基于特征模型的PID控制器参数的满意解

本文提出一种通过PID控制器使系统同时满足暂态指标和稳态指标约束的满意控制设计方法.该方法避免了PID参数的图形和经验求解法.根据控制对象的特征参数模型,通过离散状态方程对原连续系统进行控制器设计.在控制系统的多指标约束下,将PID参数的计算转化为离散Lyapunov矩阵不等式,使用PID三个参数,配置系统闭环极点于指定圆形区域而使闭环系统具有较好的动态品质和一定的稳定裕度.积分器的引入,保证了闭环系统稳态无差.给使用计算机自动求解PID参数提供了新的方法,计算实例表明了该方法的有效性.

Satisfactory solution of PID controller parameter value based on the characteristic model

The paper presents a method of PID controller's design that satisfying the conditions of transient index and stability index. The method avoids solving PID parameter by sketch and experience. According to characteristic model of controlling object, the controller of initial continuous system is designed by discrete state equations. Subjecting to multi index of control system, the calculation of PID parameters is translated into discrete Lyapunov matrix inequality. And using three PID parameters, the poles of closed loop system are collocated in appointed circular region. Thereby closed loop system has better dynamic quality and wider stability margin. It is guaranteed the steady state error to be zero by introducing integral calculus into the closed loop system. It is providing a new method for automatically solving the PID parameter values by computer and the calculating example proofs the validity of the method.