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An Improved Continuous Integral Variable Structure Systems with Prescribed Control Performance for Regulation Controls of Uncertain General Linear Systems

불확실 일반 선형 시스템의 레귤레이션 제어를 위한 사전 제어 성능을 갖는 개선된 연속 적분 가변구조 시스템

  • Lee, Jung-Hoon (Dept. of Control & Instrumentation Eng. Gyeongsang Nat. University)
  • Received : 2017.08.18
  • Accepted : 2017.11.23
  • Published : 2017.12.01
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Abstract

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the $G_1$ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.

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References

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