출력 예측 성능을 갖는 제어 입력 변환 터미널 적분 슬라이딩 모드 제어

Abstract

In this note, the discontinuous and continuous control input transformation integral terminal sliding mode control(TSMC)s by using the integral sliding surface without the reaching phase and with the output prediction performance as the one approach are presented for second order uncertain plants. Theoretically discontinuous and practically continuous control input transformed TSMCs are proposed when Δb ≠ 0, while it is assumed that Δb=0 in most of the TSMCs for easy design. Applying the idea of [32] for the linear sliding mode control(LSMC), the integral sliding surface without the reaching phase is suggested for the TSMCs. The exponent of the power function can be any positive numbers satisfying q＞p＞0 such that 0＜p/q＜1. The ideal sliding dynamics of the integral sliding surface is derived and the real robust output can be predicted, predesigned, predetermined by means of the solution of the ideal sliding dynamics. The transformed control input is suggested for generating the sliding mode for the entire trajectory from any given initial condition to the origin based on defining a new auxiliary nonlinear state. The closed loop exponential stability together with the existence condition of the sliding mode on the predetermined sliding surface is investigated theoretically for the complete formulation of the TSMC design for the output prediction performance. As a remedy of the singularity, a certain limit is imposed on the new auxiliary nonlinear state. For practical applications, a continuous approximation of the discontinuous TSMC is made by means of the modified boundary layer function. In addition, the closed loop bounded stability together with the existence condition of the sliding mode by the continuous TSMC is analyzed. The discontinuity of the control input as the inherent property of the sliding mode control is much improved in view of the practical applications. Through a design example and simulation studies, the effectiveness of the proposed discontinuous and continuous control input transformed TSMCs is verified.