Nonlinear thermal control of a PEM fuel cell stack
View Patent ↗A temperature control scheme for a fuel cell stack thermal sub-system in a fuel cell system that uses a non-linear thermal model and disturbance rejection to provide an optimum stack temperature. The thermal sub-system includes a coolant loop directing a cooling fluid through the stack, a pump for pumping the cooling fluid through the coolant loop, and a radiator for cooling the cooling fluid outside of the fuel cell stack. The system includes a controller for controlling the speed of the pump so as to maintain the temperature of the stack at a desired temperature. The controller uses the thermal model to anticipate a temperature of the cooling fluid out of the fuel cell stack to control the speed of the pump.
1. A method for controlling the temperature of a fuel cell stack in a fuel cell system, said method comprising:
developing a thermal model of the fuel cell stack that employs non-linear equations;
generating an error signal that is the difference between a desired stack temperature and a temperature of a cooling fluid out of the fuel cell stack;
applying feedback control to the error signal to generate a control signal;
modifying a disturbance signal to generate a modified disturbance signal;
adding the control signal to the modified disturbance signal to generate a linearization variable;
generating a mass flow rate signal using the linearization variable; and
linearizing the thermal model using the mass flow rate signal to reject the disturbance in the modified disturbance signal, wherein linearizing the thermal model includes using the mass flow rate signal, the disturbance and a temperature of the cooling fluid into the stack; said fuel cell system including a controller that controls the temperature of the fuel cell stack using the linear thermal model.
2. The method according to claim 1 wherein the disturbance is a measured stack power and wherein modifying a disturbance signal to generate a modified disturbance signal includes multiplying the stack power by
-
1
ρ
VolC
p
.
3. The method according to claim 1 wherein applying feedback control to the error signal includes using a proportional-integral-derivative controller.
4. The method according to claim 1 wherein generating a mass flow rate signal using the linearization variable includes generating a mass flow rate signal using the linearization variable, a temperature of the cooling fluid into the stack and the temperature of the cooling fluid out of the stack.
5. The method according to claim 4 wherein generating a mass flow rate signal includes determining the mass flow rate signal by the equation:
m
.
=
ρ
Volv
(
T
stk
,
in
-
T
stk
,
out
)
where {dot over (m)} is the mass flow rate signal, v is the linearization variable, T stk,in is the temperature of the cooling fluid into the stack, T stk,out is the temperature of the cooling fluid out of the stack and C p is the specific heat of the stack.
6. The method according to claim 1 wherein developing a thermal model of the fuel cell stack that employs non-linear equations includes developing a lumped parameter non-linear model.
7. The method according to claim 1 wherein linearizing the thermal model includes using the equation:
T
stk
,
out
=
m
.
ρ
Vol
(
T
stk
,
in
-
T
stk
,
out
)
+
E
.
gen
ρ
VolC
ρ
where {dot over (m)} is the mass flow, Vol is an effective volume of the stack, ρ is the stack pressure, T stk,in is the temperature of the cooling fluid into the stack, T stk,out is the temperature of the cooling fluid out of the stack, C p is the specific heat of the stack and Ė gen is the stack power.
8. The method according to claim 1 further comprising using the mass flow rate signal to control the speed of a pump that pumps the cooling fluid through the fuel cell stack.
9. The method according to claim 1 wherein the fuel cell system is part of a fuel cell engine on a vehicle.
10. A fuel cell system comprising:
a fuel cell stack;
a pump for pumping a cooling fluid through the stack; and
a controller for controlling the speed of the pump so as to maintain the temperature of the stack at a desired temperature, said controller generating an error signal that is the difference between a desired stack temperature and a temperature of the cooling fluid out of the fuel cell stack, applying feedback control to the error signal to generate a control signal, modifying a disturbance signal to generate a modified disturbance signal, adding the control signal to the modified disturbance signal to generate a linearization variable, generating a mass flow rate signal using the linearization variable, and linearizing a thermal model using the mass flow rate signal to reject the disturbance in the modified disturbance signal, wherein the controller uses the mass flow rate signal to control the speed of the pump, wherein the controller linearizes the thermal model using the mass flow rate signal, the disturbance and a temperature of the cooling fluid into the stack.
11. The system according to claim 10 wherein the disturbance is a measured stack power and wherein the controller modifies the disturbance signal to generate the modified disturbance signal by multiplying the stack power by
-
1
ρ
VolC
p
.
12. The system according to claim 10 wherein the controller includes a proportional-integral-derivative controller to generate the control signal.
13. The system according to claim 10 wherein the controller generates the mass flow rate signal using the linearization variable, the temperature of the cooling fluid into the stack and the temperature of the cooling fluid out of the stack.
14. The system according to claim 13 wherein the controller generates the mass flow rate signal by the equation:
m
.
=
ρ
Volv
(
T
stk
,
in
-
T
stk
,
out
)
where {dot over (m)} is the mass flow rate signal, v is the linearization variable, T stk,in is the temperature of the cooling fluid into the stack, T stk,out is the temperature of the cooling fluid out of the stack and C p is the specific heat of the stack.
15. The system according to claim 10 wherein the controller linearizes the thermal model using the equation:
T
stk
,
out
=
m
.
ρ
Vol
(
T
stk
,
in
-
T
stk
,
out
)
+
E
.
gen
ρ
VolC
ρ
where {dot over (m)} is the mass flow, Vol is an effective volume of the stack, ρ is the stack pressure, T stk,in is the temperature of the cooling fluid into the stack, T stk,out is the temperature of the cooling fluid out of the stack, C p is the specific heat of the stack and Ė gen is the stack power.
16. The system according to claim 10 wherein the fuel cell system is pad of a fuel cell engine on a vehicle.
17. A method for controlling the temperature of a fuel cell stack in a fuel cell system, said method comprising:
developing a thermal model of the fuel cell stack that employs non-linear equations;
generating an error signal that is the difference between a desired stack temperature and a temperature of a cooling fluid out of the fuel cell stack;
applying feedback control to the error signal to generate a control signal;
-
1
ρ
VolC
p
ing a disturbance signal to generate a modified disturbance signal, wherein the disturbance is a measured stack power and wherein modifying a disturbance signal to generate a modified disturbance signal includes multiplying the stack power by;
adding the control signal to the modified disturbance signal to generate a linearization variable;
generating a mass flow rate signal using the linearization variable; and
linearizing the thermal model using the mass flow rate signal to reject the disturbance in the modified disturbance signal; said fuel cell system including a controller that controls the temperature of the fuel cell stack using the linear thermal model.
18. A method for controlling the temperature of a fuel cell stack in a fuel cell system, said method comprising:
developing a thermal model of the fuel cell stack that employs non-linear equations;
generating an error signal that is the difference between a desired stack temperature and a temperature of a cooling fluid out of the fuel cell stack;
applying feedback control to the error signal to generate a control signal;
modifying a disturbance signal to generate a modified disturbance signal;
adding the control signal to the modified disturbance signal to generate a linearization variable;
generating a mass flow rate signal using the linearization variable, wherein generating a mass flow rate signal using the linearization variable includes generating a mass flow rate signal using the linearization variable, a temperature of the cooling fluid into the stack and the temperature of the cooling fluid out of the stack; and
linearizing the thermal model using the mass flow rate signal to reject the disturbance in the modified disturbance signal; said fuel cell system including a controller that controls the temperature of the fuel cell stack using the linear thermal model.
19. A fuel cell system comprising:
a fuel cell stack;
a pump for pumping a cooling fluid through the stack; and
a controller for controlling the speed of the pump so as to maintain the temperature of the stack at a desired temperature, said controller generating an error signal that is the difference between a desired stack temperature and a temperature of the cooling fluid out of the fuel cell stack, applying feedback control to the error signal to generate a control signal, modifying a disturbance signal to generate a modified disturbance signal, adding the control signal to the modified disturbance signal to generate a linearization variable, generating a mass flow rate signal using the linearization variable, and linearizing a thermal model using the mass flow rate signal to reject the disturbance in the modified disturbance signal, wherein the disturbance is a measured stack power and wherein the controller modifies the disturbance signal to generate the modified disturbance signal by multiplying the stack power by
-
1
ρ
VolC
p
,
wherein the controller uses the mass flow rate signal to control the speed of the pump.
20. A fuel cell system comprising:
a fuel cell stack;
a pump for pumping a cooling fluid through the stack; and
a controller for controlling the speed of the pump so as to maintain the temperature of the stack at a desired temperature, said controller generating an error signal that is the difference between a desired stack temperature and a temperature of the cooling fluid out of the fuel cell stack, applying feedback control to the error signal to generate a control signal, modifying a disturbance signal to generate a modified disturbance signal, adding the control signal to the modified disturbance signal to generate a linearization variable, generating a mass flow rate signal using the linearization variable, and linearizing a thermal model using the mass flow rate signal to reject the disturbance in the modified disturbance signal, wherein the controller generates the mass flow rate signal using the linearization variable, the temperature of the cooling fluid into the stack and the temperature of the cooling fluid out of the stack, and wherein the controller uses the mass flow rate signal to control the speed of the pump.