Multiobjective Gaussian Particle Swarm Approach Applied to Multi-loop PI Controller Tuning of a Quadruple-Tank System


The use of PI (Proportional-Integral), PD (Proportional-Derivative) and PID (Proportional-Integral-Derivative) controllers have a long history in control engineering and are acceptable for most of real applications because of their simplicity in architecture and their performances are quite robust for a wide range of operating conditions. Unfortunately, it has been quite difficult to tune properly the gains of PI, PD, and PID controllers because many industrial plants are often burdened with problems such as high order, time delays, and nonlinearities. Recently, several metaheuristics, such as evolutionary algorithms, swarm intelligence and simulated annealing, have been proposed for the tuning of mentioned controllers. In this context, different metaheuristics have recently received much interest for achieving high efficiency and searching global optimal solution in problem space. Multi-objective evolutionary and swarm intelligence approaches often find effectively a set of diverse and mutually competitive solutions. A multi-loop PI control scheme based on a multi-objective particle swarm optimization approach with updating of velocity vector using Gaussian distribution (MGPSO) for multi-variable systems is proposed in this chapter. Particle swarm optimization is a simple and efficient population-based optimization method motivated by social behavior of organisms such as fish schooling and bird flocking. The proposal of PSO algorithm was put forward by several scientists who developed computational simulations of the movement of organisms such as flocks of birds and schools of fish. Such simulations were heavily based on manipulating the distances between individuals, i.e., the synchrony of the behavior of the swarm was seen is an effort to keep an optimal distance between them. In theory, at least, individuals of a swarm may benefit from the prior discoveries and experiences of all the members of a swarm when foraging. The fundamental point of developing PSO is a hypothesis in which the exchange of information among creatures of the same species offers some sort of evolutionary advantage. PSO demonstrates good performance in many function optimization problems and parameter optimization problems in recent years. Application of the proposed MGPSO using concepts of Pareto optimality to a multi-variable quadruple-tank process is investigated in this paper. Compared to a classical multi-objective PSO algorithm which is applied to the same process, the MGPSO shows considerable robustness and efficiency in PI control timing.