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

Marko Bošković, Milan Rapaić, Zoran Jeličić


This paper presents a design procedure of the PID controller where optimal parameters of controller * * * *
p i d f (k ,k ,k ,T ) are
obtained 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 setup
are desired maximum sensitivity, desired maximum complementary sensitivity and maximum sensitivity to measurement noise under
high frequencies. The optimization problem is transformed to an unconstrained problem using penalty function approach. Solution to
the optimization problem is obtained using Particle Swarm algorithm (PSO) which leads to an efficient suppression of disturbance as
well as an adequate reference tracking performance of the closed-loop system with negligible overshoot. The suggested method is
applicable 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 typically
encountered 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 those
using recently proposed maximization of proportional gain denoted with max(kp) method. Although the present paper is focused to tune
the PID controller, the same procedure may be used to design PI controller, lead and lag compensators, high-order controllers as well as
fractional-order controllers.

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