Conditions for Ensuring Aperiodic Transients in Automatic Control Systems with a PID Controller

Abstract

Research Problem: The purpose of the study was to obtain the relatively simple conditions for ensuring aperiodic transients in remote control systems with a PID controller. Research Questions: 1. Does the control loops model with the cubic characteristic equation leads the to the relatively simple conditions for ensuring aperiodic transients? 2. Does the simple terms derived by approximate formula for Q-factor in line with the terms of oscillability lack by using the certain inequality, which is correct for the cubic equation with the real roots only? 3. Does the simple regulators good in overdamping the transition oscillations? 4. Does the conditions for ensuring aperiodic transients in automatic control systems helpful for the quick robust PID tuning? Literature Review: The purpose of the literature review was to provide a brief historical background of the research task. The key research results are achieved in the quasi-optimal PID tuning field. The attempts of synthesis the relatively simple PID tunung analytical methods was undertaken for partial narrow tasks. Methodology: The case study is based on the qualitative analysis of cubic control loops characteristic equation. The results of qualitative analysis proved by the LabView simulation using the Control Design and Simulation Module. Results and Conclusions: Several examples of oscillation transients occurs at automatic control systems described by a mathematical model with a cubic characteristic equation were discussed in this paper. There were obtained matching sufficient conditions for aperiodic transient PID tuning based on the known condition of none complex conjugate transfer function poles and approximate formulas for finding the exception in such process granting the complex-conjugate poles element. The aperiodic transition has been provided by using the PID regulator in the context of none of loops elements with the resonant behavior with the best time response.The achievement of * Address correspondence to this author at the National Research Nuclear University “MEPhI”, 115409, Kashirskoe shosse, 31, Moscow, Russia; Tel: 8 (495) 687-23-41; E-mail: vmaslennikov@mail.ru Received: April 18, 2018 Revised: June 5, 2018 Accepted: July 20, 2018 roots of cubic equations. Shown the condition of is the sufficient criterion for oscillation transition exception in the control process with the loop elements where is the real poles. The condition of is the sufficient criterion for oscillation 0 0 G   