Improved Adaptive Sliding Mode Control for a Class of Second‐Order Mechanical Systems

Cong, Beihua; Liu, Xiangdong; Chen, Zhe

doi:10.1002/asjc.568

Cited by 13 publications

(18 citation statements)

References 15 publications

(24 reference statements)

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“…Remark 2. The proposed adaptive TSM controller (16) associated with (17) to (19) can also be applied to the chaos control problem of system class (1) and the problem of anti-synchronization between two of the same kind of systems belonging to class (1). Similar results can be extended according to the aforementioned procedures.…”

Section: U T M N E T E T K T K T E T K T E Tmentioning

confidence: 98%

“…For the adaptive TSM controller (16) associated with (17) to (19), the positive constants are chosen as m = 15, n = 1.2857, g0 = 15, g1 = 25, and g2 = 40. The initial conditions of the drive and the driven systems are chosen (x1(0), y1(0)) = (-2.0, 2.0) and (x2(0), y2(0)) = (2.0, -2.0), respectively.…”

Section: Synchronization Between Two Non-autonomous Horizontal Platformsmentioning

confidence: 99%

“…The idea of synchronizing two identical chaotic systems from different initial conditions was introduced by Pecora and Carrols [1]. Thereafter, many researchers interested in the topic have developed several efficient technologies of chaotic synchronization for various systems, such as active control [2,3], adaptive control [4][5][6][7][8], backstepping design [9], passive feedback control [10], sliding mode control [11][12][13][14][15][16][17][18][19], and internal mode approach [20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Adaptive Terminal Sliding Mode Synchronized Control for a Class of Non‐Autonomous Chaotic Systems

Chao¹

2013

Asian Journal of Control

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For a general class of non‐autonomous chaotic systems, the purpose of this study is to introduce a robust adaptive terminal sliding mode controller for achieving synchronization between two of the same kind of systems in the presence of system uncertainties and external disturbances. The proposed controller, associated with adaptive feedback gains, can compensate nonlinear dynamics of the synchronous error system without active elimination. Meanwhile, these feedback gains are not to be determined in advance but updated by the adaptive rules without known bounds of system uncertainties and external disturbances. In the sense of the Lyapunov stability theorem, sufficient conditions to guarantee the stable synchronization are given. Numerical case studies are performed to verify the effectiveness of presented scheme.

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Section: U T M N E T E T K T K T E T K T E Tmentioning

confidence: 98%

Section: Synchronization Between Two Non-autonomous Horizontal Platformsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Adaptive Terminal Sliding Mode Synchronized Control for a Class of Non‐Autonomous Chaotic Systems

Chao¹

2013

Asian Journal of Control

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“…In literatures [8][9][10][11][12], an adaptive neural network controller is designed by using a neural network to approximate uncertain continuous nonlinear functions. The advantage of sliding mode controller is that it has strong robustness to disturbances and unmodeled dynamics, so it has also been widely applied [13][14][15][16][17][18]. However, all the above methods require that the system meet an important condition, that is, the unknown nonlinearity and the control input appear in the same equation of the state space model, which is usually regarded as the matching condition.…”

Section: Introductionmentioning

confidence: 99%

An improved adaptive fuzzy backstepping control for nonlinear mechanical systems with mismatched uncertainties

Wan

Liu

2019

Automatika

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When the nonlinear mechanical system has mismatched uncertainties, it is difficult to design control algorithm to achieve high precision trajectory tracking control. Traditional backstepping control is an effective control method for uncertain, mismatched nonlinear systems, but there is inherent problem of "complexity due to the explosion of terms". In this paper, based on the backstepping method, only one fuzzy system is used to approximate the unknown nonlinear functions, the unknown control gain and the differential of virtual control law of each subsystem. In order to reduce the influence of fuzzy approximation error and external interference, the above control scheme is further improved by designing special adjustable control parameters and first order low pass filter. The improved control scheme not only improves the control precision of the system obviously, but also solves the problem of "explosion of terms", and greatly reduces the initial control input, and provides the conditions for the practical application. The simulation results show the effectiveness of the proposed methods.

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“…The advantage of sliding mode controller is that it has strong robustness to disturbances and unmodeled dynamics, so it has also been widely applied. [12][13][14][15] However, all the above methods require that the system meets an important condition, that is, the unknown nonlinearity and the control input appear in the same equation of the state space model, which is usually regarded as the matching condition. In the actual system, there is a large class of nonlinear systems that do not meet the matching condition, such as the system of the mechanical hand which is driven by the motor.…”

Section: Introductionmentioning

confidence: 99%

Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints

Wan

Liu

2019

Advances in Mechanical Engineering

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This article deals with the design of adaptive fuzzy backstepping control for uncertain nonlinear systems in strictfeedback form with tracking error constraints. In this article, a fuzzy system is used to approximate the unknown nonlinear functions and the differential of virtual control law of each subsystem. In order to satisfy the limitation of tracking error constraints, the barrier Lyapunov function is introduced. Moreover, by applying the minimal learning parameters technique, the number of online parameters update for each subsystem is reduced to only 1. The control scheme not only ensures the tracking error is not to transgress the constraint bounds but also solves the problem of ''explosion of complexity'' and greatly reduces the initial control input and the number of the adaptive parameters; this provides the conditions for the practical application. The simulation results show the effectiveness of the proposed method.

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Improved Adaptive Sliding Mode Control for a Class of Second‐Order Mechanical Systems

Cited by 13 publications

References 15 publications

Robust Adaptive Terminal Sliding Mode Synchronized Control for a Class of Non‐Autonomous Chaotic Systems

Robust Adaptive Terminal Sliding Mode Synchronized Control for a Class of Non‐Autonomous Chaotic Systems

An improved adaptive fuzzy backstepping control for nonlinear mechanical systems with mismatched uncertainties

Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints

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