Open AccessParametric synthesis of a robust PID-controller for interval control system with aperiodic transient process
Author(s) -
Tatiana Ezangina,
Sergey An. Gayvoronskiy,
Ivan Khozhaev
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/707/1/012009
Subject(s) - control theory (sociology) , pid controller , aperiodic graph , parametric statistics , controller (irrigation) , polynomial , mathematics , transient (computer programming) , interval (graph theory) , process (computing) , control system , computer science , control engineering , engineering , control (management) , temperature control , artificial intelligence , statistics , mathematical analysis , agronomy , electrical engineering , combinatorics , operating system , biology
The paper is dedicated to a problem of synthesizing a PID-controller, which provides and aperiodical transient process of desired duration in a control system of the third order with interval parametric uncertainty. To solve the problem, a new method of synthesis was developed. It is based on a decomposing a characteristic polynomial of a considered system in two multipliers: dominant polynomial, which determines allocation of a dominant pole and, consequently, quality of a transient process in a considered system, and non-dominant polynomial, which determines allocation of all other system poles. In order to provide a desired allocation of system poles, parameters of a PID-controller are divided to unrestricted ones and dependent ones. The research resulted in algebraic expressions for calculating dependent parameters of a PID-controller and a system of inequalities for finding its unrestricted parameter. Developed method of a PID-controller parametric synthesis allows placing an interval real dominant pole according to desired control quality and placing all other poles of a system in a desired part of a complex plane to provide necessary degree of a robust pole domination.