A novel FOPID2FF2 controller optimized by a new Opposition based learning (OBL)-Black Widow Optimization (BWO) algorithm: application to CSTR

Abstract In this study a novel controller FOPID2FF2 which is a FOPID controller with two fractional order filter in the two fractional order derivatives was proposed to improve the performance of the Continuous Stirred Tank Reactor (CSTR) system. The proposed controller has nine independent tunable parameters which are optimized by a new metaheuristic algorithm opposition based learning (OBL)-Black widow optimization (BWO). The OBL-BWO chooses its initial population using the opposition based learning (OBL). The OBL helps in improving the exploration capability of the algorithm, avoids the stagnation in local optima, and improves the quality of the initial population for the BWO. The proposed OBL-BWO was tested on standard benchmark functions using the statistical performance and the non-parametric analysis such as Wilcoxon signed rank test, convergence performance was carried out and compared to other state-of-art algorithms. To verify the superiority of the FOPID2FF2 controller optimized using OBL-BWO; FOPID without any filter, FOPID with a integer order filter (FOPIDF), FOPID with one fractional order filter (FOPIDFF) optimized using the same was proposed. The performance of the controller was analysed using the time domain response, frequency domain response and robustnesscriterion. From the statistical analysis the new OBL-BWO was better compared to the state of art algorithms and was used to optimize the FOPID2FF2 controller. From the performance analysis of the mentioned controllers it was identified that the OBL-BWO optimized FOPID2FF2 controller outperforms the other controllers.