${\mathit{\boldsymbol{H}}_\infty }$ reference tracking control design for a class of nonlinear systems with time-varying delays

LIU Mei-qin; CHEN Hai-yang; ZHANG Sen-lin

doi:10.1631/FITEE.1500053

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${\mathit{\boldsymbol{H}}_\infty }$ reference tracking control design for a class of nonlinear systems with time-varying delays

Computer & Automation | Updated：2022-06-06

- ${\mathit{\boldsymbol{H}}_\infty }$ reference tracking control design for a class of nonlinear systems with time-varying delays
- 一类时变时滞非线性系统的H_∞参考跟踪控制设计
- Frontiers of Information Technology & Electronic Engineering Vol. 16, Issue 9, Pages: 759-768(2015)
- Affiliations：
  
  1.State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou~310027, China
  2.College of Electrical Engineering, Zhejiang University, Hangzhou~310027, China
- Author bio：
  
  Mei-qin LIU, E-mail: liumeiqin@zju.edu.cn
  [ "Hai-yang CHEN, E-mail: zjdxchy163@163.com" ]
  [ "Sen-lin ZHANG, E-mail: slzhang@zju.edu.cn" ]
- Funds：
- DOI：10.1631/FITEE.1500053
  CLC： TP273
- Received：10 February 2015，
  
  Revised：2015-08-14，
  
  Published：2015-12
- Accepted：
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LIU Mei-qin, CHEN Hai-yang, ZHANG Sen-lin. ${\mathit{\boldsymbol{H}}_\infty }$ reference tracking control design for a class of nonlinear systems with time-varying delays[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(9): 759-768.
DOI：

LIU Mei-qin, CHEN Hai-yang, ZHANG Sen-lin. ${\mathit{\boldsymbol{H}}_\infty }$ reference tracking control design for a class of nonlinear systems with time-varying delays[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(9): 759-768. DOI： 10.1631/FITEE.1500053.

摘要

目的

针对一类具有时变时滞的非线性系统，设计状态控制器实现闭环系统输出对参考轨迹的

∞

跟踪。

创新点

利用统一模型表示所研究的时变时滞非线性系统，修正参考模型使其更具一般性，引入缩放系数提高系统的跟踪精度。

方法

采用一个由线性时滞动态系统和有界静态非线性项组成的统一模型来描述所要研究的时变时滞非线性系统。完成系统建模后，首先给出参考轨迹跟踪的定义，以修正后的跟踪模型为参考轨迹，采用状态反馈法实现闭环控制（图1）。并对闭环系统的

∞

性能进行分析，基于此分析结果推导得到以线性矩阵不等式形式表示的跟踪控制器参数所满足的条件。该条件可以确保闭环系统

∞

意义下跟踪给定的参考信号。在控制器设计中引入缩放系数以提高跟踪精度。图2和图4分别给出跟踪控制器对正弦信号和方波信号的

∞

跟踪；图3和图5则分别表示在正弦参考信号和方波参考信号输入下，缩放系数的变大对提高跟踪效果的具体影响。

结论

针对一类具有时变时滞的非线性系统，以修正后的跟踪模型为参考轨迹，设计状态反馈控制器实现闭环系统输出对参考轨迹的

∞

跟踪，并可通过增大缩放系数提高跟踪效果。

Abstract

This paper investigates the $H_{\infty}$ trajectory tracking control for a class of nonlinear systems with time-varying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. A unified model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced

which covers most of the nonlinear systems with bounded nonlinear terms

such as the one-link robotic manipulator

chaotic systems

complex networks

the continuous stirred tank reactor (CSTR)

and the standard genetic regulatory network (SGRN). First

the definition of the tracking control is given. Second

the $H_{\infty}$ performance analysis of the closed-loop system including this unified model

reference model

and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the $H_{\infty}$ sense. The reference model adopted here is modified to be more flexible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally

a CSTR system is provided to demonstrate the effectiveness of the established control laws.

关键词

Keywords

references

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