Abstract

This paper aims to achieve control-relevant identification of unstable inertial systems with, or without time delay. This approach involves collecting data from the system's operation, constructing mathematical models and analyzing their stability. The study contributes in enhancing of the understanding the identification process of the unstable inertial systems models in the closed-loop, offering insights into effective synthesizing strategies of the PID control algorithm. The proposed algorithm for control-relevant identification offers a systematic approach to accurately determine the transfer function, which characterizes the dynamic behavior of the unstable inertial systems and to synthesize the PID controller. The verification of the proposed algorithm and simulation experiment is carried out on the software package MATLAB. The results demonstrate that the proposed control identification approach for unstable systems offers good results in model estimation and control algorithm ensures the system stability.

Abstract

Nowadays, with the rise of computing power, control-relevant identification methods have gained attention in various industrial applications, incorporating the requirements for control design into the process of system identification. Mathematical identification of stable linear dynamical systems is a widely studied problem in the literature, and it is prevalently performed in open-loop structures that may lead to high-order models suitable for control system design with imposed control objectives. However, in the case of unstable systems identification can become a challenge task, and usually is performed using closed-loop identification techniques. This paper presents the control-relevant identification approach for two kinds of unstable processes. The contribution focuses on establishing a well-fitted identified model by using a strategy that involves collecting data from the closed-loop system’s operation with a proportional controller when the system achieves an underdamped step response. In addition, a proportional-integral-derivative (PID) controller for each process was synthesized using maximal stability degree method. Concerning identification, the simulation results were compared with those of the genetic algorithm and offered better model estimation than the genetic algorithm. On the other hand, it is also demonstrated that the designed control algorithm offered a high degree of stability to the system and is more reliable in stabilizing the behavior of the unstable system than the genetic algorithm and the parametric optimization method.