Fractional-Order Controller for Course-Keeping of Underactuated Surface Vessels Based on Frequency Domain Specification and Improved Particle Swarm Optimization Algorithm

Abstract

In this paper, a new fractional-order (FO) PIλ Dµ controller is designed with the desired gain and phase margin for the automatic rudder of underactuated surface vessels (USVs). The integral order λ and the differential order μ are introduced in the controller, and the two additional adjustable factors make the FO PIλ Dµ controller have better accuracy and robustness. Simulations are carried out for comparison with a ship’s digital PID autopilot. The results show that the FO PIλ Dµ controller has the advantages of a small overshoot, short adjustment time, and precise control. Due to the uncertainty of the model parameters of USVs and two extra parameters, it is difficult to compute the parameters of an FO PIλ Dµ controller. Secondly, this paper proposes a novel particle swarm optimization (PSO) algorithm for dynamic adjustment of the FO PIλ Dµ controller parame-ters. By dynamically changing the learning factor, the particles carefully search in their own neigh-borhoods at the early stage of the algorithm to prevent them from missing the global optimum and converging on the local optimum, while at the later stage of evolution, the particles converge on the global optimal solution quickly and accurately to speed up PSO convergence. Finally, comparative experiments of four different controllers under different sailing conditions are carried out, and the results show that the FO PIλ Dµ controller based on the IPSO algorithm has the advantages of a small overshoot, short adjustment time, precise control, and strong anti-disturbance control.