不确定线性时滞系统模型参考自适应控制研究  

Model reference adaptive control of uncertain linear system with time delay

作　　者：李美超 陈龙祥[1] 蔡国平[1] Li Meichao;Chen Longxiang;Cai Guoping(Department of Engineering Mechanics,School of Naval Architecture,Ocean &Civil Engineering, Shanghai Jiao Tong University,200240,Shanghai,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院工程力学系,上海200240

出　　处：《应用力学学报》2018年第6期1207-1213,1415,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11472171;11772187);上海市自然科学基金(14ZR1421000)

摘　　要：以具有不确定参数和时滞的线性时滞系统为对象,开展时滞系统的模型参考自适应控制研究。首先利用时滞控制力项的差分方程对系统的状态变量进行增广,将时滞系统动力学方程变为形式上不含有时滞项的增广状态方程。然后根据时滞系统动力学方程和已确定的参数建立相应参考模型,并采用线性二次调节器(LQR)设计参考模型控制律,以保证闭环参考模型系统稳定。最后基于参考模型的LQR控制律,采用基于类观测器的模型参考自适应控制方法设计相应的自适应控制律。因此,针对原时滞系统动力学方程,本文所设计的时滞控制律由LQR控制律和自适应控制律两部分组成。数值仿真结果表明:本文所使用的基于LQR的自适应控制方法在系统参数和时滞不确定的情况下,能够有效地跟踪稳定的参考模型的动力学行为,从而对系统进行控制。该方法可以作为LQR控制方法的有益补充,进一步改善控制系统的动力学行为。A study of model reference adaptive control of linear systems with time delay and uncertain parameters is presented in this paper.Firstly,by means of augmented state variables of a differential equation with input-delay, the dynamic equation of a delayed system is changed to an augmented state equation without delay in the form. Then a reference model is introduced based on the dynamic equation of the delayed system and known variables, and the control law for the reference model is derived by using linear quadratic regulator (LQR)approach to keep the closed-loop reference model stable.Finally,a model reference adaptive control law with like-observer is implemented based on LQR.Hence,the time-delay control law which consists of LQR control law and adaptive control law is designed for the original dynamic equation with delay.Numerical examples have been exhibited to illustrate the effectiveness of the proposed adaptive control scheme based on LQG for uncertain time-delay system to track the desired dynamic response of a reference model.Furthermore,under the condition of uncertain parameters and delay,this method can be regarded as a kind of beneficial supplement of LQR and will further improve the dynamic behavior of a controlled system.

关 键 词：时滞 不确定参数 自适应控制 

分 类 号：O322[理学—一般力学与力学基础]