A modified shuffled frog leaping algorithm for optimal tuning of multivariable PID controllers

This paper presents a modified shuffled frog leaping algorithm (SFLA) for optimal tuning of proportional-integral-derivative (PID) controller gains for multivariable processes. The SFLA is a meta-heuristic search method inspired from the memetic evolution of a group of frogs when seeking for food. It consists of a frog leaping rule for local search and a memetic shuffling rule for global information exchange. In this paper, a new frog leaping rule is proposed to improve the local exploration of the SFLA. The main idea behind the new frog leaping rule is to extend the direction and the length of each frog’s jump by emulating frog’s perception and action uncertainties. The modification widens the local search space, thus helps to prevent premature convergence and improves the performance of the SFLA. The modified SFLA is then used to tune multivariable PID controllers such that a specified performance criterion is minimized. The effectiveness of the proposed SFLA-based PID tuning method is illustrated via an application to the Wood-Berry distillation column. Simulation results show that the proposed SFLA is able to find better PID controllers than other methods such as the biggest log-modulus tuning (BLT) method and the multi-crossover genetic algorithm (GA).