Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties
Abstract
:1. Introduction
- (1)
- A novel sliding surface is proposed for an extended nth order single input–single output (SISO) system with arbitrarily unknown matched/unmatched uncertainties.
- (2)
- An efficient LPO are presented to approximate the true lumped perturbations produced by arbitrarily unknown uncertainties/disturbances in all channels of a SISO system through the presented multiple surfaces. Following this, a robust controller is designed, to guarantee a strong stability of the control system under the variation of disturbance.
- (3)
- The steps of designing the proposed controller and LPO do not require any knowledge of bound conditions of matched and unmatched uncertainties.
2. Problem Formulation
3. Main Results
3.1. Robust Controller Design
3.2. Lumped Perturbation Observer (LPO)
4. Stability Analysis
- *
- The convergence of a sliding surface,, is analyzed through a Lyapunov function chosen by:
- *
- The convergence of sliding surfaces,, (i = 1, 2,…, n−1) is analyzed by:
5. Simulation Results and Discussions
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol | |||||||||||
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Value | 250 | 1300 | 0.1 | 0.5 | 0.001 | 0.01 | 0.001 | 0.07 | 20 | 50 | 80 |
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Thanh, H.L.N.N.; Vu, M.T.; Mung, N.X.; Nguyen, N.P.; Phuong, N.T. Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties. Mathematics 2020, 8, 1371. https://doi.org/10.3390/math8081371
Thanh HLNN, Vu MT, Mung NX, Nguyen NP, Phuong NT. Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties. Mathematics. 2020; 8(8):1371. https://doi.org/10.3390/math8081371
Chicago/Turabian StyleThanh, Ha Le Nhu Ngoc, Mai The Vu, Nguyen Xuan Mung, Ngoc Phi Nguyen, and Nguyen Thanh Phuong. 2020. "Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties" Mathematics 8, no. 8: 1371. https://doi.org/10.3390/math8081371