Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning

Nowadays, a variety of controllers used in process industries are still of the proportional-integral-derivative (PID) types. PID controllers have the advantage of simple structure, good stability, and high reliability. A relevant issue for PID controllers design is the accurate and efficient tuning of parameters. In this context, several approaches have been reported in the literature for tuning the parameters of PID controllers using evolutionary algorithms, mainly for single-input single-output systems. The systematic design of multi-loop (or decentralized) PID control for multivariable processes to meet certain objectives simultaneously is still a challenging task. This paper proposes a new chaotic firefly algorithm approach based on Tinkerbell map (CFA) to tune multi-loop PID multivariable controllers. The firefly algorithm is a metaheuristic algorithm based on the idealized behavior of the flashing characteristics of fireflies. To validate the performance of the proposed PID control design, a multi-loop multivariable PID structure for a binary distillation column plant (Wood and Berry column model) and an industrial-scale polymerization reactor are taken. Simulation results indicate that a suitable set of PID parameters can be calculated by the proposed CFA. Besides, some comparison results of a genetic algorithm, a particle swarm optimization approach, traditional firefly algorithm, modified firefly algorithm, and the proposed CFA to tune multi-loop PID controllers are presented and discussed.