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

人们普遍认为，鲁棒伺服系统是基于内模原理的，对于给定类别的期望输出进行跟踪并抑制干扰输入，它可以实现零稳态控制误差。本研究的目的是从实用的角度出发，开发新的有效的鲁棒伺服系统。在这项研究中，我们提出了许多有趣的鲁棒伺服系统，例如具有最优稳态性能的伺服系统、具有最优抗干扰性能的伺服系统和具有最优鲁棒性能的伺服系统等等。特别是在我们对具有最优鲁棒性能的伺服系统的研究中，我们提出并解决了一个新的实用的时变扰动鲁棒性能问题。然而，在存在时间变化的情况下，可以证明，即使采用内模原理，稳态误差也可能不再为零，实际上可能相当大。本文提出了一种鲁棒伺服控制系统的设计方法，在存在时变范数有界非结构不确定性的鲁棒稳定性下，使最坏情况下的稳态控制误差最小化。重点是用显式形式显示在时变范数有界非结构不确定性存在下使稳态控制误差最大化的最坏情况摄动。最后，导出了计算最坏情况下稳态误差的简单表达式。该表达式为解决最坏情况下稳态控制误差最小化的控制器设计问题提供了一种可行的方法。通过求解一个简单的线性规划问题，可以很容易地得到所提出的控制器。此外，本文提出的设计方法不需要以往研究中对不确定性加权函数和目标的保守假设。最后通过仿真验证了该方法的有效性。少

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