Sliding Mode Control for Linear Uncertain Systems with Input and State Delays

Abstract

The problem of designing sliding mode controllers investigated the feasibility of the sliding surface combined for a class of linear systems with uncertainties and both input with a predictor to compensate for the input delay of the and time state delays is investigated. A particular linear system. Robust integral sliding mode control for uncertain transformation is defined to transform the time-delay system into stochastic systems with time-varying delay was researched by a delay-free form first. Then, the sliding mode controller is Niu and Ho [9]. designed based on the transformed system. Optimal control The study of uncertain systems with either state-delay or theory is adopted to construct the optimal sliding manifold with a quadratic performance index minimized. The selected control nput-delay has been pad much attention in the past decade law can ensure the existence of the sliding mode and alleviate[7]-[1O]. However, with regard to the control of system chattering effectively in the sliding motion. About the featuring both state and input delays, only a few studies have uncertainties, the cases of matched condition and unmatched been reported in the literature. In this paper, based on SMC, a condition are studied respectively. Furthermore, a sufficient class of linear uncertain systems with both input delay and condition that guarantees the global asymptotic stability of the state delay are investigated. A novel systematic SMC system original system is derived. Finally, a numerical example is given design methodology is proposed. to illustrate the proposed approach.This paper is organized as follows. The next section describes the system that will be studied. In Section III a linear Index Terms -Sliding mode control, uncertain systems, timetransformation is defined to map the original system into a delay systems, optimal control. delay-free form. Section IV presents the design of the sliding I. INTRODUCTION mode controller in detail. The optimal sliding manifold design based on optimal control theory is presented in Section A. Time delay is quite common in various engineering systemsThe design of the control law that consists of a continuous such as chemical processes, hydraulic systems, biological control action and a discontinuous control action is carried out systems and economic systems. Compared to the systems in Section B. A sufficient condition for the asymptotic without delay, the presence of delay makes it more difficult to stability of the original system with the proposed control law achieve the satisfactory performance of the systems. Another is given in Section C. Section V performs a simulation major problem in real-world systems is the robust control to example to verify the effectiveness of the proposed scheme. minimize the effects of uncertainties. In recent years, there is II. PROBLEM STATEMENTS an increasing interest in the development of robust control systems for processes having time delays and uncertainties.Consider the uncertain retarded system described by Many approaches have be...

Application of the Preview Control Method to the Optimal Tracking Control Problem for Continuous-Time Systems with Time-Delay

“…First, we eliminate the time-delay of system (1) through a transformation. Utilizing the transformation in the literature [7],…”

“…References [2,3] introduced state-delay systems according to this insight, and in the literature [4][5][6] they have studied input-delay systems. Reference [7] has discussed systems with state and input delays.…”

“…We notice that [7] studied sliding mode control and the regulator problem, but the method of eliminating time-delay is universally applicable. Furthermore, a preview control system will be a normal control system when the preview length goes to zero.…”

“…Based on these observations, the contribution of this paper is to apply preview control theory to the optimal tracking control problem for continuous-time control systems that are subject to state and input delays. First, according to a transformation in the literature [7], the timedelay system is transformed into the form of a nondelayed system. Second, by dealing with the reference signal, the tracking problem of the time-delay system is converted to the tracking problem of the nondelayed system.…”

Sliding Mode Control of Vibration in Uncertain Time-delay Systems

“…However, they did not consider the mismatched parameter uncertainties and external disturbances. Pang et al (2006) proposed a SMC method for a class of linear uncertain systems with both state delays and input delays. A key step in both methods is to use a state predictor for eliminating the input delays.…”