基于采样PD反馈的倒立摆控制系统的稳定性  

STABILITY OF AN INVERTED PENDULUM WITH A SAMPLED-DATA PD FEEDBACK CONTROL

作　　者：王强 梁松 王在华 Wang Qiang;Liang Song;Wang Zaihua(Army Engineering University ofP LA,Nanjing 211101,China;State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]解放军陆军工程大学,南京211101 [2]南京航空航天大学机械结构力学及国家重点实验室,南京210016

出　　处：《动力学与控制学报》2018年第4期377-384,共8页Journal of Dynamics and Control

基　　金：国家自然科学基金(11372354)~~

摘　　要：数字采样控制是当代主流控制技术,具有变更控制律方便、可靠性高、实时性好、抗干扰能力强等特点.本文研究基于采样PD反馈的倒立摆控制系统自平衡问题,其受控方程是一类具有时变时滞的时滞微分方程,其时滞是分段线性函数.首先将闭环系统方程转化为一个差分方程,然后研究了时滞量和采样周期对差分方程的稳定性区域的影响,进而给出了使差分方程具有最快收敛速度的最优增益的计算方法,最后研究了时滞量和采样周期对差分方程收敛速度的影响.数值算例表明,时滞量和采样周期对倒立摆控制系统稳定性以及收敛速度具有重要影响.Sampled-data control is a major technology in contemporary control engineering,with a number of advantages such as easy modification of the control law,high reliability,good real-time performance and strong robustness against disturbance,and so on. This paper studies a controlled inverted pendulum with a sampled-data PD feedback,which is described by a differential equation with a time-variant delay,where the delay is piecewise linear with respect to time. The motion equation of the closed-loop is firstly converted into a difference equation,the effect of the delay value and the sampling period on the stable region in the gain plan is discussed,and then a method is given for calculating the optimal feedback gains that minimize the maximal module of the characteristic roots of the difference equation within the stable region. Finally,the influence of the delay and the sampling period on the convergent speed of the difference equation is analyzed. The numerical results show that both the delay and the sampling period have significant influence on the stability and convergent speed of the controlled inverted pendulum.

关 键 词：倒立摆 采样控制 时滞 稳定区域 最优增益 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]