Study on design of the optimal robust servo control systems and the application to real systems

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It is widely accepted that a robust servo system is based on the internal model principle and can achieve zero steady-state controlled error for a given class of the desired outputs to be tracked and disturbance inputs to be rejected. The purpose of this study is to develop new and effective robust servo systems from the practical point of view.In this study, we have proposed many interesting robust servo systems, for example, servo systems with the optimal steady-state performance, with the optimal disturbance rejection and with the optimal robust performance, and so on. In particular, in our study on servo system with the optimal robust performance, we have posed and have solved on a novel and practical robust performance problem against time-varying perturbations.In the presence of time variation in the plant, however, it can be shown that the steady-state error may no longer be zero and can in fact be quite large even if the internal model principle is employed. This study has pres … More ented a design method of robust servo control system that minimizes the worst case steady-state controlled error under the robust stability in the presence of time-varying norm-bounded unstructured uncertainty. The key point is to show the worst case perturbation that maximizes the steady-state controlled error in the presence of time-varying norm-bounded unstructured uncertainty in an explicit form. As a result, a simple expression is derived for calculating the worst case steady-state error. This expression can provide a feasible method to solve the design problem of controller that minimizes the worst case steady-state controlled error. The proposed controller is obtained easily by solving a simple linear programming problem. Moreover, the proposed design method does not require the conservative assumptions on the weighting function of uncertainty and the plant, which had been imposed on the previous studies. Finally a numerical example illustrates the validity of the proposed method by a simulation. Less