Convergence analysis on a tracking differentiator used in active disturbance rejection control
Huixia Zhang1, Yan Liang1, Haiyan Cheng2
1School of Automation, Northwestern Polytechnical University, Xi'an, 710072 China.
ISA Transactions
|July 22, 2023
Summary
This study analyzes the tracking differentiator in active disturbance rejection control, proving tracking errors are uniformly ultimately bounded. This provides a basis for parameter adjustment in this widely used control method.
Area of Science:
- Control Systems Engineering
- Nonlinear Control Theory
Background:
- Active disturbance rejection control (ADRC) is widely applied in engineering.
- Theoretical analysis for ADRC's tracking differentiator is lacking.
- Nonlinear piecewise functions in tracking differentiators complicate convergence analysis.
Purpose of the Study:
- To provide convergence analysis for the tracking differentiator in ADRC.
- To address the theoretical gap in ADRC's tracking differentiator.
- To establish relationships between tracking error bounds and adjustment parameters.
Main Methods:
- Convergence proof divided into three cases based on the nonlinear piecewise function.
- Lyapunov approach used for stability analysis.
- Mathematical analysis of tracking errors.
Main Results:
- Tracking errors of the tracking differentiator are proven to be uniformly ultimately bounded.
- Relationships between tracking error upper bounds and tuning parameters are established.
- The analysis provides a foundation for ADRC parameter tuning.
Conclusions:
- The proposed convergence analysis is effective for ADRC tracking differentiators.
- Simulation and experimental results validate the theoretical findings.
- The study contributes to the theoretical understanding and practical application of ADRC.
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