Analytic Time Domain Specifications PID Controller Design for a Class of 2nd Order Linear Systems: A Genetic Algorithm Method

• Published in: IEEE access Vol. 9; pp. 99266 - 99275
• Main Authors: Lee, Chia-Ling, Peng, Chao-Chung
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Computer simulation; Control systems design; Controllers; Exact solutions; Feedback control; genetic algorithm; Genetic algorithms; Linear systems; Mathematical models; Optimized production technology; PD control; PID analytical solution; PID tuning; Proportional integral derivative; servo motor control; Servocontrol; Servomechanisms; Servomotors; Specifications; Steady-state; Time domain analysis; time domain specifications
• ISSN: 2169-3536
• DOI: 10.1109/ACCESS.2021.3093427

In this paper, an analytical approach of a Proportional-Integral-Derivative (PID) controller design for a servo motor position control with precise desired performance demands is presented. When designing linear controllers, the resulting closed-loop system is often considered as an approximation of a standard <inline-formula> <tex-math notation="LaTeX">2^{\mathrm {nd}} </tex-math></inline-formula> order system to simplify the gain design process. However, in reality, model discrepancies could exist in such approximation, which inevitably lead to performance mismatches between the actual system's behavior and the desired one. In order to solve this issue, this paper presents an analytical PID controller solution, which is able to achieve desired time domain specifications precisely. In addition, a disturbance is added to the system and the associated PID controller will be designed to reject disturbance. Given a <inline-formula> <tex-math notation="LaTeX">2^{\mathrm {nd}} </tex-math></inline-formula> order linear system along with a PID controller, the related analytical solutions are derived first. Next, the associated fitness functions and constraints are constructed under given prescribed time domain specifications. Lastly, the PID control gains are determined using Genetic Algorithm. To demonstrate the effectiveness of the proposed solution, many numerical simulations are performed. A set of control gains is also found using the standard <inline-formula> <tex-math notation="LaTeX">2^{\mathrm {nd}} </tex-math></inline-formula> order system formulas in order to prove the accuracy of the presented method. Moreover, a comparison study with respect to the MATLAB PID Tuner is considered to illustrate the advantage of the proposed PID design scheme. The main contributions of this study include precisely satisfying given control performance demands with exact analytical solutions, avoiding the existing model discrepancies between the standard <inline-formula> <tex-math notation="LaTeX">2^{\mathrm {nd}} </tex-math></inline-formula> order system and the exact closed-loop model. Simulations firmly prove that the proposed method can fulfill users' different control demands as well as remove the frequently used trial-and-error strategy.