Multiobjective optimization of 2DOF controller using Evolutionary and Swarm intelligence enhanced with TOPSIS

Abstract

In this paper, Evolutionary (NSGA-II and NSGA-III) and Swarm Intelligence (MOPSO) based algorithms enhanced with Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is employed to optimize five parameters of Two Degree Of Freedom (2DOF) controller. Three objective functions, one for set point tracking and two for disturbance rejections (flow variation of input fluid and temperature variation of input fluid both are in conflict) are deployed for the problem of shell and tube heat exchanger. Three test criteria IAE, ISE and ITAE function of error (set point tracking and disturbance rejection) and time are used for evaluation of objective functions. The Pareto set of solutions are obtained after optimizing all the five parameters of 2DOF controller. In order to obtain the comparative analysis of optimization algorithms (NSGA-II, NSGA-III, and MOPSO) all the Pareto optimal solutions are combined under three separate evaluation criteria IAE, ISE, and ITAE. TOPSIS a multiple criteria decision making method is used to rank the set of Pareto optimal solutions for reducing number of Pareto optimal solutions to a single solution. The best rank solution obtain for 2DOF controller parameters after applying TOPSIS on set of Pareto optimal solutions using Evolutionary (NSGA-II and NSGA-III) algorithms are compared with Swarm Intelligence (MOPSO) algorithm. To evaluate the performance optimization of 2DOF controller tuning, we compared the values of peak overshoot of step response, set point tracking error, disturbance rejection (both flow and temperature), settling time, and the percentage of solutions obtained from optimization algorithms under all three evaluation criteria IAE, ISE, and ITAE. MATLAB software tool is used to implement the above algorithms.