An improved swarm intelligence algorithms-based nonlinear fractional order-PID controller for a trajectory tracking of underwater vehicles

Abstract

This paper presents a nonlinear fractional order proportional integral derivative (NL-FOPID) for autonomous underwater vehicle (AUV) to solve the path tracking problem under the unknown disturbances (model uncertainty or external disturbances). The considered controller schemes are tuned by two improved swarm intelligence optimization algorithms, the first on is the hybrid grey wolf optimization with simulated annealing (HGWO-SA) algorithm and an improved whale optimization algorithm (IWOA). The developed algorithms are assessed using a set of benchmark function (unimodal, multimodal, and fixed dimension multimodal functions) to guarantee the effectiveness of both proposed swarm algorithms. The HGWO-SA algorithm is used as a tuning method for the AUV system controlled by NL-FOPID scheme, and the IWOA is used as a tuning algorithm to obtain the PID controller’s parameters. The evaluation results show that the HGWO-SA algorithm improved the minimal point of the tested benchmark functions by 1-200 order, while the IWOA improved the minimum point by (1-50) order. Finally, the obtained simulation results from the system operated with NL-FOPID shows the competence in terms of the path tracking by 1-15% as compared to the PID method.