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Synthesized variable structure control and gray prediction for a class of perturbed systems
1Department of Electronic Engineering, Yungta Institute of Technology & Commerce, 316 Chunshan Rd., Linlo, Pingtung, Taiwan 909, ROC. shyu_chou@yahoo.com.tw
ISA Transactions
|April 24, 2003
Summary
This study introduces a gray prediction control to overcome chattering in variable structure control systems. The new method effectively manages system dynamics and perturbations without needing prior knowledge of their bounds.
Area of Science:
- Control Systems Engineering
- Nonlinear Dynamics
- Applied Mathematics
Background:
- Traditional variable structure control (VSC) suffers from the 'chattering' phenomenon, which can degrade performance and excite unmodeled high-frequency dynamics.
- Chattering in VSC arises from the rapid switching of control signals near the sliding surface.
- Existing methods to mitigate chattering often require prior knowledge of the upper bounds of system perturbations, which is not always available.
Purpose of the Study:
- To develop an improved variable structure control scheme that eliminates the chattering disadvantage.
- To propose a novel approach utilizing gray prediction for enhanced control performance.
- To ensure robust stability properties for the controlled system.
Main Methods:
- Application of Lyapunov stability theorem to analyze system stability.
- Integration of a gray prediction scheme with a moving window of recent data to identify system dynamics and unknown perturbations directly.
- Design of a control law that does not require prior knowledge of the upper bound of perturbations.
Main Results:
- The proposed gray prediction-based variable structure control effectively eliminates the chattering phenomenon.
- The method successfully identifies system dynamics and unknown perturbations online using historical data.
- The control scheme guarantees globally uniformly ultimate boundedness for the entire controlled system.
- A numerical example validates the feasibility and effectiveness of the proposed control strategy.
Conclusions:
- The developed gray prediction control scheme offers a robust solution to the chattering problem in variable structure control.
- This approach enhances control system performance by accurately estimating system dynamics and perturbations online.
- The guaranteed stability properties make the proposed method suitable for various control applications where perturbation bounds are unknown.