Extremum-seeking control system with constraint handling

1. An extremum-seeking control system comprising:

a plant operable to affect a variable state or condition of a building;

an extremum-seeking controller configured to:

provide a control input to the plant and receive a performance variable as a first feedback from the plant, wherein the plant uses the control input to affect the performance variable and the performance variable represents a resource consumption of the plant;

receive a measurement of the variable state or condition as a second feedback from the plant;

calculate a performance penalty by applying a penalty function to the measurement, wherein the penalty function is configured such that:

if the measurement is greater than a setpoint or deadzone, the performance penalty increases as the measurement moves away from the setpoint or deadzone; and

if the measurement is less than the setpoint or deadzone, the performance penalty increases as the measurement moves away from the setpoint or deadzone;

modify the performance variable with the performance penalty to generate a modified cost function;

estimate a gradient of the modified cost function with respect to the control input; and

drive the gradient of the modified cost function toward zero by modulating the control input.

2. The extremum-seeking control system of claim 1 , wherein the penalty function increases monotonically based on an amount by which the measurement deviates from the deadzone.

3. The extremum-seeking control system of claim 2 , wherein modulating the control input comprises applying a dither signal to the control input; and

wherein the extremum-seeking controller is further configured to automatically define a range of the deadzone to contain variations in the measurement caused by the dither signal.

4. The extremum-seeking control system of claim 1 , wherein the penalty function is based on a deadzone function, the deadzone function:

having a zero value when the measurement is between a minimum value of the measurement and a maximum value of the measurement;

decreasing linearly when the measurement is below the minimum value; and

increasing linearly when the measurement is above the maximum value.

5. The extremum-seeking control system of claim 4 , wherein the extremum-seeking controller is configured to calculate the performance penalty by:

calculating a value of the deadzone function based on the measurement to generate a deadzone value; and

calculating a square or absolute value of the deadzone value.

6. The extremum-seeking control system of claim 5 , wherein the extremum-seeking controller is further configured to calculate the performance penalty by multiplying the square or absolute value of the deadzone value by a scaling parameter.

7. The extremum-seeking control system of claim 1 , wherein the extremum-seeking controller is configured to modify the performance variable with the performance penalty to generate the modified cost function by multiplying the performance variable by a sum of one and the performance penalty.

8. The extremum-seeking control system of claim 1 , wherein the extremum-seeking controller is configured to augment the control input with a dither signal.

9. A method comprising:

operating a plant to affect a variable state or condition of a building;

providing a control input to the plant and receiving a performance variable as a first feedback from the plant, wherein the plant uses the control input to affect the performance variable and the performance variable represents a resource consumption of the plant;

receiving a measurement of the variable state or condition as a second feedback from the plant;

calculating a performance penalty by applying a penalty function to the measurement, wherein the penalty function is configured such that:

if the measurement is greater than a setpoint or deadzone, the performance penalty increases as the measurement moves away from the setpoint or deadzone; and

if the measurement is less than the setpoint or deadzone, the performance penalty increases as the measurement moves away from the setpoint or deadzone;

modifying the performance variable with the performance penalty to generate a modified cost function;

estimating a gradient of the modified cost function with respect to the control input; and

driving the gradient of the modified cost function toward zero by modulating the control input.

10. The method of claim 9 , wherein the penalty function increases monotonically based on the amount by which the measurement deviates from the deadzone.

11. The method of claim 10 , further comprising automatically determining a range of the deadzone by applying a dither signal to the control input and defining the deadzone to contain oscillations in the measurement brought about by action of the dither signal.

12. The method of claim 9 , wherein the penalty function is based on a deadzone function, the deadzone function:

having a zero value between when the measurement is between a minimum value and a maximum value;

decreasing linearly when the measurement is below the minimum value; and

increasing linearly when the measurement is above the maximum value.

13. The method of claim 12 , wherein calculating the performance penalty comprises:

calculating a value of the deadzone function based on the measurement to generate a deadzone value; and

calculating a square or absolute value of the deadzone value.

14. The method of claim 13 , wherein calculating the performance penalty further comprises multiplying the square or absolute value of the deadzone by a scaling parameter.

15. The method of claim 9 , wherein modifying the performance variable with the performance penalty to generate the modified cost function comprises multiplying the performance variable by a sum of one and the performance penalty.

16. The method of claim 9 , further comprising augmenting the control input with a dither signal.

17. An extremum-seeking controller, comprising:

a constraint handler communicably coupled to a plant to receive a performance variable and a measurement of a variable state or condition of a building, the plant operable to affect the performance variable and the measurement in response to a control input from the extremum-seeking controller, and the constraint handler configured to:

calculate a performance penalty by applying a penalty function to the measurement, wherein the penalty function is configured such that:

if the measurement is greater than a setpoint or deadzone, the performance penalty increases as the measurement moves away from the setpoint or deadzone; and

if the measurement is less than the setpoint or deadzone, the performance penalty increases as the measurement moves away from the setpoint or deadzone;

modify the performance variable with the performance penalty to generate a modified cost function; and

provide the modified cost function to a performance gradient probe, the performance gradient probe configured to estimate a gradient of the modified cost function with respect to the control input and provide the gradient to a manipulated variable updater;

wherein the manipulated variable updater is configured to generate an updated control signal for the plant to drive the gradient towards zero.

18. The extremum-seeking controller of claim 17 , wherein the penalty function increases monotonically based on the amount by which the measurement deviates from the deadzone.

19. The extremum-seeking controller of claim 17 , wherein the manipulated variable updater is configured to augment the updated control signal with a dither signal.

20. The extremum-seeking controller of claim 17 , wherein the constraint handler is configured to modify the performance variable with the penalty function to generate the modified cost function by multiplying the performance variable by a sum of one and the performance penalty.