This paper treats a tuning of PID controllers method using multiobjective ant colony optimization. The design objective was to apply the ant colony algorithm in the aim of tuning the optimum solution of the PID controllers ( , , and ) by minimizing the multiobjective function. The potential of using multiobjective ant algorithms is to identify the Pareto optimal solution. The other methods are applied to make comparisons between a classic approach based on the “Ziegler-Nichols” method and a metaheuristic approach based on the genetic algorithms. Simulation results demonstrate that the new tuning method using multiobjective ant colony optimization has a better control system performance compared with the classic approach and the genetic algorithms. 1. Introduction Proportional-integral-derivative (PID) controllers are frequently used in the control process to regulate the time domain behavior of many different types of dynamic plants. These controllers are extremely popular because of their simple structure and they can usually provide a good closed loop response characteristic. Despite its simple structure it seems so hard to find a proper PID controller [1]. Considering this problem, various methods have been proposed to tune these parameters. Ziegler-Nichols tuning method is the most standard one but it is often difficult to find optimal PID parameters with these methods. Therefore many optimization methods are developed to tune the PID controllers such as fuzzy logic [2, 3], neural network [4], neural-fuzzy logic [5], immune algorithm [6], simulated annealing [7], and pattern recognition [8]. In addition, we have many other optimum tuning PID methods based on many random search methods such as genetic algorithm (GA) [9, 10], particle swarm optimization [11], and ant colony optimization [12]. In this work, we developed the problem of design PID controllers as a multiobjective optimization problem taking in consideration the ant colony optimization algorithm (ACO). Researchers have reported the capacity of ACO to efficiently search for and locate an optimum solution. This method was mainly inspired by the fact that ants are able to find the shortest route between their nest and a food source. Ant colony optimization (ACO) [13, 14] is a recently developed metaheuristic approach for solving hard combinatorial optimization problems such as the travelling salesman problem TSP [15], quadratic assignment problem [16], graph coloring problems [17], hydroelectric generation scheduling problems [18], vehicle routing [19], sequential ordering, scheduling [20],
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