Pulse Width Modulated Extremum-Seeking Control for On/Off Systems
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Solution Overview
Problem
Extremum-seeking control (ESC) systems face challenges in optimizing two-position systems, where variables cannot be adjusted continuously, as the optimum operating conditions may exist at extreme states or somewhere in between, requiring a different approach to determine optimal operating conditions.
Innovation Solution
An extremum-seeking controller for on/off systems uses pulse width modulated (PWM) control signals with a duty cycle to adjust the time spent in on/off states, extracting a gradient of the performance variable with respect to the duty cycle and modulating it to drive the gradient towards zero, optimizing the duty cycle to achieve maximum or minimum performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional ESC is applied to two-position systems by manipulating time spent in on/off states, then the system can search for optimal operating conditions, but the difficulty arises because the optimum may exist at extreme conditions or somewhere in between, making it hard to determine the optimal operating point
Solution Approach 1:
The patent applies periodic dither signals to perturb the duty cycle of the PWM control signal. By adding a small sinusoidal perturbation to the duty cycle, the system periodically varies the time spent in on/off states, allowing the extremum-seeking controller to detect the gradient of the performance variable and determine whether the current operating point is approaching an optimum. This periodic perturbation enables the system to distinguish between extreme conditions and intermediate optima.
2Ease of operation
If a variable is adjusted continuously over a range of operation in traditional ESC systems, then the system can smoothly optimize performance, but two-position systems lack this continuous adjustment capability, restricting optimization to only two discrete states
Solution Approach 1:
The patent introduces dynamic control by varying the duty cycle of the PWM signal, which continuously adjusts the effective operation time of the on/off system. Although the physical system remains in discrete on/off states, the duty cycle provides a continuous control parameter that can be smoothly adjusted between 0% and 100%. This dynamic adjustment of the duty cycle, combined with periodic dither signals, enables the system to effectively explore the entire operating range and locate optimal points, bridging the gap between discrete system states and continuous optimization needs.
Data Source
AI summary
An on/off system operates to affect a variable state or condition of a building by switching between an on state and an off state. An extremum-seeking controller operates the on/off system by providing a pulse width modulated (PWM) control signal having a duty cycle to the on/off system. The extremum-seeking controller is configured to generate the PWM control signal by receiving a performance variable as feedback from the on/off system, extracting a gradient of the performance variable with respect to the duty cycle, modulating the duty cycle using an extremum-seeking control technique to determine an optimal value of the duty cycle that drives the gradient toward zero, and generating the PWM control signal such that each period of the PWM control signal has a pulse width proportional to the duty cycle.