Fractional-Order PI^λD^μ Controller Using Adaptive Neural Fuzzy Model for Course Control of Underactuated Ships

Abstract

For the uncertainty caused by the time-varying modeling parameters with the sailing speed in the course control of underactuated ships, a novel identification method based on an adaptive neural fuzzy model (ANFM) is proposed to approximate the inverse dynamic characteristics of the ship in this paper. This model adjusts both its own structure and parameters as it learns, and is able to automatically partition the input space, determine the number of membership functions and the number of fuzzy rules. The trained ANFM is used as an inverse controller, in parallel with a fractional-order PIλDμ controller for the course control of underactuated ships. Meanwhile, the sine wave curve and the sawtooth wave curve are considered as the input learning samples of ANFM, respectively, and the inverse dynamics simulation experiments of the ship are carried out. Two different ANFM structures are obtained, which are connected in parallel with the fractional-order PIλDμ controller respectively to control the course of ship. The simulation results show that the proposed method can effectively overcome the influence of uncertainty of ship modeling parameters, track the desired course quickly and effectively, and has a good control effect. Finally, comparative experiments of four different controllers are carried out, and the results show that the FO PIλDμ controller using ANFM has the advantages of small overshoot, short adjustment time, and precise control.

Keywords

• adaptive neural fuzzy model
• system identification
• inverse dynamic characteristics
• fractional-order PI^λD^μ controller
• underactuated ships
• course control