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Sliding Mode Control for Uncertain Systems with TimeDelay
Author: ZuoDi
Tutor: JingLi
School: Shenyang Normal
Course: Operational Research and Cybernetics
Keywords: Uncertainty Timedelay systems Sliding mode control discretetime systems
CLC: O231
Type: Master's thesis
Year: 2012
Downloads: 77
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Abstract
In actual process of industry, timedelays and uncertainties are very common invarious systems, they’re also two of the important factors which lead to instability.Therefore, it’s very important to research the uncertain control systems withtimedelays and the study has very important value in practice. Sliding mode controlhas selfadaptabilty of the uncertainty for internal parameters and externaldisturbances, it’s a very effective control method. Because of this, it has a strongappeal to the researchers. In this paper, we consider the sliding mode variablestructure control problem of uncertain systems with timedelays.The main content is summarized as follows：Firstly, simply introduce the development history of sliding mode control and thedevelopment history of variable structure control for discretetime systems, brieflyintroduce the elementary definitions, the elementary methods and design method ofsliding mode control.Secondly, the slide mode control problem is considered for a class of variabletimedelay system. There exist many variable timedelay and uncertainties. Using theLyapunov method and the Schur Complement Lemma, the stability of the slide modeis demonstrated. A variable structure controller is designed, which is more easy andefficient. It makes the system’s state trajectories can be ensured to reach the chosenslide mode surface at initial time and keep on the slide mode surface. Simulationresults demonstrate the effectiveness of the presented method.Thirdly, the slide mode control problem is considered for a class of multydelaydiscretetime system. First, by using the linear matrix inequalities method, proceedlinear transformation for the system, the slide mode surface is designed for the system.Based on the Lyapunov function method, the stability of the slide mode is proved.Then, the controller is designed to make sure the state of the system will arrive at theslide mode. Last, it gives the corresponding controller and the correspondingsimulation example.Fourthly, the slide mode control problem is considered for a class of uncertaindiscretetime systems with input and state delays. First, by using two time lineartransformation for the system to transform the original system into a linear systemwithout delay. Then the slide mode surface and the control law are designed for thesystem without delay, the stability for the system is discussed, and the simulationexample is given for the system.

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