Self-configuring extremum-seeking control system
A self-configuring extremum-seeking controller includes a dither signal generator, a communications interface, a phase delay estimator, and a bandwidth estimator. The dither signal generator identifies a stored dither frequency, generates a dither signal having the stored dither frequency, and uses the dither signal to perturb a control input for a plant. The communications interface provides the perturbed control input to the plant and receives an output signal from the plant resulting from the perturbed control input. The phase delay estimator estimates a phase delay between the output signal and the dither signal. The bandwidth estimator estimates a bandwidth of the plant based on the estimated phase delay. The dither signal generator updates the stored dither frequency based on the estimated bandwidth.
1. A self-configuring extremum-seeking controller comprising:
a processor; and
a memory comprising a non-transitory machine readable medium storing instructions that, when executed by the processor, cause the processor to:
receive an output signal from a plant representative of an operation of the plant in response to a first control input perturbed using a first dither signal having a first dither frequency;
estimate a phase delay between the output signal and the first dither signal;
estimate a bandwidth of the plant based on the phase delay;
perturb a second control input using a second dither signal having a second dither frequency based on the bandwidth of the plant; and
transmit the perturbed second control input to the plant.
2. The controller of claim 1 , wherein the instructions, when executed by the processor, further cause the processor to:
estimate a natural frequency of the plant based on the phase delay; and
use the natural frequency of the plant as the bandwidth of the plant.
3. The controller of claim 1 , wherein the instructions, when executed by the processor, further cause the processor to estimate the bandwidth of the plant as a function of the phase delay and the first dither frequency.
4. The controller of claim 1 , wherein the instructions, when executed by the processor, further cause the processor to:
calculate a dot product of the first dither signal and the output signal;
calculate 2-norms of the first dither signal and the output signal; and
estimate the phase delay as a function of the dot product and the 2-norms.
5. The controller of claim 1 , wherein the instructions, when executed by the processor, further cause the processor to:
calculate a first exponentially-weighted moving average (EWMA) of the first dither signal;
calculate a second EWMA of the output signal from the plant; and
estimate the phase delay of the as a function of the first EWMA and the second EWMA.
6. The controller of claim 1 , wherein the instructions, when executed by the processor, further cause the processor to:
estimate a system gain based on the bandwidth and the first dither frequency; and
use the system gain to scale a step size of a gradient descent procedure performed by the controller.
7. The controller of claim 6 , wherein the instructions, when executed by the processor, further cause the processor to:
calculate a first exponentially-weighted moving average (EWMA) of the dither signal;
calculate a second EWMA of the output signal from the plant; and
estimate the system gain as a function of the first EWMA and the second EWMA.
8. A method for self-configuring one or more extremum-seeking control parameters used by an extremum-seeking controller to modulate a control input for a plant, the method comprising:
receiving an output signal from the plant representative of an operation of the plant in response to a first control input perturbed using a first dither signal having a first dither frequency;
estimating a phase delay between the output signal and the first dither signal;
estimating a bandwidth of the plant based on the phase delay; and
perturbing a second control input using a second dither signal having a second dither frequency based on the bandwidth of the plant; and
transmitting the perturbed second control input to the plant.
9. The method of claim 8 , wherein estimating the bandwidth of the plant comprises:
estimating a natural frequency of the plant based on the phase delay; and
using the natural frequency of the plant as the bandwidth.
10. The method of claim 8 , wherein the bandwidth of the plant is estimated as a function of the phase delay and the first dither frequency.
11. The method of claim 8 , wherein estimating the phase delay between the output signal and the first dither signal comprises:
calculating a dot product of the first dither signal and the output signal;
calculating 2-norms of the first dither signal and the output signal; and
estimating the phase delay as a function of the dot product and the 2-norms.
12. The method of claim 8 , further comprising calculating a first exponentially-weighted moving average (EWMA) of the first dither signal and a second EWMA of the output signal from the plant, wherein the phase delay is estimated as a function of the first EWMA and the second EWMA.
13. The method of claim 8 , further comprising:
estimating a system gain based on the bandwidth and the first dither frequency; and
using the system gain to scale a step size of a gradient descent procedure performed by the controller.
14. The method of claim 13 , further comprising calculating a first exponentially-weighted moving average (EWMA) of the first dither signal and a second EWMA of the output signal from the plant, wherein the system gain is estimated as a function of the first EWMA and the second EWMA.
15. A self-configuring extremum-seeking controller comprising:
a processor; and
a non-transitory machine readable medium storing instructions that, when executed by the processor, cause the processor to:
receive an output signal from a plant representative of an operation of the plant in response to a first control input perturbed using a first dither signal;
generate a set of one or more extremum-seeking control parameters based on the output signal and the first dither signal;
perturb a second control input to the plant using a second dither signal based on the set of one or more extremum-seeking control parameters; and
transmit the perturbed second control input to the plant.
16. The controller of claim 15 , wherein the instructions, when executed by the processor, cause the processor to generate the set of one or more extremum-seeking control parameters by:
estimating a phase delay between the output signal and the first dither signal; and
estimating a bandwidth of the plant.
17. The controller of claim 16 , wherein the instructions, when executed by the processor, further cause the processor to:
estimate a system gain based on the bandwidth; and
use the system gain to scale a step size of a gradient descent procedure performed by the controller.
18. The controller of claim 17 , wherein the instructions, when executed by the processor, further cause the processor to calculate a first exponentially-weighted moving average (EWMA) of the first dither signal and a second EWMA of the output signal from the plant, wherein at least one of the phase delay and the system gain is estimated as a function of the first EWMA and the second EWMA.
19. The controller of claim 16 , wherein the bandwidth of the plant is estimated as a function of the phase delay and the first dither frequency.
20. The controller of claim 16 , wherein estimating the phase delay between the output signal and the first dither signal comprises:
calculating a dot product of the first dither signal and the output signal;
calculating 2-norms of the first dither signal and the output signal; and
estimating the phase delay as a function of the dot product and the 2-norms.