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Journal ArticleDOI: 10.1080/00207179.2019.1605205

Discrete-time sliding-surface based control of parametrically uncertain nonlinear systems with unknown time-delay and inaccessible switching mode detection

04 Mar 2021-International Journal of Control (Informa UK Limited)-Vol. 94, Iss: 3, pp 623-642
Abstract: This paper focuses on proposing a novel method regarding general tracking control of discrete high-order parametrically uncertain systems with unknown arbitrary switching signals and unknowable tim...

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21 results found


Journal ArticleDOI: 10.1016/J.MECHMACHTHEORY.2019.103763
Abstract: This paper proposes a new method for control of nonlinear multi input – multi output (MIMO) mechanical systems that incorporate viscoelastic dampers (VED) for reducing undesired vibrations of actuators. To this end, a control algorithm is proposed based on considering various characteristics of the described dynamical systems (namely mechanical dynamics, viscoelasticity and actuator dynamics) in generation of control inputs guaranteeing convergence of system response to desired reference signals. This procedure features three consecutive parts within the control loop which are conducted iteratively at each control sample. At each sample, initially necessary forces and moments exerted to mechanical system are calculated as virtual control inputs generated based on a MIMO discrete-time sliding mode control (DSMC) algorithm. As the aim of control model is obtaining a closed-loop system without resulting in notable vibrational effects, undesired chattering effects should be eliminated from inputs generated by DSMC. This objective is attained by calculation of appropriate input bounds. Next, an additional virtual input is assigned corresponding to viscoelastic strain such that virtual mechanical input from previous part of the control loop is generated. To this end, Maxwell model for viscoelastic material is considered. Finally, actual controller input is generated such that all virtual control objectives are satisfied. The effectiveness of control procedure is numerically illustrated for a 3-PRR manipulator.

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Topics: Control theory (62%), Sliding mode control (60%), Control system (56%) ... read more

19 Citations


Journal ArticleDOI: 10.1016/J.JSV.2019.114902
Abstract: In this paper, a novel method for control of uncertain MIMO flexible systems is proposed. The control system is constructed such that it is capable of stabilizing a flexible dynamical system based on rigid approximation of continuum dynamics, resulting in facilitation of modeling and control procedures for complicated vibrational systems. In order to ensure system stability in real-time applications, the control system is obtained in discrete-time basis. To these ends, a sliding hyper-plane based sliding mode control (SMC) algorithm is constructed featuring sliding functions for individual subsystems. An approximated dummy model of the real system is used alongside the dynamical system in order to estimate parametric and unstructured uncertainties which are evaluated through comparisons between the dummy model, data obtained from the real system and corresponding mathematical model. Conventional SMC techniques introduce undesired effects of chattering which result in amplifying vibrations in flexible systems. To address this issue, an alternate algorithm based on selection of control signals within appropriate bounds is used in order to eliminate chattering and provide superior performance in comparison with conventional SMC techniques. The accuracy of proposed method has been verified through ANSYS® mechanical APDL-based simulations and its effectiveness has been verified in multiple operating conditions.

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Topics: Sliding mode control (65%), Control system (54%), Dynamical system (51%) ... read more

19 Citations


Journal ArticleDOI: 10.1007/S40313-020-00583-Y
Abstract: This paper proposes a novel method for simultaneous estimation of unknown switched external disturbance and precise position control of dynamical systems which employ worm gear drive reducers. This algorithm is based on an improved discrete sliding mode control (DSMC) design which ensures convergence to the desired sliding set without introducing chattering effects to the dynamical system. In order to improve the performance of DSMC and to obtain an accurate estimation of gearbox model, a new method for incorporation of switched friction is proposed in the presence of external disturbance. To this end, the dynamical response of worm gear drive reducer is investigated in distinct switched disturbance modes of resistive disturbances, assistive disturbances and no disturbance to obtain approximate functions describing system dynamics in aforementioned configurations. In comparison with the feedback data, the obtained models permit appropriate incorporation of friction into the improved DSMC scheme. Based on multiple common Lyapunov functions and calculation of virtual reference signals for armature currents, the feasibility of control algorithm is ensured in all modes of switched dynamics. The effectiveness of the proposed estimation and control schemes has been verified using an experimental setup employing a worm gear drive reducer on which multiple permanent magnet DC motors are installed, and improvements resulted from incorporation of friction estimation algorithm are analyzed.

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Topics: Worm drive (62%), Sliding mode control (59%), Reducer (53%) ... read more

10 Citations


Journal ArticleDOI: 10.1016/J.ASOC.2020.106265
Abstract: In control of switched systems with undetectable switching signals, robustness and precision are on two different sides of a spectrum. In one hand, robustness to significant modeling uncertainties arising from undetectability of switching modes can be attained by designing the control scheme for worst-case switching configurations. On the other hand, such a control scheme would potentially be overly conservative and imprecise. A natural solution to this problem is pinpointing active switched dynamics at any given moment. However, this is no trivial task. In this study, we propose that the aforementioned problems can be overcome by designing a control scheme that prioritizes appropriate objectives according to operating conditions. In other words, the control scheme adjusts itself such that either of robustness to unknowable switching or increased tracking precision is selected as the primary control objective. As a result, the control model can be considered as dual-mode featuring a safe control mode and a precise control mode. In precise control mode, a model generation scheme using a modified Fuzzy-Wavelet Neural Network (FWNN) for Multi Input-Multi Output (MIMO) systems is incorporated for precise estimation of active dynamics which potentially features unknowable switching dynamics, external disturbances and parametric modeling uncertainty. However, this approximate model cannot be used immediately since convergence of the FWNN-based model to actual system dynamics takes place after a limited interval. In such periods (which often correspond to discontinuities in switching dynamics and references), using the FWNN scheme is perilous. Therefore, a robust discrete-time sliding mode control (DSMC) is used to ensure stabilization of closed-loop system in all potential modes of switched dynamics at the cost of reduced tracking precision. In combination, the dual-mode scheme ensures robust stabilization in safe control modes corresponding to transient-state stage and accurate tracking in steady-state stage of system response based on the proposed precise mode scheme. Numerical and experimental examples highlight the key features and improvements of the presented control algorithm.

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10 Citations


Journal ArticleDOI: 10.1177/1077546320916637
Abstract: In this article, a new control method is proposed based on finite-time discrete sliding mode control for uncertain multi-input multi-output systems which are affine to their inputs considering unce...

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Topics: Matrix (mathematics) (66%), Affine transformation (62%), Linear matrix inequality (62%) ... read more

9 Citations


References
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35 results found


Open accessBook
24 Jun 2003-
Abstract: I. INTRODUCTION 1. Basic Concepts II . STABILITY OF SWITCHED SYSTEMS 2. Stability under Arbitrary Switching 3. Stability under Constrained Switching III. SWITCHING CONTROL 4. Systems not Stabilizable by Continuous Feedback 5. Systems with Sensor or Actuator Constraints 6. Systems with Large Modeling Uncertainty IV. SUPPLEMENTARY MATERIAL A. Stability B. Lie Algebras Notes and References Bibliography Index

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5,278 Citations


Journal ArticleDOI: 10.1016/J.AUTOMATICA.2008.12.004
Jenq-Lang Wu1Institutions (1)
01 Apr 2009-Automatica
Abstract: This paper considers the stabilization problem for a class of switched nonlinear systems under arbitrary switching. Based on the backstepping method and the control Lyapunov function approach, it is shown that, under a simultaneous domination assumption, a switched nonlinear system in strict-feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller. A universal formula for constructing stabilizing feedback laws is presented. One example is included for verifying the obtained results.

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Topics: Strict-feedback form (64%), Backstepping (63%), Nonlinear control (60%) ... read more

248 Citations


Journal ArticleDOI: 10.1016/J.AUTOMATICA.2016.01.047
01 Jun 2016-Automatica
Abstract: To avoid the chattering problem in the reaching-law-based discrete-time sliding mode control (DSMC) and the generation of over-large control action in the equivalent-control-based DSMC, a new DSMC method based on non-smooth control is proposed in this paper. Since there is no use of any switching term in the proposed DSMC, it is a chattering-free SMC method. Meanwhile, it is shown that the newly proposed non-smooth control-based DSMC can guarantee the same level of accuracy for the sliding mode motion as that of an equivalent control-based DSMC. To demonstrate the effectiveness of the proposed approach, a simulation example is presented.

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Topics: Sliding mode control (58%)

191 Citations


Journal ArticleDOI: 10.1016/J.AUTOMATICA.2017.12.033
Xiaojie Su1, Xinxing Liu1, Peng Shi2, Peng Shi3  +1 moreInstitutions (3)
01 Apr 2018-Automatica
Abstract: This paper is devoted to solving the problem of sliding mode control for discrete-time switched systems via an event-triggered strategy. First, a new linear switching function combined with corresponding networked sliding mode dynamics is constructed using a time-delay system design method and event-triggering scheme. Then, on the basis of the Lyapunov functional technique and the average dwell time approach, sufficient conditions for the existence of the concerned networked sliding mode control are established in terms of linear matrix inequalities. Furthermore, an event-triggered sliding mode control law is developed to drive the resultant closed-loop system trajectories into a bounded switched region and maintain them therein for subsequent periods. Finally, a verification example is given to show the effectiveness of the proposed new design techniques.

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Topics: Sliding mode control (67%), Lyapunov function (54%)

134 Citations


Journal ArticleDOI: 10.1109/TIE.2018.2815942
Haibo Du1, Xiuping Chen1, Guanghui Wen2, Xinghuo Yu3  +1 moreInstitutions (4)
Abstract: The main objective of this paper is to solve the position tracking control problem for the permanent magnet linear motor by using the discrete-time fast terminal sliding mode control (SMC) method. Specifically, based on Euler's discretization technique, the approximate discrete-time model is first obtained and analyzed. Then, by introducing a new type of discrete-time fast terminal sliding surface, an improved discrete-time fast SMC method is developed and an equivalent-control-based fast terminal SMC law is subsequently designed. Rigorous analysis is provided to demonstrate that the fast terminal SMC law can offer a higher accuracy than the traditional linear SMC law. Numerical simulations and experimental results are finally performed to demonstrate the effectiveness of the proposed approach and show the advantages of the present discrete-time fast terminal SMC approach over some existing approaches, such as discrete-time linear sliding mode control approach and the PID control method.

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127 Citations