Controller design for delay systems via eigenvalue assignment - on a new result in the distribution of quasi-polynomial roots

Wang Honghai; Liu Jianchang; Yang Feisheng; Zhang Yu

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Controller design for delay systems via eigenvalue assignment - on a new result in the distribution of quasi-polynomial roots

机译：通过特征值分配的延迟系统控制器设计-准多项式根分布的新结果

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摘要

This paper considers the eigenvalue distribution of a linear time-invariant (LTI) system with time delays and its application to some controllers design for a delay plant via eigenvalue assignment. First, a new result on the root distribution for a class of quasi-polynomials is developed based on the extension of the Hermite-Biehler theorem. Then, such result is applied to proportional-integral (PI) controller parameter design for a first-order plant with time delay through pole placement. The complete region of PI gains can be obtained so that the rightmost eigenvalues in the infinite eigenspectrum of the closed-loop system with delay plant are assigned to desired positions in the complex plane. Furthermore, on the basis of the previous result, this paper also extended the PI control to the proportional-integral-derivative (PID) control. It is worth pointing out that this work aims to improve the performance of the closed-loop system on the premise of guaranteeing the stability.

机译：本文考虑了具有时滞的线性时不变（LTI）系统的特征值分布及其在通过特征值分配的延迟工厂的某些控制器设计中的应用。首先，基于Hermite-Biehler定理的扩展，得出了一类拟多项式根分布的新结果。然后，将这样的结果应用于一阶设备的比例积分（PI）控制器参数设计，该参数具有通过极点放置而产生的时间延迟。可以获得PI增益的完整区域，以便将具有延迟植物的闭环系统的无限本征谱中最右边的本征值分配给复杂平面中的所需位置。此外，在先前结果的基础上，本文还将PI控制扩展到比例积分微分（PID）控制。值得指出的是，这项工作的目的是在保证稳定性的前提下提高闭环系统的性能。

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《International Journal of Control》 |2015年第12期|共20页
作者
Wang Honghai; Liu Jianchang; Yang Feisheng; Zhang Yu;
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正文语种 eng
中图分类控制论、信息论（数学理论）;自动控制、自动控制系统;
关键词
Hermite-Biehler theorem; eigenvalue assignment; time delay; proportional-integral (PI) control; proportional-integral-derivative (PID) control;

机译：Hermite-Biehler定理;特征值分配;时间延迟;比例积分（PI）控制;比例积分微分（PID）控制;

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专利

1. Controller design for delay systems via eigenvalue assignment - on a new result in the distribution of quasi-polynomial roots [J] . Wang Honghai, Liu Jianchang, Yang Feisheng, International Journal of Control . 2015,第10a12期

机译：通过特征值分配的延迟系统控制器设计-准多项式根分布的新结果
2. Delay Margin Computation and Controller Design of Time-delayed AGC System Based on Root Locus Analysis [J] . Liufu Chen, Tao Zhou, Zhenlin Xu, E3S Web of Conferences . 2021,第a期

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3. New method of fault-distribution-dependent memory-reliable controller design for discrete-time systems with stochastic input delays [J] . Gu Z.Wang D.Yue D. Control Theory & Applications, IET . 2011,第1期

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4. New Result on Low-Order Controller Design for First-Order Delay Processes via Eigenvalue Assignment [C] . Honghai Wang, Jianchang Liu, Feisheng Yang, IFAC World Congress . 2014

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5. Design of controllers for nonlinear electrohydraulic systems with time delays. [D] . Ge, Jianlin. 1992

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6. An alternative design approach for Fractional Order Internal Model Controllers for time delay systems [O] . C.I. Muresan, I. Birs, R. De Keyser 2021

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7. Eigenvalue assignment for systems with multiple time-delays [O] . Robert Schmid, Qingbin Gao, Nejat Olgac 2015

机译：具有多个延时的系统的特征值分配
8. Design of Constant Gain Dissipative Controllers for Eigensystem Assignment in Passive Systems [R] . Maghami, P. G. , Gupta, S. 2004

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Controller design for delay systems via eigenvalue assignment - on a new result in the distribution of quasi-polynomial roots

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