Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays

Cong-Trang Nguyen, Thanh Long Duong, Minh Quan Duong and Duc Tung Le
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Cong-Trang Nguyen: Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
Thanh Long Duong: Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City 700000, Vietnam
Minh Quan Duong: Faculty of Electrical Engineering, The University of Danang—University of Science and Technology, Danang City 550000, Vietnam
Duc Tung Le: Department of Power Systems, School of Electrical Engineering, Hanoi University of Science and Technology, Hanoi City 100000, Vietnam

Energies, 2020, vol. 13, issue 1, 1-27

Abstract: Variable structure control with sliding mode can provide good control performance and excellent robustness. Unfortunately, the chattering phenomenon investigated due to discontinuous switching gain restricting their applications. In this paper, a chattering free improved variable structure control (IVSC) for a class of mismatched uncertain interconnected systems with an unknown time-varying delay is proposed. A sliding function is first established to eliminate the reaching phase in traditional variable structure control (TVSC). Next, a new reduced-order sliding mode estimator (ROSME) without time-varying delay is constructed to estimate all unmeasurable state variables of plants. Then, based on the Moore-Penrose inverse approach, a decentralized single-phase robustness sliding mode controller (DSPRSMC) is synthesized, which is independent of time delays. A DSPRSMC solves a complex interconnection problem with an unknown time-varying delay term and drives the system’s trajectories onto a switching surface from the initial time instance. Particularly, by applying the well-known Barbalat’s lemma, the chattering phenomenon in control input is alleviated. Moreover, a sufficient condition is established by using an appropriate Lyapunov theory and linear matrix inequality (LMI) method such that a sliding mode dynamics is asymptotically stable from the beginning time. Finally, a developed method is validated by numerical example with computer simulations.

Keywords: variable structure control; chattering avoidance; reduced-order sliding mode estimator; without reaching phase; interconnected systems; unknown time-varying delay (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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