Noise-adaptive extremum-seeking controller
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Solution Overview
Problem
Existing extremum-seeking control (ESC) systems require tuning and are sensitive to noise in performance variable signals, making them inefficient in optimizing system performance without accurate model-based control.
Innovation Solution
The method involves determining an adjusted correlation coefficient by scaling a first value based on covariance and variance, using a forgetting factor to filter estimates, and dampening convergence rates, allowing the ESC system to operate effectively despite noise and without requiring model-based tuning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional extremum-seeking control is used, then the system can optimize performance, but it requires tuning and is sensitive to noise in performance variable signals
Solution Approach 1:
The patent replaces traditional gradient descent mechanical control with a correlation coefficient-based control mechanism. Instead of using gradient calculations that require tuning and are noise-sensitive, the system uses correlation coefficients between control inputs and performance variables, which are inherently more robust to noise and do not require system-specific tuning parameters.
Solution Approach 2:
The patent changes the fundamental parameter used for control from gradient values to correlation coefficients. This parameter transformation allows the system to maintain optimization capability while eliminating tuning requirements and reducing noise sensitivity, as correlation coefficients naturally normalize the relationship between inputs and outputs.
2Reliability
If gradient descent is used for optimization, then the system can find optimal inputs, but it requires tuning based on the plant characteristics
Solution Approach 1:
The patent implements a self-service control system where the correlation coefficient automatically adapts to the plant characteristics without requiring external tuning. The system computes the correlation between control inputs and performance variables directly from operational data, enabling self-adjustment to changing plant conditions without manual intervention or complex tuning procedures.
Solution Approach 2:
The correlation coefficient-based approach provides a universal control mechanism that can be applied to any plant without customization. Unlike gradient descent which requires plant-specific tuning, the correlation-based method works universally across different systems and operating conditions, eliminating the need for complex tuning procedures while maintaining optimization accuracy.
3Measurement precision
If noise is present in performance variable signals, then measurement accuracy decreases, but the system still needs to optimize effectively
Solution Approach 1:
The patent introduces the correlation coefficient as an intermediary between the noisy performance variable measurements and the control decisions. This intermediary statistic naturally filters out random noise by measuring the systematic relationship between inputs and outputs, allowing effective optimization even when direct measurements are noisy.
Solution Approach 2:
The patent implements feedback through the correlation coefficient that continuously monitors the relationship between control inputs and performance variables. This feedback mechanism is inherently robust to noise because it measures the statistical relationship over time rather than relying on instantaneous noisy measurements, maintaining optimization effectiveness despite measurement imprecision.
Data Source
AI summary
A method for performing extremum-seeking control of a plant includes determining multiple 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 includes a noise-free portion and an amount of noise. The method includes determining an adjusted correlation coefficient by scaling a first value of the correlation coefficient selected from the multiple values relative to a second value of the correlation coefficient selected from the multiple values. The adjusted correlation coefficient relates the noise-free portion of the performance variable to the control input. The method includes using the adjusted correlation coefficient to modulate the control input provided as an input to the plant.