Embedding-Based Sliding Mode Control for Linear Time Varying Systems

Author(s)
Mohammad Reza Zarrabi,
Mohammad Hadi Farahi,
Ali Jafar Koshkouei,
Sohrab Effati,
Keith Burnham

Abstract

In this paper, a novel strategy using embedding process and sliding surface is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a sliding surface in the minimum time, and then tends to the origin along the sliding surface (SS). In the first, a SS is designed, then using an appropriate measure, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, after that a control is designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of sliding mode controls (SMCs) is a phenomenon, the so-called chattering. The proposed SMC here is piecewise continuous and chattering free. Some numerical examples is presented to illustrate the effectiveness and reliability of the proposed method.

In this paper, a novel strategy using embedding process and sliding surface is proposed. In this method, a state trajectory starting from a given initial point reaches a definite point on a sliding surface in the minimum time, and then tends to the origin along the sliding surface (SS). In the first, a SS is designed, then using an appropriate measure, an embedding is constructed to solve a time optimal control problem such that the system trajectory reaches the SS in minimum time, after that a control is designed such that the system trajectory tends to the origin along the SS. It is well-known that the main disadvantage of the use of sliding mode controls (SMCs) is a phenomenon, the so-called chattering. The proposed SMC here is piecewise continuous and chattering free. Some numerical examples is presented to illustrate the effectiveness and reliability of the proposed method.

Keywords

Time Optimal Control Problem, Measure Theory, Sliding Mode Control, Sliding Surface Design, Equivalent Control

Time Optimal Control Problem, Measure Theory, Sliding Mode Control, Sliding Surface Design, Equivalent Control

Cite this paper

nullM. Zarrabi, M. Farahi, A. Koshkouei, S. Effati and K. Burnham, "Embedding-Based Sliding Mode Control for Linear Time Varying Systems,"*Applied Mathematics*, Vol. 2 No. 4, 2011, pp. 487-495. doi: 10.4236/am.2011.24063.

nullM. Zarrabi, M. Farahi, A. Koshkouei, S. Effati and K. Burnham, "Embedding-Based Sliding Mode Control for Linear Time Varying Systems,"

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