具有采样反馈的力控制系统稳定性

STABILITY OF A FORCE CONTROL SYSTEM WITH SAMPLED-DATA FEEDBACK

基于计算机的数字采样控制对离散信号进行运算并向作动器提供控制输入,是当前的主流控制技术.数字采样控制系统是这样一类控制系统,其控制对象由微分方程(组)描述,而控制律由离散采样信号给出.以采样PD(proportional-derivative)反馈作用下的单自由度力控制系统为例,基于离散系统的稳定性分析方法,研究采样控制律对控制系统稳定性的影响.为了突出采样反馈的作用,将系统取为无刚度、无阻尼的最简单形式.不同于已有研究假设位移采样信号与速度采样信号相互同步,本文研究当位移采样信号与速度采样信号不同步时受控系统的稳定性,发现位移采样信号与速度采样信号的采样周期不同组合对受控系统在增益平面上的稳定性区域有重要影响.结果表明,对所关心的三种数字采样反馈控制律,当位移采样信号滞后于速度采样信号一个采样周期时,受控系统具有最大的稳定性区域且对相同的增益值可以有最好的稳定效果.论文对这种现象进行分析,给出了一种力学解释.

Sampled-data control,or digital control,is a major control technology in modern engineering.Based on digital computers,it provides actuators with control inputs in terms of discrete signals.A sampled-data control system is a controlled time-continuous system under sampled-data control.The paper investigates the effects of sampled-data controls on the system stability via an SDOF force control system under sampled PD(proportional-derivative) feedbacks,by means of stability analysis for discrete systems.In order to highlight the role of the sampled-data controls,the uncontrolled system is assumed to be fully free.Unlike in the previous studies where the sampled displacement signal and the sampled velocity signal are synchronic,the study focuses on the system stability for the case when the sampled displacement signal and the sampled velocity signal are not synchronic.A key observation is that when the controller uses the sampled velocity signal as well as the sampled displacement signal delayed an additional sampling period,the controlled system admits a largest stable region of the feedback gains and it decays fastest to the unique equilibrium,among the three sampled-data controllers.The paper gives a discussion of this phenomenon from the viewpoint of mechanics.