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跟踪的输出和要抑制的干扰输入，可以实现零稳态控制误差。本研究的目的是从实用的角度开发新的有效的鲁棒伺服系统，提出了许多有趣的鲁棒伺服系统，例如具有最优稳态性能、最优干扰抑制和最优鲁棒性能的伺服系统等。特别是，在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颖而实用的抗时变摄动的鲁棒性能问题。然而，在对象存在时变的情况下，可以证明即使采用内模原理，稳态误差也可能不再是零，而实际上可能是相当大的。这项研究有…的压力提出了一种在存在时变范数有界非结构不确定性的情况下，使最坏情况下的稳态控制误差最小化的鲁棒伺服控制系统的设计方法。重点是以显式形式证明了在时变范数有界非结构不确定性存在的情况下，使稳态控制误差最大的最坏情况摄动。由此得到了计算最坏情况下的稳态误差的简单表达式。该表达式为解决最小化最坏情况下稳态控制误差的控制器设计问题提供了一种可行的方法。所提出的控制器很容易通过求解一个简单的线性规划问题来获得。此外，所提出的设计方法不需要对不确定性和对象的权重函数进行保守假设，这是以往研究中强加的。最后，通过数值算例验证了该方法的有效性。较少

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