Noise-adaptive extremum-seeking controller

1. A method for performing extremum-seeking control of a plant, the method comprising:

determining a plurality of values of a correlation coefficient that relates a control input provided as an input to the plant to a performance variable that characterizes a performance of the plant in response to the control input, the performance variable comprising a noise-free portion and an amount of noise;

determining an adjusted correlation coefficient by scaling a first value of the correlation coefficient selected from the plurality of values relative to a second value of the correlation coefficient selected from the plurality of values, the adjusted correlation coefficient relating the noise-free portion of the performance variable to the control input; and

operating equipment of the plant by using the adjusted correlation coefficient to modulate the control input provided as an input to the equipment of the plant;

wherein:

the amount of noise in the performance variable causes the first value of the correlation coefficient to underrepresent a true correlation between the performance variable and the control input; and

the adjusted correlation coefficient reduces an impact of the amount of noise in the performance variable and more accurately represents the true correlation relative to the first value of the correlation coefficient.

2. The method of claim 1 , wherein the first value of the correlation coefficient is determined based on a covariance of the control input and the performance variable, a variance of the control input, and a variance of the performance variable.

3. The method of claim 1 , wherein the second value of the correlation coefficient is determined based on a first filtered value of a plurality of estimated values of the correlation coefficient and a forgetting factor.

4. The method of claim 3 , further comprising calculating the forgetting factor based on a dominant time constant of the plant.

5. The method of claim 1 , further comprising scaling the adjusted correlation coefficient to dampen a convergence rate of the control input toward an optimum value as the correlation coefficient approaches zero.

6. The method of claim 1 , wherein using the adjusted correlation coefficient to modulate the control input comprises determining a new value of the control input based on a previous value of the control input, the adjusted correlation coefficient, and a controller gain value.

7. The method of claim 1 , further comprising selecting an extremum of the plurality of values of the correlation coefficient as the second value of the correlation coefficient.

8. The method of claim 1 , further comprising adjusting the second value of the correlation coefficient by causing the second value of the correlation coefficient to decay toward zero over time.

9. The method of claim 1 , wherein the correlation coefficient comprises at least one of a gradient of the performance variable with respect to the control input or a normalized indication of the gradient.

10. An extremum-seeking controller comprising a processing circuit configured to:

determine a plurality of values of a gradient that relates a control input provided as an input to a plant to a performance variable that characterizes a performance of the plant in response to the control input, the performance variable comprising a noise-free portion and an amount of noise;

determine an adjusted gradient by scaling a first value of the gradient selected from the plurality of values relative to a second value of the gradient selected from the plurality of values, the adjusted gradient relating the noise-free portion of the performance variable to the control input;

scale the adjusted gradient to dampen a convergence rate of the control input toward an optimum value as the gradient approaches zero; and

operate equipment of the plant by using the adjusted gradient to modulate the control input provided as an input to the equipment of the plant.

11. The extremum-seeking controller of claim 10 , wherein the processing circuit is configured to determine the first value of the gradient based on a covariance of the control input and the performance variable, a variable of the control input, and a variance of the performance variable.

12. The extremum-seeking controller of claim 10 , wherein the second value of the gradient is determined based on a first filtered value of the plurality of values of the gradient and a forgetting factor.

13. The extremum-seeking controller of claim 12 , wherein the processing circuit is further configured to calculate the forgetting factor based on a dominant time constant of the plant.

14. The extremum-seeking controller of claim 10 , wherein the processing circuit is further configured to adjust the second value of the gradient by causing the second value of the gradient to decay toward zero over time.

15. The extremum-seeking controller of claim 10 , wherein the processing circuit is configured to select an extremum of the plurality of values of the gradient as the second value of the gradient.

16. A controller comprising a processing circuit configured to:

determine a plurality of values of a correlation coefficient that relates a control input provided as an input to a plant to a performance variable that characterizes a performance of the plant in response to the control input, the performance variable comprising a noise-free portion and an amount of noise;

determine an adjusted correlation coefficient by scaling a first value of the correlation coefficient selected from the plurality of values relative to a second value of the correlation coefficient selected from the plurality of values, the adjusted correlation coefficient relating the noise-free portion of the performance variable to the control input, wherein the first value of the correlation coefficient is a maximum value of the plurality of values of the correlation coefficient that decays over time; and

operate equipment of the plant by using the adjusted correlation coefficient to modulate the control input provided as an input to the equipment of the plant.

17. The controller of claim 16 , wherein the plurality of values of the correlation coefficient are filtered values of the correlation coefficient.