Sliding mode controller for linear systems with mismatched time-varying uncertainties

Abstract. In this paper, fuzzy logic is meshed with sliding mode control, in order to control vibrations of a cantilevered plate. Test plate is instrumented with a piezoelectric sensor patch and a piezoelectric actuator patch. Finite element method is used to obtain mathematical model of the test plate. A design approach of a sliding mode controller for linear systems with mismatched time-varying uncertainties is used in this paper. It is found that chattering around the sliding surface in the sliding mode control can be checked by the proposed fuzzy sliding mode control approach. With presented fuzzy sliding mode approach the actuator voltage time response has a smooth decay. This is important because an abrupt decay can excite higher modes in the structure. Fuzzy rule base consisting of nine rules, is generated from the sliding mode inequality. Experimental implementation of the control approach verify the theoretical findings. For experimental implementation, size of the problem is reduced using modal truncation technique. Modal displacements as well as velocities of first two modes are observed using real-time kalman observer. Real time implementation of fuzzy logic based control has always been a challenge because a given set of rules has to be executed in every sampling interval. Results in this paper establish feasibility of experimental implementation of presented fuzzy logic based controller for active vibration control. Nomenclature

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“…with B 2 being non-singular with rank m. Mismatched time-varying uncertainty, ∆A 1 (t) can be assumed to have the form [5] …”

Section: Discussionmentioning

confidence: 99%

“…For the basic sliding mode control, the formulation given by Chan et al [5] has been adopted for a vibratory system. In the work done by Chan et al [5], the additional flexibility offered by the controller is that the uncertainties in the plant can be mismatched i.e. they need not be expressible in terms of the control matrix.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Sliding Mode Control of Plate Vibrations

Sharma

Singh

2010

Shock and Vibration

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“…Constant value α > 0, so inequality (26) implies that the state trajectory will reach the sliding surface. Thus, the proof is completed.…”

Section: Theorem 2 Suppose That the Lmimentioning

confidence: 99%

“…Some of the key technical problems associated with SMC are chattering, matched and mismatched uncertainties, and unmodeled dynamics. Many new approaches have been developed in the last decade to address these problems [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Cluster synchronization in nonlinear complex networks under sliding mode control

2015

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This paper investigates the cluster synchronization for network of nonlinear systems via differential mean value theorem method and sliding mode control strategy. Because of the existence of the nonlinear dynamics, the differential mean value theorem method is used to transform the nonlinear error complex network system into a linear parameter-varying system. Since the robustness to the uncertainties of the sliding mode, we can deal with the linear parametervarying system which contains the time-varying mismatched uncertainties by applying the sliding mode control strategy through the equivalent transformation. In addition, appropriate linear matrix inequality stability condition by the Lyapunov method is derived such that each subsystem in the new sliding mode is completely invariant to both matched and mismatched uncertainties. Finally, simulation example is shown to illustrate the effectiveness of the proposed method.

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“…The main phenomenon in VSS is what so called Sliding mode [1][2][3]. The VSS is mainly a discontinuous control technique.…”

Section: Introductionmentioning

confidence: 99%

Decoupled Fuzzy Sliding Mode Control for a Synchronous Motor Speed Control

Abdelsalam¹,

Areed²

2012

IJCA

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This paper introduces a new technique for controlling the speed of Permanent Magnet Synchronous Motor (PMSM). This technique depends on two well known control methods; the first control method is known the variable structure system (VSS), which has a main advantage known as an sliding mode property. The second method depends on fuzzy logic control. A combination between the two mentioned above methods is suggested in this paper. In addition for simplifying the suggested technique, the model of PMSM is decoupled. Simulation results illustrate the validity and the effectiveness of the new suggested technique.

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Sliding mode controller for linear systems with mismatched time-varying uncertainties

Cited by 67 publications

References 9 publications

Fuzzy Sliding Mode Control of Plate Vibrations

Fuzzy Sliding Mode Control of Plate Vibrations

Cluster synchronization in nonlinear complex networks under sliding mode control

Decoupled Fuzzy Sliding Mode Control for a Synchronous Motor Speed Control

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