混合系统PID控制及稳定性分析

来源期刊：中南大学学报(自然科学版)2003年第4期

论文作者：王新华 陈增强 袁著祉

文章页码：377 - 379

关键词：连续系统;离散; PID控制;混合系统;稳定性

Key words：continuous system; discrete; PID control; hybrid system; stability

摘    要：由于被控对象为常见的二阶线性连续系统,而计算机通常只对离散信号进行处理,所以控制器采用离散的PID控制器,并在连续模块与离散模块之间采用零阶保时器,从而构成一个混合反馈控制系统.由于Z变换使得时域与频域系统形成一一对应的关系,故在分析过程中把整个闭环系统都化成统一的Z变换形式,并给出此系统的开环与闭环传递函数计算公式,从而推导出开环传递函数的幅值裕度和相角裕度.应用线性矩阵不等式(LMI)方法,先设定一个线性不等式区域,形成LMI区域的特征函数来分析整个闭环系统的稳定性,通过构造一个矩阵不等式并求解出一个正定对称矩阵,使得闭环系统Z变换后的特征值都在单位圆内部,从而所得到的闭环系统具有稳定性及较强的鲁棒性.

Abstract: The PID controller is adopted as the discrete form because computers deal with discrete signals only,and zero-order holders are used between continuous and discrete modules, constructing a hybrid feedback controlling system. Because Z transformation forms a corresponding relation between time and frequency domains,the whole closed loop system is transferred into the form with Z transformation, and open loop and closed loop transformation functions are carried out, and accordingly, the magnitude and phase angle ranges are obtained for the open loop transformation function. The method of LMI is adopted, a LMI domain is designed firstly, and the eigen function of a LMI domain is formed, so we can analyse the stability of the closed system. A positive symmetrical matrix is carried out by formatting a LMI making all the eigenvalues in the unit circle. A conclusion can be drawn that the closed system is stable and has a strong robustness.