Control Systems Design Based on the Principle of Matching and Its Application to Mechanical Systems

匹配原理是由英国Zakian博士提出的一种新的设计原理，它能明确地考虑控制系统的实际运行条件。该原理特别适用于要求控制变量的大小小于预定值的关键控制系统的设计。该原理将一个关键控制系统的设计转化为一个用不等式法表示的问题。在这个项目中，为了在实际设计中有效地使用该原理，解决了一些问题。1)由于大多数控制系统都是通过数字控制器实现的，因此被控变量的样本间行为对于关键控制系统的设计是非常重要的。对于一类重要的外源输入，给出了样本数据控制系统的匹配条件。2)提出了线性矩阵不等式的应用，作为求解该原理所要求的一组不等式的有效计算方法。3)讨论了多目标遗传算法在参数搜索中的应用。阐明了传统多目标优化与不等式求解的根本区别。提出了一种新的遗传算法来求解该原理所要求的一组不等式。4)匹配原理通常需要一个具有积分作用的控制器。讨论了一类积分控制器的系统设计方法。提出了回路传递恢复技术在关键控制系统设计中的应用。5)作为机械系统的一种应用，研制了救护车主动控制床。通过控制床的倾斜，可以减少离心力对病人的影响。

The principle of matching proposed by Dr. Zakian in UK is a new design principle which can explicity take account of real operating conditions of a control system. The principle is especially useful to design critical control systems which require to keep the magnitude of the controlled variables less than prescribed values. The principle converts a design of a critical control system to a problem formulated as the method of inequalities.In this project some issues are resolved for the effective use of the principle in practical designs. The results are summarized as follows:1) Since most control systems are realized by using a digital controller, inter-sample behavior of the controlled variables are important for the critical control systems design. The matching conditions for sample-data control systems have been derived for an important class of exogenous inputs.2) An application of linear matrix inequalities has been proposed as an efficient computational method for solving a set of inequalities required by the principle.3) An application of multiobjective genetic algorithms for the parameter search is discussed. The fundamental difference of the conventional multiobjcetive optimization and the solution of inequalities has been clarified. A new genetic algorithm has been proposed to solve a set of inequalities required by the principle.4) The principle of the matching often requires a controller with integral action. A systematic design method of a class of integral controllers has been discussed. An application of a loop transfer recovery technique to critical control systems design has been proposed.5) As an application of mechanical systems, actively controlled bed for an ambulance has been developed. The effect of the centrifugal force acting on a patient is reduced by controlling the tilt of bed.