Memory-Based Integral Sliding-Mode Control for T–S Fuzzy Systems With PMSM via Disturbance Observer

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H ∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example. Index Terms-Interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, persistent dwell-time (PDT) switching rule, quantized control, singularly perturbed nonlinear systems. I. INTRODUCTION S OME parasitic parameters, such as small time constants, capacitances, and inductances, may increase the order of dynamic equations and lead to the numerical ill-conditioning problem. In order to overcome these obstacles, the singular perturbation technique is usually employed. Examples of singularly perturbed systems (SPSs) are power systems, airplanes, and so on [1]-[3]. When discretizing continuous-time SPSs, the sampling period influences the discrete-time model, which

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“…Meanwhile, by performing congruent transformations to (32) with diag{R θ , I} and the Schur complement, it ensures the establishment of (31).…”

Section: Appendix B Proof Of Theoremmentioning

confidence: 99%

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

Wang

Liu

Xia

et al. 2022

IEEE Trans. Cybern.

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“…Ref. [40] deals with a memory integral sliding‐mode control problem for the permanent magnet synchronous motor model with mismatched disturbance based on disturbance observer and T‐S fuzzy approach. In [41], a T‐S fuzzy functional observer is investigated to detect the fault for fuzzy systems with time‐delay and exogenous disturbance.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy adaptive observer‐based fault estimation design with adjustable parameter for satellite under unknown actuator faults and perturbations

Chang

2022

IET Control Theory & Appl

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This study considers the problem of fault estimation for rigid satellite in the presence of external disturbances, parameter perturbations, and actuator time‐varying faults. Firstly, a Takagi‐Sugeno (T‐S) fuzzy model with interval matrix for satellite attitude system under large attitude angle scope is established, along with a detailed analysis of actuator faults in terms of additive and multiplicative descriptions. Then, a novel fuzzy adaptive observer with adjustable parameter is proposed to estimate both system states and actuator faults. The estimated errors are proved to be uniformly ultimately bounded, based on descriptor augmentation technique and Lyapunov stability theory. The proposed observer realizes a lower estimation performance index in terms of quantitative assessment compared to existing observer methods. Furthermore, an auxiliary optimization variable and the elimination method are applied to decrease the conservatism of the proposed design. And an intuitive quantitative performance index of fault estimation is introduced to obtain reliable evaluation and decision. Finally, numerical simulations and analyses of rigid satellite illustrate the effectiveness and benefit of the proposed strategy.

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“…Consequently, the matched uncertainties can be compensated for throughout the integral sliding mode control (ISMC) process. Therefore, the issue of applying an integral sliding mode technique to design observers and controllers for fuzzy systems has received significant attention, such as in (Jiang et al, 2018;Kuppusamy and Joo, 2019). In (Jiang et al, 2018), a novel integral sliding surface function was proposed for the observer space of T-S fuzzy systems with semi-Markov switching and immeasurable premise variables.…”

Section: Introductionmentioning

confidence: 99%

“…In (Jiang et al, 2018), a novel integral sliding surface function was proposed for the observer space of T-S fuzzy systems with semi-Markov switching and immeasurable premise variables. An integral-type fuzzy switching surface function was defined that simultaneously involved a state-dependent input matrix and a memory parameter in Kuppusamy and Joo (2019).…”

Section: Introductionmentioning

confidence: 99%

“…To the best of the authors' knowledge, to date, the problem of observer design for T-S fuzzy descriptor systems with unmeasurable premise variables and a different derivative matrix E has not been previously studied. Second, from what we can ascertain, the existing integral sliding mode observer and controller in (Jiang et al, 2018;Kuppusamy and Joo, 2019) were designed only for T-S fuzzy systems or T-S descriptor systems with measurable premise variables. The problem of observerbased adaptive ISMC for T-S fuzzy descriptor systems with unmeasurable premise variables and uncertainties has not been previously studied.…”

Section: Introductionmentioning

confidence: 99%

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Non-Fragile Observer-Based Adaptive Integral Sliding Mode Control for a Class of T-S Fuzzy Descriptor Systems With Unmeasurable Premise Variables

et al. 2022

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The issue of non-fragile observer-based adaptive integral sliding mode control for a class of Takagi–Sugeno (T-S) fuzzy descriptor systems with uncertainties and unmeasurable premise variables is investigated. General nonlinear systems are represented by nonlinear T-S fuzzy descriptor models, because premise variables depend on unmeasurable system states and fuzzy models have different derivative matrices. By introducing the system state derivative as an auxiliary state vector, original fuzzy descriptor systems are transformed into augmented systems for which system properties remain the same. First, a novel integral sliding surface, which includes estimated states of the sliding mode observer and controller gain matrices, is designed to obtain estimation error dynamics and sliding mode dynamics. Then, some sufficient linear matrix inequality (LMI) conditions for designing the observer and the controller gains are derived using the appropriate fuzzy Lyapunov functions and Lyapunov theory. This approach yields asymptotically stable sliding mode dynamics. Corresponding auxiliary variables are introduced, and the Finsler's lemma is employed to eliminate coupling of controller gain matrices, observer gain matrices, Lyapunov function matrices, and/or observer gain perturbations. An observer-based integral sliding mode control strategy is obtained to assure that reachability conditions are satisfied. Moreover, a non-fragile observer and a non-fragile adaptive controller are developed to compensate for system uncertainties and perturbations in both the observer and the controller. Finally, example results are presented to illustrate the effectiveness and merits of the proposed method.

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Memory-Based Integral Sliding-Mode Control for T–S Fuzzy Systems With PMSM via Disturbance Observer

Cited by 54 publications

References 34 publications

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

Fuzzy adaptive observer‐based fault estimation design with adjustable parameter for satellite under unknown actuator faults and perturbations

Non-Fragile Observer-Based Adaptive Integral Sliding Mode Control for a Class of T-S Fuzzy Descriptor Systems With Unmeasurable Premise Variables

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