scholarly journals Sliding mode control of continuous-time switched systems with signal quantization and actuator nonlinearity

2020 ◽  
Vol 103 (1) ◽  
pp. 003685042091215
Author(s):  
Yiming Cheng ◽  
Tianhe Liu ◽  
Rui Weng ◽  
Bo Cai ◽  
Changhong Wang
Keyword(s):  
Sliding Mode Control ◽  
Continuous Time ◽  
Switched Systems ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Signal Quantization ◽  
Mode Control ◽  
Uniformly Asymptotical Stability ◽  
Actuator Nonlinearity

This article investigates sliding mode control for a class of continuous-time switched systems with signal quantization, actuator nonlinearity and persistent dwell-time switching that can guarantee the globally uniformly asymptotical stability of the closed-loop system. First, a sliding surface is devised for the switched system and sufficient conditions are proposed to ensure the globally uniformly asymptotical stability of the sliding motion equation by utilizing multiple Lyapunov function technique. Second, the sliding mode control laws, based on the parameters of quantizer, actuator nonlinearity and disturbance, are devised to stabilize the closed-loop systems. Moreover, sufficient conditions are given to guarantee the devised sliding surface’s reachability. Finally, the superiority and effectiveness of developed results is illustrated via a numerical simulation.

Adaptive sliding mode control for stochastic switched systems with actuator faults

2018 ◽  
Vol 41 (7) ◽  
pp. 1880-1887
Author(s):  
Yonghui Liu
Keyword(s):  
Sliding Mode Control ◽  
Switched Systems ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Adaptive Sliding Mode Control ◽  
Sliding Surface ◽  
Actuator Faults ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Actuator Degradation

The problem of adaptive sliding mode control is considered for a class of stochastic switched systems with actuator degradation. In this work, the input matrix for each subsystem is unnecessarily the same. Thus, a weighted sum approach of the input matrices is introduced such that a common sliding surface is designed. By online estimating the loss of effectiveness of the actuators, an adaptive sliding mode controller is designed. It can not only compensate the effect of the actuator degradation effectively, but also reduce the conservatism that the bound of the actuator faults should be known in advance. Moreover, it is shown that the reachability of the sliding surface can be guaranteed. Furthermore, sufficient conditions on the mean-square exponential stability of the sliding mode dynamics are obtained via the average dwell time method. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed method.

Sliding Mode Control for Uncertain Markov Switched Systems

2015 ◽  
Vol 740 ◽  
pp. 278-282
Author(s):  
Zhao Lan He ◽  
Zong Ze Liu ◽  
Xian Xian Tang
Keyword(s):  
Sliding Mode Control ◽  
Switched Systems ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Sufficient Condition ◽  
Closed Loop System ◽  
Standard Type ◽  
Mode Control ◽  
Sliding Mode Dynamics

This Paper deals with the sliding mode control of a class of uncertain Markov switched systems. By using linear transformation, the system is transformed into standard type. A sufficient condition of the existence of a sliding mode dynamics is derived, and an explicit parameterization of desired sliding surface is also given. A sliding mode controller is then designed to guarantee exponential stability of the overall switched closed-loop system. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approaches.

Robust Observer-Based Finite Time Sliding Mode Control for One-Sided Lipschitz Systems With Uncertainties

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Junchao Ren ◽  
Jie Sun ◽  
Fangfang Li
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Parameter Uncertainties ◽  
Robust Observer ◽  
Mode Control ◽  
Finite Time Boundedness

Abstract This paper investigates the problem of observer-based finite time sliding mode control (SMC) for a class of one-sided Lipschitz (OSL) systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and output matrices but also in the nonlinear function. For a time interval [0,T], we divide it into two parts: one part is the reaching phase within [0,T*] and another part is the sliding motion phase within [T*,T]. First, the reachability of the sliding mode surface with T*≤T is proved. Next, several conditions are proposed which ensure robust finite time boundedness (FTB) of the corresponding closed-loop systems in the interval [0,T*] and [T*,T], respectively. Then, the sufficient conditions, which guarantee robust finite time boundedness of the closed-loop system in whole time interval [0,T], are given in terms of linear matrix inequalities (LMIs), and further the robust observer and controller can be designed in an LMI frame. A convex optimization problem subject to LMIs is formulated to optimize the desired performance indices of interest to us. Finally, a practical example is given to demonstrate the effectiveness of the proposed methods.

Optimal Sliding Mode Control for a Class of Underactuated Nonlinear Systems

2011 ◽  
Author(s):  
Parham Ghorbanian ◽  
Sergey G. Nersesov ◽  
Hashem Ashrafiuon
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Domain Of Attraction ◽  
Loop System ◽  
Closed Loop System ◽  
Sliding Surfaces ◽  
Mode Control

In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using an optimal sliding mode control in the presence of system uncertainties is presented. A performance objective is used to optimally select the parameters of the sliding mode control surfaces subject to state and input constraints. It is shown that the closed-loop system trajectories reach the optimal sliding surfaces in finite time and a constructive methodology to determine exponential stability of the closed-loop system on the sliding surfaces is developed which ensures asymptotic stability of the overall closed-loop system. The framework further provides the basis to determine an estimate of the domain of attraction for the closed-loop system with uncertainties. The results developed in this work are experimentally validated using a linear inverted pendulum testbed which show a good match between the actual domain of attraction of the upward equilibrium state and its analytical estimate.

scholarly journals New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3811
Author(s):  
Katarzyna Adamiak ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Continuous Time ◽  
Sliding Mode ◽  
Representative Point ◽  
Time Varying ◽  
Sliding Surface ◽  
External Disturbances ◽  
Mode Control ◽  
Switching Type ◽  
Time Systems

This study considers the problem of energetical efficiency in switching type sliding mode control of discrete-time systems. The aim of this work is to reduce the quasi-sliding mode band-width and, as follows, the necessary control input, through an application of a new type of time-varying sliding hyperplane in quasi-sliding mode control of sampled time systems. Although time-varying sliding hyperplanes are well known to provide insensitivity to matched external disturbances and uncertainties of the model in the whole range of motion for continuous-time systems, their application in the discrete-time case has never been studied in detail. Therefore, this paper proposes a sliding surface, which crosses the system’s representative point at the initial step and then shifts in the state space according to the pre-generated demand profile of the sliding variable. Next, a controller for a real perturbed plant is designed so that it drives the system’s representative point to its reference position on the sliding plane in each step. Therefore, the impact of external disturbances on the system’s trajectory is minimized, which leads to a reduction of the necessary control effort. Moreover, thanks to a new reaching law applied in the reference profile generator, the sliding surface shift in each step is strictly limited and a switching type of motion occurs. Finally, under the assumption of boundedness and smoothness of continuous-time disturbance, a compensation scheme is added. It is proved that this control strategy reduces the quasi-sliding mode band-width from O(T) to O(T3) order from the very beginning of the regulation process. Moreover, it is shown that the maximum state variable errors become of O(T3) order as well. These achievements directly reduce the energy consumption in the closed-loop system, which is nowadays one of the crucial factors in control engineering.

scholarly journals Position Tracking Control for Permanent Magnet Linear Motor via Continuous-Time Fast Terminal Sliding Mode Control

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Gao ◽  
Xiuping Chen ◽  
Haibo Du ◽  
Song Bai
Keyword(s):  
Sliding Mode Control ◽  
Continuous Time ◽  
Control Method ◽  
Sliding Mode ◽  
Terminal Sliding Mode Control ◽  
Terminal Sliding Mode ◽  
Mode Control ◽  
Nonsingular Terminal Sliding Mode ◽  
Fast Terminal Sliding Mode ◽  
Permanent Magnet Linear Motor

For the position tracking control problem of permanent magnet linear motor, an improved fast continuous-time nonsingular terminal sliding mode control algorithm based on terminal sliding mode control method is proposed. Specifically, first, for the second-order model of position error dynamic system, a new continuous-time fast terminal sliding surface is introduced and an improved continuous-time fast terminal sliding mode control law is proposed. Then rigorous theoretical analysis is provided to demonstrate the finite-time stability of the closed-loop system by using the Lyapunov function. Finally, numerical simulations are given to verify the effectiveness and advantages of the proposed fast nonsingular terminal sliding mode control method.

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