Real/binary co-operative and co-evolving swarms based multivariable PID controller design of ball mill pulverizing system

Abstract

In this paper, multivariable PID controller design based on cooperative and coevolving multiple swarms is demonstrated. A simplified multi-variable MIMO process model of a ball mill pulverizing system with steady state decoupler is considered. In order to formulate computational models of cooperative and coevolving multiple swarms three different algorithms like real coded PSO, discrete binary PSO (DBPSO) and probability based discrete binary PSO (PBPSO) are employed. Simulations are carried out on three composite functions simultaneously considering multiple objectives. The cooperative and coevolving multiple swarms based results are compared with the results obtained through single swarm based methods like real coded particle swarm optimization (PSO), discrete binary PSO (DBPSO), and probability based discrete binary PSO (PBPSO) algorithms. The cooperative and coevolving swarms based techniques outperform the real coded PSO, PBPSO, and the standard discrete binary PSO (DBPSO) algorithm in escaping from local optima. Furthermore, statistical analysis of the simulation results is performed to calculate the comparative reliability of various techniques. All of the techniques employed are suitable for controller tuning, however, the multiple cooperative and coevolving swarms based results are considerably better in terms of mean fitness, variance of fitness, and success rate in finding a feasible solution in comparison to those obtained using single swarm based methods.