Particle Swarm Optimization of PID Controller under Constraints on Performance and Robustness

Abstract

This paper presents a design procedure of the PID controller where optimal parameters of controller * * * *p i d f (k ,k ,k ,T ) areobtained by solving the constrained optimization problem. The objective function is given in the form of the Integral of Absolute Error(IAE) under specifications to achieve predictable performance and robustness. The constraints within the optimization problem setupare desired maximum sensitivity, desired maximum complementary sensitivity and maximum sensitivity to measurement noise underhigh frequencies. The optimization problem is transformed to an unconstrained problem using penalty function approach. Solution tothe optimization problem is obtained using Particle Swarm algorithm (PSO) which leads to an efficient suppression of disturbance aswell as an adequate reference tracking performance of the closed-loop system with negligible overshoot. The suggested method isapplicable to the large class of stable, integral and unstable processes, processes with oscillatory dynamics with and without dead-time.Effectiveness of the proposed design procedure is verified via numerical simulations on test batch consisting of processes typicallyencountered in industry. Paper also provides two another solutions of the defined optimization problem using genetic algorithm (GA)and fminunc trust region based approach (TR). Performance of the PSO, GA, and TR based control system is compared with thoseusing recently proposed maximization of proportional gain denoted with max(kp) method. Although the present paper is focused to tunethe PID controller, the same procedure may be used to design PI controller, lead and lag compensators, high-order controllers as well asfractional-order controllers.

Performance evaluation of PI controller for positive output Luo converter

“…PSO is programmed on the swarm intellect concept and impersonators the collective performances of simple agents that are nearby interconnecting with their situation [22]. PSO algorithm is effective in resolving difficult non-convex problems and multimodal problems, which is cause of its productive purpose in many areas of science and engineering [23].…”

“…The optimization program is employed by MATLAB computer software/script program and connected with the system model program in MATLAB/SIMULINK. The major factors of the PSO algorithm (the number of particles, the number of generations, initial rate of the global-best factor, span of the initial population, the initial velocity span, absolute cost of the individual best factor, absolute value of the global-best factor, initial value of the individual best Factor) are selected by the designer of the algorithm and the problem to be resolved [23,27,28]. The procedures tracked by the intended PSO algorithm for positive output luo converter to attune the PI controller coefficients are summarized in in Figure . 6.…”

Adaptive PI Controller Based on a Reinforcement Learning Algorithm for Speed Control of a DC Motor

“…Therefore, it is necessary to thoroughly explore the process, key concerns, and the fundamental relevance of concepts such as stability and robustness [ 6 , 7 , 8 ]. Stability refers to a system’s ability to remain bounded and converge towards a desired state over time, avoiding undesirable oscillations or divergence, while robustness relates to a controller’s ability to maintain satisfactory performance despite uncertainties, operational changes, or external disturbances [ 9 , 10 ]. In this context, the necessity to prevent severe consequences due to instability and to adapt to differences between theory and reality to maintain predictable performance is framed.…”

Design of Cascaded and Shifted Fractional-Order Lead Compensators for Plants with Monotonically Increasing Lags

“…In addition, as regards the time-domain optimization approaches, many authors employed evolutionary algorithms for tuning FPID controllers. For example, they applied Particular Swarm Optimization (PSO) or Genetic Algorithms to minimize the Integral Time Absolute Error (ITAE) [31,32] or a combination of the ITAE and the Integral Square Error (ISE) [33] or the integral absolute error (IAE) [34] or a combination of the integral gain and closed-loop system bandwidth [35]. Additionally, a combination of differential evolution and PSO was proposed to design and realize FOC based on time-domain performance specifications [36].…”