Optimal temperature tracking for necessary and accurate thermal control of a fuel cell system
A temperature control scheme for a fuel cell stack thermal sub-system in a fuel cell system. The thermal sub-system includes a coolant loop directing the cooling fluid through the stack, a pump for pumping the cooling fluid through the coolant loop, a radiator for cooling the cooling fluid outside of the fuel cell stack and a bypass valve for selectively directing the cooling fluid in the coolant loop through the radiator or around the radiator. The control scheme generates an optimal model of the thermal sub-system using non-linear equations, and controls the speed of the pump and a position of the bypass valve in combination.
1 . A method for controlling the temperature of a fuel cell stack in a fuel cell system, said fuel cell system including a coolant loop directing a cooling fluid through the stack, a pump for pumping the cooling fluid through the coolant loop, a radiator for cooling the cooling fluid outside of the stack and a bypass valve for selectively directing the cooling fluid in the coolant loop through the radiator or around the radiator, said method comprising:
determining a first matrix that is representative of the temperature of the cooling fluid coming out of the stack and the temperature of the cooling fluid coming out of the radiator;
determining a second matrix based on a desired temperature set-point of the fuel cell stack;
determining a third matrix based on the output power of the fuel cell stack; and
generating a control matrix for controlling the speed of the pump and the position of the bypass valve by combining the first, second and third matrices.
2 . The method according to claim 1 wherein determining the first matrix includes calculating the first matrix based on a state matrix that defines the physical properties of the fuel cell system, an input matrix that defines input effects on the fuel cell system, an output matrix that defines variables being measured, a matrix tuned to a desired response and an R matrix.
3 . The method according to claim 2 wherein determining the first matrix includes calculating the first matrix as:
0 =−KA−A T K+KBR −1 B T K−C T QC,
where K is the first matrix, A is the state matrix that defines the physical properties of the fuel cell system, B is the input matrix that defines input effects on the fuel cell system, C is the output matrix that defines variables being measured and Q is the matrix tuned to a desired response.
4 . The method according to claim 1 wherein determining a second matrix includes calculating the second matrix based on a state matrix that defines physical properties of the fuel cell system, an input matrix that defines input effects on the fuel cell system, an output matrix that defines variables being measured and a matrix tuned to a desired response.
5 . The method according to claim 4 wherein determining a second matrix includes calculating the second matrix as:
h =( BR −1 B T −A T ) −1 C T QZ,
where h is the second matrix, A is the state matrix that defines physical properties of the fuel cell system, B is the input matrix that defines input effects on the fuel cell system, C is the output matrix that defines variables being measured, Q is the matrix tuned to a desired response, and z is the desired temperature set-point of the fuel cell stack.
6 . The method according to claim 1 wherein determining a third matrix includes calculating the third matrix using the first matrix, a state matrix that defines physical properties of the fuel cell system, an input matrix that defines input effects on the fuel cell system, an input matrix that defines the effect of stack power and an R matrix.
7 . The method according to claim 6 wherein determining a third matrix includes calculating the third matrix as:
f =−( BR −1 B T −A T ) −1 KEd,
where f is the third matrix, K is the first matrix, A is the state matrix that defines physical properties of the fuel cell system, B is the input matrix that defines input effects on the fuel cell system, E is the input matrix that defines the effect of stack power and d is the output power of the fuel cell stack.
8 . The method according to claim 1 wherein generating a control matrix includes adding the first, second and third matrices and multiplying by the inverse of an R matrix and the transpose of an input matrix that defines input effects on the system as:
u=−R −1 B T ( Kx ( t )+ f ( t )+ h ( t )),
where u is the control matrix, K is the first matrix, h is the second matrix, f is the third matrix and B is the input matrix that defines input effects on the system.
9 . The method according to claim 1 wherein the pump and the bypass valve are positioned downstream from an output of the radiator in the coolant loop.
10 . The method according to claim 9 wherein the bypass valve is positioned farther downstream than the pump.
11 . The method according to claim 1 wherein the fuel cell system is on a vehicle.
12 . A method for controlling the temperature of a fuel cell stack in a fuel cell system, said method comprising:
developing a model of the fuel cell system that employs non-linear equations; and
controlling the speed of a pump for pumping a cooling fluid through a coolant loop in the fuel cell system and a position of a bypass valve that selectively directs the cooling fluid in the cooling loop through the radiator or around the radiator, wherein controlling the speed of the pump and the position of the bypass valve includes combining the control of the speed of the pump and the position of the bypass valve.
13 . The method according to claim 12 wherein controlling the speed of the pump and the position of the bypass valve includes determining a first matrix that is representative of the temperature of the cooling fluid coming out of the stack and the temperature of the cooling fluid coming out of the radiator, determining a second matrix based on a desired temperature set-point of the fuel cell stack, determining a third matrix based on the output power of the fuel cell stack and generating a control matrix for controlling the speed of the pump and the position of the bypass valve by combining the first, second and third matrices.
14 . A fuel cell system comprising:
a fuel cell stack;
a radiator;
a coolant loop directing a cooling fluid through the fuel cell stack and the radiator and receiving the cooling fluid from the fuel cell stack and the radiator, said coolant loop including a bypass portion;
a pump for pumping the cooling fluid through the coolant loop, the fuel cell stack and the radiator;
a bypass valve for selectively directing the cooling fluid through the radiator and the bypass portion around the radiator;
an input temperature sensor for measuring the temperature of the cooling fluid entering the fuel cell stack;
an output temperature sensor for measuring the temperature of the cooling fluid exiting the fuel cell stack; and
a controller for controlling the bypass valve and the pump based on the temperature of the cooling fluid, said controller controlling the bypass valve and the pump in combination.
15 . The system according to claim 14 wherein the controller determines a first matrix that is representative of the temperature of the cooling fluid coming out of the stack and the temperature of the cooling fluid coming out of the radiator, determines a second matrix based on a desired temperature set-point of the fuel cell stack, determines a third matrix based on the output power of the fuel cell stack, and generates a control matrix for controlling the speed of the pump and the position of the bypass valve by combining the first, second and third matrices.
16 . The system according to claim 15 wherein the controller determines the first matrix based on a state matrix that defines the physical properties of the fuel cell system, an input matrix that defines input effects on the fuel cell system, an output matrix that defines variables being measured, a matrix tuned to a desired response and an R matrix.
17 . The system according to claim 16 wherein the controller determines the first matrix as:
0 =−KA−A T K+KBR −1 B T K−C T QC,
where K is the first matrix, A is the state matrix that defines the physical properties of the fuel cell system, B is the input matrix that defines input effects on the fuel cell system, C is the output matrix that defines variables being measured and Q is the matrix tuned to a desired response.
18 . The system according to claim 15 wherein the controller determines the second matrix based on a state matrix that defines physical properties of the fuel cell system, an input matrix that defines input effects on the fuel cell system, an output matrix that defines variables being measured and a matrix tuned to a desired response.
19 . The system according to claim 18 wherein the controller determines the second matrix as:
h =( BR −1 B T −A T ) −1 C T QZ,
where h is the second matrix, A is the state matrix that defines physical properties of the fuel cell system, B is the input matrix that defines input effects on the fuel cell system, C is the output matrix that defines variables being measured, Q is the matrix tuned to a desired response, and z is the desired temperature set-point of the fuel cell stack.
20 . The system according to claim 15 wherein the controller determines the third matrix using the first matrix, a state matrix that defines physical properties of the fuel cell system, an input matrix that defines input effects on the fuel cell system, an input matrix that defines the effect of stack power and an R matrix.
21 . The system according to claim 20 wherein the controller determines the third matrix as:
f =−( BR −1 B T −A T ) −1 KEd,
where f is the third matrix, K is the first matrix, A is the state matrix that defines physical properties of the fuel cell system, B is the input matrix that defines input effects on the fuel cell system, E is the input matrix that defines the effect of stack power and d is the output power of the fuel cell stack.
22 . The system according to claim 15 wherein the controller generates the control matrix by adding the first, second and third matrices and multiplying by the inverse of an R matrix and the transpose of an input matrix that defines input effects on the system as:
u=−R −1 B T ( Kx ( t )+ f ( t )+ h ( t )),
where u is the control matrix, K is the first matrix, h is the second matrix, f is the third matrix and B is the input matrix that defines input effects on the system.
23 . The system according to claim 14 wherein the pump and the bypass valve are positioned downstream from an output of the radiator in the coolant loop.
24 . The system according to claim 23 wherein the bypass valve is positioned farther downstream than the pump.
25 . The system according to claim 14 wherein the fuel cell system is on a vehicle.