Control system with combined extremum-seeking control and feedforward control

1. A control system configured to operate a plant to achieve an optimal value for a performance variable of the plant, the control system comprising:

a feedforward controller configured to receive a measurable disturbance to the plant and generate a feedforward contribution to a control input to the plant using the measurable disturbance;

an extremum-seeking controller configured to receive the performance variable from the plant and generate an extremum-seeking contribution to the control input to drive the performance variable to the optimal value; and

a control input element configured to generate the control input by combining the extremum-seeking contribution and the feedforward contribution and provide the control input to the plant, wherein the plant uses the control input to operate equipment of the plant, thereby driving the performance value to the optimal value,

wherein the feedforward controller generates the feedforward contribution without requiring knowledge of the extremum-seeking contribution.

2. The control system of claim 1 , wherein the feedforward controller is configured to generate the feedforward contribution based on a lookup table that maps the measurable disturbance to the control input.

3. The control system of claim 1 , wherein the feedforward controller is configured to generate the feedforward contribution based on a feedforward model that maps the measurable disturbance to the control input.

4. The control system of claim 3 , wherein the feedforward model is established based on data collected during tests and/or actual applications.

5. The control system of claim 1 , wherein the feedforward controller is further configured to:

receive a previous optimal control input that corresponds to a previous optimal value for the performance variable under a previous measurable disturbance; and

correct the feedforward contribution using the previous optimal control input.

6. The control system of claim 1 , wherein the extremum-seeking controller is further configured to:

perturb the control input with a periodic signal;

monitor the performance variable from the perturbed control input;

estimate a gradient of the performance variable with respect to the control input; and

modulate the extremum-seeking contribution to drive the estimated gradient to zero.

7. The control system of claim 1 , wherein the extremum-seeking controller is further configured to:

perturb the control input with a stochastic excitation signal;

monitor the performance variable from the perturbed control input;

estimate a gradient of the performance variable with respect to the control input; and

modulate the extremum-seeking contribution to drive the estimated gradient to zero.

8. The control system of claim 7 , wherein the stochastic excitation signal is a non-periodic signal comprising at least one of a random walk signal, a non-deterministic signal, and a non-repeating signal.

9. A control system configured to operate equipment of a chilled water plant to achieve an optimal value for a total power consumption of the chilled water plant, the equipment comprising at least one of a chiller compressor, a condenser water pump, and a cooling tower fan; the control system comprising:

a feedforward controller configured to receive an ambient temperature and generate a feedforward contribution to a temperature setpoint for condenser water temperature in the chilled water plant using the ambient temperature;

an extremum-seeking controller configured to receive the total power consumption from the plant and generate an extremum-seeking contribution to the temperature setpoint to drive the total power consumption to the optimal value; and

a control input element configured to generate the temperature setpoint by combining the extremum-seeking contribution and the feedforward contribution and provide the temperature setpoint to the chilled water plant, wherein the chilled water plant uses the temperature setpoint to operate the equipment of the chilled water plant, thereby driving the total power consumption to the optimal value,

wherein the feedforward controller generates the feedforward contribution without requiring knowledge of the extremum-seeking contribution.

10. The control system of claim 9 , wherein the feedforward controller is configured to generate the feedforward contribution based on a lookup table that maps the ambient temperature to the temperature setpoint.

11. The control system of claim 9 , wherein the feedforward controller is configured to generate the feedforward contribution based on a feedforward model that maps the ambient temperature to the temperature setpoint.

12. The control system of claim 11 , wherein the feedforward model is established based on data collected during tests and/or actual applications.

13. The control system of claim 9 , wherein the feedforward controller is further configured to:

receive a previous optimal temperature setpoint that corresponds to a previous optimal value for the total power consumption under a previous ambient temperature; and

correct the feedforward contribution using the previous optimal temperature setpoint.

14. The control system of claim 9 , wherein the extremum-seeking controller is further configured to:

perturb the temperature setpoint with a stochastic signal;

monitor the total power consumption from the perturbed temperature setpoint;

estimate a gradient of the total power consumption with respect to the temperature setpoint; and

modulate the extremum-seeking contribution to drive the estimated gradient to zero.

15. A control system configured to operate equipment of a chilled water plant to achieve an optimal value for a total power consumption of the chilled water plant, the equipment comprising at least one of a chiller compressor, a condenser water pump, and a cooling tower fan; the control system comprising:

a feedforward controller configured to receive a load on the chilled water plant and generate a feedforward contribution to a fan speed for the cooling tower fan using the load;

an extremum-seeking controller configured to receive the total power consumption from the plant and generate an extremum-seeking contribution to the fan speed to drive the total power consumption to the optimal value; and

a control input element configured to generate the fan speed by combining the extremum-seeking contribution and the feedforward contribution and provide the fan speed to the chilled water plant, wherein the chilled water plant uses the fan speed to operate the cooling tower fan, thereby driving the total power consumption to the optimal value,

wherein the feedforward controller generates the feedforward contribution without requiring knowledge of the extremum-seeking contribution.

16. The control system of claim 15 , wherein the feedforward controller is configured to generate the feedforward contribution based on a lookup table that maps the load to the fan speed.

17. The control system of claim 15 , wherein the feedforward controller is configured to generate the feedforward contribution based on a feedforward model that maps the load to the fan speed.

18. The control system of claim 17 , wherein the feedforward model is established based on data collected during tests and/or actual applications.

19. The control system of claim 15 , wherein the feedforward controller is further configured to:

receive a previous optimal fan speed that corresponds to a previous optimal value for the total power consumption under a previous load; and

correct the feedforward contribution using the previous optimal fan speed.

20. The control system of claim 15 , wherein the extremum-seeking controller is further configured to:

perturb the fan speed with a stochastic signal;

monitor the total power consumption from the perturbed fan speed;

estimate a gradient of the total power consumption with respect to the fan speed; and

modulate the extremum-seeking contribution to drive the estimated gradient to zero.