A New Method for Computing Quadratic Cost Functionals and Its Application to Control System Design

• Main Authors: Chuang Ying-Hung, 莊英鴻
• Other Authors: Hwang Chyi
• Format: Others
• Language: zh-TW
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/70532551787532645994

碩士 === 國立成功大學 === 化學工程研究所 === 81 === The integral of the squared error is often used as a performance index in the design of control systems. The evaluation of ISE for systems having no delays can be easily accomplished by a parametric method which does not need to find the time response of the system. For systems with time delays, however, the evaluation of ISE is not an easy task. In this thesis, a direct numerical approach is presented to the evaluation of quadratic cost functionals for linear systems having multiple time delays. It is based on making use of the Parseval theorem and the bilinear transformation so that the computation of ISE involving time delays can be evaluated accurately and efficiently by means of a numerical integration method with automatic step-size adjustment. With this numerical algorithm of computing ISE, the following three control problems are solved: (1)Optimal reduced-order models with time delay: By representing the delay-free part of the reduced-order model in the Routh .gamma.-.delta. canonical form, the optimal parameters and the time delay are searched by an existing gradient-based method such that the ISE between the unit step responses of the system and model is minimized. (2)Design of an optimal PID controller satisfying prescribed gain and phase margins: The PID controller is find for a system such that the integral of the squared error of the closed-loop system subject to a unit step input is minimized, while satisfying the prescribed gain and phase margins. (3)Design of an optimal digital controller for sampled-data systems: With the integral of squared-error as the performance index, the parameters of the digital PID controller are searched to minimize the performance index.