PI control partial derivative based I-term for wind-up prevention

1. A system for heating or cooling a fuel cell stack of a vehicle, comprising:

a fuel cell stack having a plurality of fuel cells;

an actuator having an actuator position and configured to control fluid flow 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 feedforward control of the actuator with a feedforward control signal, the feedforward control signal configured to cause the actuator to control the fluid flow to increase or decrease the fluid temperature of the fluid 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 control the fluid flow to cause the fluid temperature of the fluid to increase or decrease to reduce a temperature difference, wherein the feedback control signal applies an I-term saturation limit calculated using a partial derivative term; and

control the actuator based on a combination of the feedforward control signal and the feedback control signal.

2. The system of claim 1 , wherein 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.

3. The system of claim 1 , wherein the actuator is a three-way valve.

4. The system of claim 1 , wherein the target temperature of the fluid and the fluid temperature of the fluid correspond to the fluid at an inlet of the fuel cell stack.

5. A method for heating or cooling a fuel cell stack of a vehicle, comprising:

providing a fuel cell stack having a plurality of fuel cells;

providing an actuator having an actuator position and configured to control fluid flow 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 feedforward control of the actuator with a feedforward control signal, the feedforward control signal configured to cause the actuator to control the fluid flow to increase or decrease the fluid temperature of the fluid 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 control the fluid flow to cause the fluid temperature of the fluid to increase or decrease to reduce a temperature difference, wherein the feedback control signal applies an I-term saturation limit calculated using a partial derivative term; and

controlling the actuator based on a combination of the feedforward control signal and the feedback control signal.

6. The method of claim 5 , further comprising 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.

7. The method of claim 5 , wherein the actuator is a three-way valve.

8. The method of claim 5 , wherein the target temperature of the fluid and the fluid temperature of the fluid correspond to the fluid at an inlet of the fuel cell stack.

9. A system for heating or cooling a fuel cell circuit of a vehicle comprising:

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 control fluid flow 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 feedforward control of the actuator with a feedforward control signal, the feedforward control signal configured to cause the actuator to control the fluid flow to increase or decrease the fluid temperature of the fluid 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 of the fluid;

apply the sensitivity to the temperature difference to determine an error signal that corresponds to an additional change in the actuator position to control the fluid flow to cause the fluid temperature of the fluid to increase or decrease to reduce the temperature difference;

receive a feedback control signal from a proportional-integral-derivative (PID) controller, the feedback control signal based on the error signal, wherein the feedback control signal applies an I-term saturation limit calculated using a partial derivative term; and

control the actuator based on the error signal.

10. The system of claim 9 , wherein the PID controller is part of the ECU.

11. The system of claim 9 , wherein 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.

12. The system of claim 9 , wherein the actuator is a three-way valve.

13. The system of claim 9 , wherein the target temperature of the fluid and the fluid temperature of the fluid correspond to the fluid at an inlet of the fuel cell stack.

14. The system of claim 9 , wherein the ECU is further configured to control the actuator based on a combination of the feedforward control signal and the feedback control signal.