Lyapunov Adaptive Control for Stable Nonlinear Actuators
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Solution Overview
Problem
Current adaptive controllers in plasma processing systems lack inherent stability, struggle with scaling to arbitrary waveforms and coupled inputs/outputs, are limited by single control laws, and face challenges with unstable systems, unbounded control values, and modeling uncertainties, leading to inefficiencies and premature system failures.
Innovation Solution
The proposed method involves a Lyapunov-based adaptive controller that uses a nonlinear model with a control portion and an estimation portion, applying tensor multiplication and updating model parameters at each control sample to generate and refine control signals, blending influences from multiple estimation laws to adapt to nonlinear and chaotic systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing adaptive controllers are used, then control adaptability is provided, but system stability is not guaranteed and control precision deteriorates
Solution Approach 1:
The controller employs Lyapunov stability theory with continuous feedback mechanisms that monitor system state and adjust control parameters in real-time. The Lyapunov function derivative is used as a feedback criterion to guarantee stability while adapting to changing system conditions, resolving the contradiction between adaptability and stability.
Solution Approach 2:
The controller dynamically changes control parameters based on system state and operating conditions. By using adaptive parameter adjustment grounded in Lyapunov stability criteria, the system maintains stability guarantees while achieving adaptability to different operating regimes and disturbances.
2Manufacturing precision
If rail voltage is held at high level for precision control, then control precision is improved, but energy dissipation increases and components overheat
Solution Approach 1:
The controller dynamically adjusts rail voltage levels based on real-time system state and control requirements. Instead of maintaining a static high voltage level, the system adaptively modulates voltage to provide precise control only when necessary, reducing energy dissipation and preventing overheating while maintaining control precision.
Solution Approach 2:
The controller uses periodic pulse-width modulation techniques to deliver precise control signals. By applying controlled pulses rather than continuous high voltage, the system achieves precision control during critical periods while allowing energy dissipation to decrease during non-critical periods, preventing thermal accumulation.
3Productivity
If actuators operate at high speed for productivity, then productivity is improved, but control complexity increases due to asynchronous responses
Solution Approach 1:
The controller implements comprehensive feedback mechanisms that monitor the state of all actuators in real-time. By using Lyapunov-based stability criteria with multi-variable feedback, the system coordinates asynchronous actuator responses without requiring complex inter-actuator synchronization, maintaining high speed operation while managing control complexity.
Solution Approach 2:
The controller uses a unified Lyapunov-based control framework that handles multiple actuators with different response characteristics through a single stability criterion. This universal approach allows high-speed operation of multiple actuators without requiring separate control strategies for each actuator, reducing overall control complexity.
Data Source
AI summary
This disclosure describes systems, methods, and apparatus for an adaptive Lyapunov controller that can operate as a standalone controller for one or more actuators of a power system, or as one of a plurality of sub-engines in an adaptive controller. The controller or sub-engine can implement a control portion and an estimation portion of a nonlinear model of the one or more actuators and/or a power system controlled by the one or more actuators. The control portion can tensor multiply an input regressor, or partially filtered version thereof, and an estimated model parameter tensor, to produce a possible control signal. The estimation portion can apply a time-varying nonlinear system to the possible control signal to estimate an estimate system output corresponding to the possible control signal. These outputs may be used in a selection and combination process to produce a control based on one or more sub-engine outputs.