多回路不同采样周期的离散系统的稳定性分析

在计算机控制系统中,多回路不同采样周期的系统是经常遇到的。对于这种系统,不能按离散系统的一般方法来分析。通常是采用这样的分析方法:通过联系两个不同采样周期的控制回路的零阶保持器,把两个回路的时间序列联系起来,以便消去其中一个整数变量,得到两个回路统一的差分方程,然后进行系统的稳定性分析。对于多回路的系统,也可用同样的方法进行处理。这种分析方法是可行的,但比较麻烦。特别是当回路数较多时,采用这种分析方法就相当费事了。本文介绍另一种分析多回路不同采样周期的系统的方法。其基本思想是,利用两个回路的Z变换算子的关系,消去其中一个算子,得到只包含一个算子的系统的闭环Z传递函数,并导出其状态方程,然后进行系统的稳定性分析。这种方法分析简单,容易掌握,而且具有普遍性。因此,它是分析计算机控制系统动态特性的一种较好的方法。

A STABILITY ANALYSIS FOR DISCRETE-TIME SYSTEM WITH MULTILOOP AND DIFFERENT SAMPLING PERIODS

In computer control system,we often come across a multiloop system with different samp-ling periods.In analyzing such a system,we always use the following method instead of the ordinary analysis method of discrete-time system,that is,using a zero-order holder,which connects two control loops with different sampl-ing periods,to bear a relation between time sequences of these two loops in order to cancel one of the integral variables and get a uniform difference quation for the two loops and then to make a stability ana-lysis of the whole system.This method is also suitable for multiloop system.However,it is quite tedious and troublesome especially when the number of loop is numerous.Another analysis method for multiloop system with different sampling periods is introduced in this paper.The basic idea of the method is to use the relationship between Z transform operators of these two loops to cancel one of them and get Z transfer function of the closed loop system which contains only one operator,and then derive its state equation and make systematic stability analysis.Because of its simplicity and flexibility,this method is a better one in analyzing the dynamic behavior of the computer control system.