lumps can vary based on the specific engine, nevertheless five engine nodal lumps were determined to provide the best balance between accuracy and complexity. The engine nodal lumps, while having no actual physical locations, are ideal conglomerations of each of the respective nodes located, for example, at the engine block, the cylinder head, the valvebridge, the cylinder liner and the engine coolant. More specifically, the nodes at the valvebridge for each cylinder are combined into one valvebridge nodal lump and the temperature of that nodal lump is the combined metal temperature estimates of the respective nodes tracked over time. Thermal capacitances and heat sources of each of the nodal lumps can include the sums of the corresponding values from each of the nodes in the detailed multi-cylinder model. The resistance of the heat transfer paths in the nodal lumps can be the sums of the resistance from the nodes, which can be adjusted to ensure that the different engine components exchange thermal energy in the simplified model at similar rates as they did in the detailed model. 
     The simplified model, therefore, includes an exemplary system of first-order differential equations for the nodal lumps that define the simplified model. It is appreciated that the system of first order different equations may not be linear but adequately track the values produced by the detailed multi-cylinder model. Each of the equations tracks temperature over time for the respective nodal lumps. 
     The exemplary first-order equation for the cylinder head is provided as follows: 
                 C   H     ⁢       ⅆ     T   H         ⅆ   t         =         Q   H     ⁡     (       m   F     ,     N   E       )       +         G   HC     ⁡     (       m   F     ,     m   CH       )       ⁢     (       T   C     -     T   H       )       +         G   VH     ⁡     (       m   F     ,     m   CH       )       ⁢     (       T   V     -     T   H       )               
The exemplary first-order equation for the valvebridge is provided as follows:
 
                 C   V     ⁢       ⅆ     T   V         ⅆ   t         =         Q   V     ⁡     (       m   F     ,     N   E       )       +         G   VH     ⁡     (       m   F     ,     m   CB       )       ⁢     (       T   H     -     T   V       )               
The exemplary first-order equation for the engine block is provided as follows:
 
                 C   B     ⁢       ⅆ     T   B         ⅆ   t         =         Q   B     ⁡     (       m   F     ,     N   E       )       +         G   BC     ⁡     (       m   F     ,     m   CB       )       ⁢     (       T   C     -     T   B       )       +         G   LB     ⁡     (     m   F     )       ⁢     (       T   L     -     T   B       )               
The exemplary first-order equation for the cylinder liner is provided as follows:
 
                 C   L     ⁢       ⅆ     T   L         ⅆ   t         =         Q   L     ⁡     (       m   F     ,     N   E       )       +         G   LC     ⁡     (       m   F     ,     m   CB       )       ⁢     (       T   C     -     T   L       )       +         G   LB     ⁡     (     m   F     )       ⁢     (       T   B     -     T   L       )               
The exemplary first-order equation for the coolant is provided as follows:
 
     
       
         
           
             
               
                 C 
                 C 
               
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                         CH 
                       
                     
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                     G 
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                         m 
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                       T 
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               + 
               
                 
                   
                     G 
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                         T 
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     Values are generated for the coefficients in the above equations by running the detailed multi-cylinder model through a pre-determined routine such as the above-mentioned exemplary engine test. In the above equations, the coefficient G XY  refers to heat transfer between arbitrary location X and arbitrary location Y. G HC , for example, refers to heat transfer between the cylinder head and the engine coolant. Q X  refers to heat generated at arbitrary location X. Q B , for example, refers to heat generated in the engine block. By way of the above example, the detailed model is run in a steady-state mode for a plurality of points selected from a standardized engine test to generate the previously mentioned coefficients. Once the coefficients of the above equations are generated in the detailed model, the coefficients are adapted to the simplified model. It can appreciated that the simplification of the detailed multi-cylinder model is an iterative process in which results obtained from the simplified model can be compared with results from the detailed model and from actual measurement so that the simplified model can be made more accurate. While the simplification of the detailed model can produce non-linear equations, the equations are less complex and can be implemented in a vehicle control system. 
     In step  120 , it is determined whether the simplified model generated in step  118  is accurate. Accuracy of the simplified model is based on results of the standardized engine test, which are used to produce the coefficients of the equations generated in step  118 . The simplified model is considered accurate when the metal and coolant temperature estimates over a time period at the nodal lumps from the simplified model are within a pre-determined margin of error of the estimates from the detailed model. When the simplified model is inaccurate, the simplified model is reformulated in step  122 . Reformulation of the simplified model can include, for example, adjusting the fit of the polynomials to produce non-linear first-order equations. When the simplified model is accurate, linearization points are selected in step  124 . 
     In step  124 , a plurality of operating or linearization points are selected from the standardized engine test and are points about which the above equations are linearized. The operating points or linearization points include known temperatures and coolant flow rates throughout the engine. The operating points also include various engine speeds, fuel flow rates and coolant temperatures of the engine. It is appreciated that the operating points can be selected from the same standardized engine test used to generate the coefficients for the above equations and iteratively improve the detailed multi-cylinder model. 
     In step  126 , the simplified model, as shown in the above exemplary non-linear equations for the head, valvebridge, block, liner and coolant temperatures, is linearized around a selected operating point. Techniques used to linearize the above exemplary equations can include, for example, Taylor Series expansions. The exemplary linearized equation for the cylinder head is provided as follows: 
                 C   H     ⁢       ⅆ     T   H         ⅆ   t         =         a   HH     ⁢     T   H       +       a   HV     ⁢     T   V       +       a   HB     ⁢     T   B       +       a   HL     ⁢     T   L       +       a   HC     ⁢     T   C       +       b     H   ⁢           ⁢   1       ⁢     m   F       +       b     H   ⁢           ⁢   2       ⁢     m   CH       +       b     H   ⁢           ⁢   3       ⁢     m   CB       +       b     H   ⁢           ⁢   4       ⁢     Q   H       +       b     H   ⁢           ⁢   5       ⁢     Q   V       +       b     H   ⁢           ⁢   6       ⁢     Q   B       +       b     H   ⁢           ⁢   7       ⁢     Q   L       +       b     H   ⁢           ⁢   8       ⁢     T   CIN       +     Cst   H             
The exemplary linearized equation for the valvebridge is provided as follows:
 
                 C   V     ⁢       ⅆ     T   V         ⅆ   t         =         a   VH     ⁢     T   H       +       a   VV     ⁢     T   V       +       a   VB     ⁢     T   B       +       a   VL     ⁢     T   L       +       a   VC     ⁢     T   C       +       b     V   ⁢           ⁢   1       ⁢     m   F       +       b     V   ⁢           ⁢   2       ⁢     m   CH       +       b     V   ⁢           ⁢   3       ⁢     m   VB       +       b     V   ⁢           ⁢   4       ⁢     Q   H       +       b     V   ⁢           ⁢   5       ⁢     Q   V       +       b     V   ⁢           ⁢   6       ⁢     Q   B       +       b     V   ⁢           ⁢   7       ⁢     Q   L       +       b     V   ⁢           ⁢   8       ⁢     T   CIN       +     Cst   V             
The exemplary linearized equation for the engine block is provided as follows:
 
                 C   B     ⁢       ⅆ     T   B         ⅆ   t         =         a   BH     ⁢     T   H       +       a   BV     ⁢     T   V       +       a   BB     ⁢     T   B       +       a   BL     ⁢     T   L       +       a   BC     ⁢     T   C       +       b     B   ⁢           ⁢   1       ⁢     m   F       +       b     B   ⁢           ⁢   2       ⁢     m   CH       +       b     B   ⁢           ⁢   3       ⁢     m   VB       +       b     B   ⁢           ⁢   4       ⁢     Q   H       +       b     B   ⁢           ⁢   5       ⁢     Q   V       +       b     B   ⁢           ⁢   6       ⁢     Q   B       +       b     B   ⁢           ⁢   7       ⁢     Q   L       +       b     B   ⁢           ⁢   8       ⁢     T   CIN       +     Cst   B             
The exemplary linearized equation for the cylinder liner is provided as follows:
 
                 C   L     ⁢       ⅆ     T   L         ⅆ   t         =         a   LH     ⁢     T   H       +       a   LV     ⁢     T   V       +       a   LB     ⁢     T   B       +       a   LL     ⁢     T   L       +       a   LC     ⁢     T   C       +       b     L   ⁢           ⁢   1       ⁢     m   F       +       b     L   ⁢           ⁢   2       ⁢     m   CH       +       b     L   ⁢           ⁢   3       ⁢     m   VB       +       b     L   ⁢           ⁢   4       ⁢     Q   H       +       b     L   ⁢           ⁢   5       ⁢     Q   V       +       b     L   ⁢           ⁢   6       ⁢     Q   B       +       b     L   ⁢           ⁢   7       ⁢     Q   L       +       b     L   ⁢           ⁢   8       ⁢     T   CIN       +     Cst   L             
The exemplary linearized equation for the coolant is provided as follows:
 
                 C   C     ⁢       ⅆ     T   C         ⅆ   t         =         a   CH     ⁢     T   H       +       a   CV     ⁢     T   V       +       a   CB     ⁢     T   B       +       a   CL     ⁢     T   L       +       a   CC     ⁢     T   C       +       b     C   ⁢           ⁢   1       ⁢     m   F       +       b     C   ⁢           ⁢   2       ⁢     m   CH       +       b     C   ⁢           ⁢   3       ⁢     m   VB       +       b     C   ⁢           ⁢   4       ⁢     Q   H       +       b     C   ⁢           ⁢   5       ⁢     Q   V       +       b     C   ⁢           ⁢   6       ⁢     Q   B       +       b     C   ⁢           ⁢   7       ⁢     Q   L       +       b     C   ⁢           ⁢   8       ⁢     T   CIN       +     Cst   C             
In the exemplary linearized equations, Q X  refers to heat generated at the nodal lumps located at an arbitrary location X, which can be based on engine speed and fuel flow. Q B , for example, refers to heat generated at the nodal lump located in the engine block.
 
     In step  128 , it is determined whether the linearized model is accurate. Results from the linearized model at each linearization point are compared to those computed with the detailed model from the first portion  102  of the methodology. An operating point or linearization point is chosen as the best linearization point when the results from the simplified model most closely match the results of the linearized model at the linearization point. When the linearized model is not accurate, a different linearization point is determined in step  130 . The linearization point that produces the best agreement between the linearized model and the simplified model becomes the linearization point for the entire system. When the linearized model is deemed accurate, the methodology continues with step  132 . 
     In step  132 , initial conditions are determined. More specifically, the initial temperatures for coolant at the entrance and the exit of the engine are determined and associated with the linear model. It is appreciated that when the initial conditions are known, the linear model can be solved to produce real-time temperatures at the nodal lumps that correspond to the metal temperature estimates at each of the nodes. When the vehicle is cold, it is appreciated the initial temperatures may be equal to the ambient temperature. When starting the vehicle after a short shut-down period, for example, the initial temperatures may be different throughout the engine, such that the coolant entering the engine may be a different temperature than the coolant exiting the engine. 
     The linearized equations can incorporate the initial conditions from step  132  and be shown in matrix form as follows: 
                 ⅆ     ⅆ   t       ⁢         [           T   H               T   V               T   B               T   L               T   C           ]     ︸         x   _     .         =         A   _     *         [           T   H               T   V               T   B               T   L               T   C           ]     ︸       x   _         =       B   _     *         [           m   f               m   CH               m   CB               Q   H               Q   V               Q   B               Q   L               T   CIN           ]     ︸       u   _                 
It will be appreciated that any uncertainty in, or perturbation to the initial conditions, can lead to an error in the estimated real-time temperatures, which are determined by solving the above matrix of equations. It will be further appreciated that the error caused by the uncertainty or perturbations is integrated during the solution of the differential equations and can drive the system to an unstable state.
 
     In step  134 , the control system determines estimated metal and coolant temperatures at the nodal lumps, which correspond to temperatures at the nodes at the plurality of engine locations. It can be appreciated that temperature estimates can be adjusted by a gain. It can also be appreciated that the estimation of metal and coolant temperatures can be based on the linear model. 
     In step  136 , a measured actual engine coolant temperature (i.e. T CA ) is determined. The engine coolant temperature is determined at a location, for example, where the coolant exits the engine block in route to the radiator. As shown in the below equation, the measured actual coolant temperature (T CA ) can be used in a feedback loop to stabilize the linear model. In step  138 , it is determined whether the error between the measured actual coolant temperature (T CA ) and the estimated coolant temperature (i.e. T CE ) by the linear model is within an acceptable margin or error. When the error between the measured actual coolant temperature (T CA ) and the estimated coolant temperature (T CE ) by the linear model is not within an acceptable margin of error, a suitable gain is determined in step  140 . The gain determined in step  140  can be based on the error as determined in step  138  and the methodology parameters that may otherwise necessitate a higher or lower gain. From step  140 , control loops back to step  134  and multiplies the estimated coolant temperature by the gain. 
     The gain derived from the difference between the measured actual coolant temperature (T CA ) and the estimated coolant temperature (T CE ) provides the methodology with a feedback loop for the linearized equations and makes the linear model self-correcting. An exemplary self-correcting feedback loop in an exemplary linear model in matrix form is as follows: 
                 ⅆ     ⅆ   t       ⁡     [             T   ~     H                 T   ~     V                 T   ~     B                 T   ~     L                 T   ~     C           ]       =         A   _     *     [             T   ~     H                 T   ~     V                 T   ~     B                 T   ~     L                 T   ~     C           ]       +       B   _     *     [           m   f               m   CH               m   CB               Q   H               Q   V               Q   B               Q   L               T   CIN           ]       -       L   _     ⁡     (       [             T   ~     H                 T   ~     V                 T   ~     B                 T   ~     L                 T   ~     C           ]     -     [         0           0           0           0             T   Coolant_measured           ]       )               
The feedback loop enables the linear model to accurately estimate metal temperatures throughout the engine for any transient operating condition. It is appreciated that the set of gains used in the feedback loop can be selected and validated against the simplified (i.e. non-linear) system of differential equations and eventually against the detailed engine model to achieve accurate predictions of system temperatures in an engine.
 
     With reference to  FIG. 3 , an exemplary control system is shown that estimates metal temperature at an engine component derived from the methodology as illustrated in  FIG. 2 . In step  202 , control measures initial temperatures of the coolant at the entrance and the exit of the engine. It is appreciated that in a cold engine, the coolant throughout the engine may be about equal to ambient temperatures. Determination of initial temperatures in a warm engine, however, may occur, for example, when an engine is started within a short period of time (i.e. less than twenty minutes) after being turned off. 
     In step  204 , control determines estimated metal and coolant temperatures at each node based on the linear model as above described. The nodes of the engine are located, for example, in the engine block, the cylinder head, the valvebridge, the cylinder liner and the engine coolant. It can be appreciated that the estimated metal and coolant temperatures can be adjusted based on a gain determined in step  212 . In step  206 , control determines a measured coolant temperature based on a temperature-measuring device located in the engine coolant. The locations of the temperature device and the engine coolant can be, for example, at the exit of the engine block where the engine coolant is routed from the engine block to the radiator. In step  208 , control determines whether the estimated coolant temperature (T CE ) is equal to the measured actual coolant temperature (T CA ). When the estimated coolant temperature (T CE ) is within an acceptable margin of error of the measured actual coolant temperature (T CA ), control ends. When the estimated coolant temperature (T CE ) is not within an acceptable margin of error of the measured actual coolant temperature (T CE ), control continues with step  210 . 
     In step  210 , the error between the estimated coolant temperature (T CE ) and the measured actual coolant temperature (T CE ) is determined. In step  212 , a gain is determined based on the error and other parameters and variables from the control system that may otherwise necessitate an increase or a decrease in gain. It can be appreciated that the other parameters can include, for example, operating parameters and communication from the telematic module. From step  212 , control loops back to step  204  and one or more of the metal or coolant temperature estimates can be multiplied by the gain. It is appreciated that the temperature estimate multiplied by the gain will ideally match the actual measured temperature that is determined in step  202 . 
     In step  214 , control distributes engine coolant to locations in the engine by adjusting the position of a valve and flow rate of the water pump. Distribution of coolant can be predetermined proportions to the top of the engine and the bottom of the engine. It can be appreciated that a three-way valve is illustrated ( FIG. 1 ) but myriad valves of suitable configurations can be used that are based on specific engine configurations. As such, control can direct multiple valves and multiple water pumps through various coolant distribution configurations based on specific engines to adequately cool the engine. 
     With reference to  FIG. 4 , an exemplary temperature estimator module  300  is shown. The exemplary temperature estimator module  300  generates an estimated metal temperature signal  302  and an estimated coolant temperature signal  304 . The metal temperature signal can include, for example, metal temperatures (T ME ) at the plurality of nodes that correspond to the plurality of engine locations. The coolant temperature signal can include, for example, coolant temperatures (T CE ) at the plurality of nodes that correspond to the plurality of engine locations. 
     The estimated metal temperature signal  302  and the estimated coolant temperature signal  304  are based on a gain adjustment signal  306  and an actual coolant temperature signal  308 . The engine  12  ( FIG. 1 ) includes a coolant temperature detection sensor  310  that generates the actual coolant temperature signal  308 . It can be appreciated that the actual coolant temperature signal  308  can be, for example, a signal from a temperature-measuring device that measures actual coolant temperature (T CA ). A comparing module  312  generates a comparison signal  314  based on the actual coolant temperature signal  308  and the estimated coolant temperature signal  304 . The comparing module, for example, can determine a difference between the actual coolant temperature (T CA ) and the estimated coolant temperatures (T CE ). 
     A gain adjustment module  316  generates a gain adjustment signal  306  based on a gain control signal  318  and the comparison signal  314 . It can be appreciated that the gain adjustment module  316  can also generate the gain adjustment signal  306  based on operating parameters  56  ( FIG. 1 ) and communication with the telematic module  58  ( FIG. 1 ). It can further be appreciated that the gain adjustment signal can be based on specific vehicle model information. The metal and coolant temperature detection module can adjust a gain based on the gain adjustment signal  306 . The estimated metal temperature signal  302  and the estimated coolant temperature signal  304  can be adjusted based on the gain to increase accuracy of the estimations. 
     The control system  54  can distribute coolant to the plurality of engine locations based on the estimated metal temperature signal  302  and the estimated coolant temperature signal  304 . The plurality of engine locations can include, for example, the engine block, the cylinder head, the valvebridge, the cylinder liner, the engine exit coolant and portions thereof. Other engine locations can include locations that are specific to the vehicle model. 
     Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims.