Partial derivative based feedback controls for pid

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 configured to increase or decrease a fluid temperature of the fluid;
• a radiator configured to receive the fluid and remove heat from the fluid;
• and
• an electronic control unit (ECU) coupled to the actuator and configured to:
• estimate an estimated parameter that affects an amount of the heat removed from the fluid by the radiator,
• determine an actuator control signal corresponding to control of the actuator to increase or decrease the fluid temperature towards a desired temperature of the fluid based on the estimated parameter,
• determine a temperature difference between the fluid temperature of the fluid and an estimated temperature of the fluid,
• adjust the estimated parameter based on the temperature difference in order to decrease the temperature difference,
• determine an updated actuator control signal based on the adjusted estimated parameter, and
• control the actuator based on the updated actuator control signal.

A method for heating or cooling a fuel cell circuit of a vehicle comprising:

• determining, by an electronic control unit (ECU), a temperature control signal corresponding to a desired temperature of a fluid of the fuel cell circuit;
• performing, by the ECU, a feedforward control of an actuator of the fuel cell circuit to cause the actuator to increase or decrease a fluid temperature of the fluid towards the desired temperature of the fluid;
• determining, by the ECU, a temperature difference between the fluid temperature of the fluid and the desired temperature of the fluid;
• determining, by the ECU, a sensitivity that corresponds a change in a parameter value or an actuator position of the actuator to a change in the fluid temperature;
• applying, by the ECU, 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;
• and
• controlling, by the ECU, the actuator based on the error signal.