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

In this paper, a new fractional-order (FO) (PID mu)-D-lambda controller is designed with the desired gain and phase margin for the automatic rudder of underactuated surface vessels (USVs). The integral order lambda and the differential order mu are introduced in the controller, and the two additional adjustable factors make the FO (PID mu)-D-lambda 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 (PID mu)-D-lambda 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 (PID mu)-D-lambda controller. Secondly, this paper proposes a novel particle swarm optimization (PSO) algorithm for dynamic adjustment of the FO (PID mu)-D-lambda controller parameters. By dynamically changing the learning factor, the particles carefully search in their own neighborhoods 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 (PID mu)-D-lambda controller based on the IPSO algorithm has the advantages of a small overshoot, short adjustment time, precise control, and strong anti-disturbance control.