Unfortunately, it has been difficult to tune up PID controller gains accurately because many industrial plants are often very complex consisting of issues such as higher order, time delays, and nonlinearities [4, 5]. Ziegler and Nichols proposed the first method utilizing the classical tuning rules. Though, it is hard to determine optimal PID controller parameters with Ziegler-Nichols formula in general [1, 3]. To overcome these difficulties, various methods have been proposed. The ability of using numerical methods for efficiently and accurately characterizing the quality of a particular design has excited control engineers to apply stochastic global optimizers.

Over the past years, several evolutionary algorithms have been proposed to search for optimal PID controllers. Among them, GA has received great attention and PSO has been successfully applied to various fields [6–10]. Also, ACO is a relatively recent approach to solve optimization problems by simulating the behavior of ant colonies and modeling the behavior of ants, which are known to be able to find the shortest path from their nest to a food source [11]. The ACO method proposed in our paper has the following advantages: applicability to any kind of optimization problems, combinatorial or continuous, easy implementation, high rate of successful optimizations, and low run time.

In this paper, we compare the efficiency of three intelligent algorithms, that is, GA, PSO, and ACO methods. These evolutionary algorithms are used to adjust the PID controller parameters in order to ensure adequate servo and regulatory behavior of the closed-loop system. Also, we formulate the problem of designing PID controllers as an optimization dilemma which adjusts five performance indexes, that is, maximum overshoot, rise time, settling time, and steady-state error of the response and system control energy.