Computation of All Stabilizing PID Gain for Second-Order Delay System

Rihem Farkh,Kaouther Laabidi,Mekki Ksouri

doi:10.1155/2009/212053

Rihem Farkh, Kaouther Laabidi + Show 1 more

Open Access

https://doi.org/10.1155/2009/212053

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Abstract

The problem of stabilizing a second-order delay system using classical proportional-integral-derivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasipolynomials, is used to seek the set of complete stabilizing PID parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid or a triangle.

Highlights

Dead times are often encountered in various engineering systems and industry processes such as electrical and communication network, chemical process, turbojet engine, nuclear reactor, and hydraulic system
The stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid or a triangle
In 22–24, the characterization of the set of all stabilizing P/PI/PID parameters is given by using the Hermit-Biehler Theorem for polynomials for a class of time delay system which verify the interlacing property at high frequencies

Summary

Introduction

Dead times are often encountered in various engineering systems and industry processes such as electrical and communication network, chemical process, turbojet engine, nuclear reactor, and hydraulic system. In 14, 15 , the authors propose a new PID neural networks PIDNN which is a dynamic multilayer network based on P, I, and D neurons This PIDNN is used to control multivariable plants 15 and has the ability to control time delay system 14. In 22–24 , the characterization of the set of all stabilizing P/PI/PID parameters is given by using the Hermit-Biehler Theorem for polynomials for a class of time delay system which verify the interlacing property at high frequencies. This method, is complex and there are difficulties to achieve the stabilizing range of proportional parameter. Our algorithm is more simple and faster in time computing than the other presented in 24

Preliminary Results for Analyzing Time Delay System

PID Control for Second Order Delay System

Conclusion