Abstract
In this paper, an extended disturbance observer-based integral sliding-mode control for a nonlinear system is proposed by the Takagi-Sugeno (T-S) fuzzy model approach. The proposed method focuses on two points: First, improving the design flexibility of integral fuzzy sliding-mode control (IFSMC) by transforming a conventional T-S fuzzy model structure into a novel form. Second, expanding a previous disturbance observer-based control (DOBC) concept by introducing a Fourier analysis to deal with the non-periodic form of disturbance. By using the modified form of the fuzzy model, a novel sliding surface combined with estimated disturbance through several fuzzy disturbance observers (FDOB) is suggested. Besides, a sufficient condition for guaranteeing asymptotic stability of the sliding dynamic with H ∞ control performance is proposed by applying a proper Lyapunov function with the linear matrix inequality (LMI) concept. Furthermore, a reachability problem of the proposed sliding surface is also handled by introducing another Lyapunov function. Finally, the effectiveness of the proposed method is demonstrated by comparing previous studies, which focused on robust control techniques, based on the simulation results of an inverted-pendulum system.
Highlights
Over the last few decades, as systems become more complex and sophisticated, many nonlinear system control techniques, such as sliding-mode control (SMC), adaptive control, and model predictive control, have successfully introduced and suggested [1]–[6], [32]–[43]
VOLUME 8, 2020 developing a general framework of designing the fuzzy disturbance observer-based control (FDOBC) method even if the mismatched disturbance is a non-periodic neutral stable (NPNS) signal can be considered as a great catalyst in terms of proposing a robust control technique
Motivated by the aforementioned statements, this paper proposes a novel theoretical framework combined with integral fuzzy sliding-mode control (IFSMC) and FDOBC concepts to deal with the matched disturbance and mismatched disturbance simultaneously
Summary
Over the last few decades, as systems become more complex and sophisticated, many nonlinear system control techniques, such as sliding-mode control (SMC), adaptive control, and model predictive control, have successfully introduced and suggested [1]–[6], [32]–[43]. VOLUME 8, 2020 developing a general framework of designing the FDOBC method even if the mismatched disturbance is a non-periodic neutral stable (NPNS) signal can be considered as a great catalyst in terms of proposing a robust control technique. The present work is outlined as follows: In Section II, modifying T–S fuzzy model into a suitable form for ISFMC and designing FDOBs and ISFMC subject to an NPNS disturbance via Fourier analysis are presented. The mismatched disturbance matrix Bdi with i ∈ Ir has a same value regardless of its fuzzy rules, which means that Bdi follows the form of Bd1 = Bd2 = · · · = Bdr. Considering Assumption 2, modifying the fuzzy model (1) into a suitable form for the design of IFSMC is important. Given the timevarying matrix U (w), Lemma 1 will be helpful when deriving a stability analysis of (8)
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