具有解耦性能的离散时间线性多变量系统最优跟踪控制  

Optimal Tracking Control Method for Discrete-time Linear Multivariable Systems With Decoupling Performance

作　　者：富月 陈威 FU Yue;CHEN Wei(State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110004)

机构地区：[1]东北大学流程工业综合自动化国家重点实验室,沈阳110004

出　　处：《自动化学报》2022年第8期1931-1939,共9页Acta Automatica Sinica

基　　金：国家自然科学基金(61991403,61991400);辽宁省教育厅创新人才项目(ZX20200070)资助。

摘　　要：在传统线性二次跟踪控制方法的基础上,针对一类具有强耦合特性的离散时间线性多变量系统,提出了一种具有解耦性能的最优跟踪控制方法.首先为实现解耦,将耦合项作为可测干扰,基于零和博弈思想提出了一种新的性能指标;然后针对该性能指标,利用极小值原理设计最优跟踪控制器,通过适当加权矩阵的选择,同步实现解耦和跟踪;最后进行仿真实验,仿真结果表明了该方法的有效性以及在最优性能等方面的优越性.In this paper,for a class of discrete-time multivariable linear systems with strong coupling property,based on the traditional linear quadratic tracking control method,an optimal tracking controller with decoupling performance is proposed.First,in order to achieve decoupling,the coupling term is viewed as the measurable disturbance,and then a novel performance index which is inspired by the two-player Zero-Sum game problem is introduced.Based on the novel performance index,the optimal tracking controller is derived by using the minimum principle.Then,it is proved that by choosing appropriate weighting matrices,the proposed method can simultaneously decouple the closed-loop system in dynamic and make the tracking error converge asymptotically.Finally,simulations are conducted,whose results demonstrate the effectiveness of the proposed method and its superiority in optimal performance comparing with the traditional controller.

关 键 词：解耦 跟踪控制 离散时间线性系统 多变量系统 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]