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Sliding Mode Control and Stability for Distributed Parameeter System with Multiple Time-delays

Author: LinYing
Tutor: GaoCunChen
School: Ocean University of China
Course: Operational Research and Cybernetics
Keywords: distribute-parameter system multiple time-delays uncertainty sliding-mode control stability
CLC: O231
Type: Master's thesis
Year: 2011
Downloads: 11
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Abstract


The distributed parameter systems have a lot of applications in the actual problems, but there are many kinds of time-delays which are more or less in the actual process of state variables, which also often contain uncertainties. These mathematical model described by the problems are often various state equation. Sliding mode variable structure control (SM-VSC) is characterized by the existence of sliding mode areas (existing sliding mode or switching surface), the phase trajectory reached to the movement will arrive in the sliding mode in finite time, then sports in sliding mode according to the predetermined way. Thus the existence of sliding mode is a key problem, it can make the system occurring changes on the structure. In practice, the system may sometimes have uncertainties, time-delays and distribution parameters. Sliding-mode control and its stability analysis problem are mainly researched for a class of distributed-parameter systems with multiple time-delays and uncertainties. The sliding-mode motion equation is established and a variable structure controller is designed, and an estimated time from the state trajectory to the sliding mode area is given. The main contents consist of several parts as follows.1. The basic theory and research situation of distributed parameter systems, sliding mode variable structure control (VSC) and stability are introduced.2. The basic theory of distributed parameter systems with time-delays and the designed methods of variable structure controller are summarized.3. Sliding-mode control problem is considered for a class of distributed-parameter systems with multiple time-delays and uncertainties. The sliding-mode motion equation is established by using a nonsingular linear transformation, a variable structure controller is designed, and an estimated time from the state trajectory to the sliding mode area is given and proved. The effectiveness and feasibility of the main result in the paper is illustrated with simulation examples. 4. Stability problem is considered for a class of distributed-parameter systems with multiple time-delays and uncertainties. By using the auxiliary functional method, dispersion theorem, Poincaréinequality, and some processing techniques of time-delays, uncertainties and external disturbances in ordinary functional differential equations, According to the sliding mode invariance for uncertainties, the stability criterion is obtained for a class of distributed-parameter systems with multiple time-delays and uncertainties.Finally, the main research results in the paper are summarized, Some problems need to be solved are proposed for the distributed parameter systems with delays.

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CLC: > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Cybernetics ( control theory, mathematical theory )
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