Extremum-seeking control for airside economizers

1. A method for controlling an economizer in a building HVAC system, the method comprising:

providing, by a processing circuit, a manipulated variable as an input to a control process;

holding, by the processing circuit, the manipulated variable at a first extremum during a first portion of an evaluation period;

applying, by the processing circuit, a dither signal to the manipulated variable during a second portion of the evaluation period, the dither signal causing the manipulated variable to deviate from the extremum;

monitoring, by the processing circuit, a variable of interest output by the control process during the first and second portions of the evaluation period;

switching, by the processing circuit, the manipulated variable to a second extremum opposite the first extremum in response to the variable of interest moving toward an optimal value during the second portion of the evaluation period;

calculating a first value for the variable of interest using one or more values of the variable of interest observed during the first portion of the evaluation period;

calculating a second value for the variable of interest using one or more values of the variable of interest observed during the second portion of the evaluation period; and

comparing the first and second calculated values to determine whether the variable of interest moves toward the optimal value;

removing the dither signal from the manipulated variable before an end of the second portion of the evaluation period in response to a determination that the variable of interest moves toward or away from the optimal value by an amount exceeding a threshold; and

applying the dither signal to the manipulated variable for an entire duration of the second portion of the evaluation period in response to a determination that the variable of interest does not move toward or away from the optimal value by the amount exceeding the threshold.

2. The method of claim 1 , wherein:

the first extremum is one of a maximum or a minimum of a range of values at which the manipulated variable can be provided to the control process; and

the second extremum is the other of the maximum or the minimum.

3. The method of claim 1 , further comprising:

returning the manipulated variable to the first extremum in response to the variable of interest moving away from the optimal value during the second portion of the evaluation period.

4. The method of claim 1 , wherein applying the dither signal to the manipulated variable comprises:

determining an amplitude of the dither signal; and

adjusting the manipulated variable toward the second extremum by an amount corresponding to the amplitude of the dither signal.

5. The method of claim 1 , wherein comparing the first and second calculated values comprises:

using the first calculated value for the variable of interest to compute at least one of an upper threshold and a lower threshold; and

determining that the variable of interest moves toward the optimal value in response to a determination that the second calculated value for the variable of interest is greater than the upper threshold or less than the lower threshold.

6. The method of claim 1 , wherein comparing the first and second calculated values comprises:

computing a difference between the first and second calculated values; and

determining that the variable of interest moves toward the optimal value in response to a determination that the difference between the first and second calculated values exceeds another threshold.

7. The method of claim 1 , wherein:

the first calculated value is an average of a plurality of observed values of the variable of interest observed during the first portion of the evaluation period; and

the second calculated value is an average of a plurality of observed values of the variable of interest observed during the second portion of the evaluation period.

8. The method of claim 1 , further comprising:

using the variable of interest to calculate a normalized value for the manipulated variable;

converting the normalized value for the manipulated variable into a control signal adapted for the control process; and

providing the control signal as an input to the control process.

9. A method for controlling an economizer in a building HVAC system, the method comprising:

providing, by a processing circuit, a manipulated variable as an input to a control process;

holding, by the processing circuit, the manipulated variable at an initial steady state value during a first portion of an evaluation period;

applying, by the processing circuit, a dither signal to the manipulated variable during a second portion of the evaluation period, the dither signal causing the manipulated variable to deviate in a first direction from the initial steady state value;

monitoring, by the processing circuit, a variable of interest output by the control process during the first and second portions of the evaluation period;

adjusting, by the processing circuit, the manipulated variable in the first direction to a new steady state value in response to the variable of interest moving toward an optimal value during the second portion of the evaluation period;

calculating a first value for the variable of interest using one or more values of the variable of interest observed during the first portion of the evaluation period;

calculating a second value for the variable of interest using one or more values of the variable of interest observed during the second portion of the evaluation period; and

comparing the first and second calculated values to determine whether the variable of interest moves toward the optimal value;

removing the dither signal from the manipulated variable before an end of the second portion of the evaluation period in response to a determination that the variable of interest moves toward or away from the optimal value by an amount exceeding a threshold; and

applying the dither signal to the manipulated variable for an entire duration of the second portion of the evaluation period in response to a determination that the variable of interest does not move toward or away from the optimal value by the amount exceeding the threshold.

10. The method of claim 9 , further comprising identifying a plurality of discrete values at which the manipulated variable can be provided to the control process;

wherein holding the manipulated variable at the initial steady state value comprises holding the manipulated variable at one of a plurality of identified discrete values.

11. The method of claim 9 , wherein the initial steady state value is a first extremum of the manipulated variable and the new steady state value is a second extremum of the manipulated variable, opposite the first extremum.

12. The method of claim 9 , wherein at least one of the initial steady state value and the new steady state value is an intermediate value between two extremums of the manipulated variable.

13. The method of claim 9 , further comprising:

returning the manipulated variable to the initial steady state value in response to the variable of interest not moving toward the optimal value during the second portion of the evaluation period.

14. The method of claim 9 , further comprising:

adjusting the manipulated variable in a second direction opposite the first direction in response to the variable of interest moving away from the optimal value during the second portion of the evaluation period.

15. An economizer controller in a building HVAC system, the controller comprising:

a communications interface configured to provide a manipulated variable as an input to a control process; and

a processing circuit comprising a processor and memory, wherein the processing circuit is configured to:

hold the manipulated variable at an initial steady state value during a first portion of an evaluation period;

apply a dither signal to the manipulated variable during a second portion of the evaluation period, the dither signal causing the manipulated variable to deviate in a first direction from the initial steady state value;

monitor a variable of interest output by the control process during the first and second portions of the evaluation period;

adjust the manipulated variable in the first direction to a new steady state value in response to the variable of interest moving toward an optimal value during the second portion of the evaluation period;

calculate a first value for the variable of interest using one or more values of the variable of interest observed during the first portion of the evaluation period;

calculate a second value for the variable of interest using one or more values of the variable of interest observed during the second portion of the evaluation period; and

compare the first and second calculated values to determine whether the variable of interest moves toward the optimal value;

remove the dither signal from the manipulated variable before an end of the second portion of the evaluation period in response to a determination that the variable of interest moves toward or away from the optimal value by an amount exceeding a threshold; and

apply the dither signal to the manipulated variable for an entire duration of the second portion of the evaluation period in response to a determination that the variable of interest does not move toward or away from the optimal value by the amount exceeding the threshold.

16. The controller of claim 15 , wherein the initial steady state value is a first extremum of the manipulated variable and the new steady state value is a second extremum of the manipulated variable, opposite the first extremum.

17. The controller of claim 15 , wherein the processing circuit is configured to return the manipulated variable to the initial steady state value in response to the variable of interest not moving toward the optimal value during the second portion of the evaluation period.