Design of integral-augmented optival variable structure controllers

Abstract

There has been a great deal of the reaches on the Variable Structure System(VSS) or Sliding Mode Control(SMC) and its applications to uncertain systems. The essential feature of the VSS is the sliding motion(mode) on the sliding surface by utilizing high frequency switching of the control structure. As a result, it is known that the controlled system in the sliding mode is theoretically robust/insensitive to the internal parameter variations and extraneous disturbances. However, most of the surfaces developed so for linear or nonlinear are fixed in the state space and independent of a given initial condition. Thus, there exist the problems of the reaching phase for an initial condition far from the sliding surface. During the reaching phase, the controlled system may be sensitive to the parameter variations and disturbances, and moreover it is difficult to obtain the designed performance in the output. Together with the reaching phase problems, the VSS inherently has problems of high frequency oscillation of the input, so called chattering, which may excite the unmodeled dynamics. In this dissertation, new linear quadratic optimal variable structure system and nonlinear optimal VSS are presented for the improved control of uncertain systems completely without the reaching phase problems by augmenting the intentional integral to the sliding surface, and the chattering problems are also handled in the tracking control of robot manipulators with prescribed tracking performance. First, to overcome the reaching phase problems, an optimal variable structure system with an integral-augmented linear sliding surface is proposed for uncertain single-input single-output(SISO) systems subject to the persistent disturbances. The sliding surface used in this algorithm is augmented by the integral with a certain initial condition so that the resultant surface can be defined from any given initial condition in the state space in order to effectively remove the reaching phase...