Soft-switching proximate time optimal heading control for underactuated autonomous underwater vehicle

In this paper, a soft-switching proximate time-optimal control (PTOC) is proposed based on the model-compensation extended state observer (ESO) and Takagi-Sugeno fuzzy switching, for the fast set-heading tracking of underactuated autonomous underwater vehicle (AUV). First, based on Pontryagin's maximum principle, a time-optimal control (TOC) law is derived for the first-order Nomoto model of the underactuated AUV. Then, a model-compensation active disturbance rejection control (ADRC) is developed; the outstanding characteristic is that the nonlinear heading dynamic model is compensated to a first-order Nomoto model rather than by a double integral system through implementing a model-compensation ESO (MC-ESO). The regular ESO is replaced with a reduced-order ESO (RESO) to reduce complexity, and the model-compensation RESO (MC-RESO) is designed by adding the known partial model to RESO. Based on the controller scaling method, a parameter self-tuning strategy is proposed for model-compensation ADRC (MC-ADRC) with changed plant parameters at different velocities. Finally, the soft-switching PTOC is developed for heading control, and the MC-RESO is adopted to estimate the unmeasured velocity and unknown total disturbances for feedback and compensation. The TOC with an unsaturated region (RTOC) is employed to enhance the robustness by using a switching region to replace the switching curve, and a soft-switching strategy between ADRC (near the origin) and RTOC (far from origin) is designed based on the Takagi-Sugeno fuzzy mode. Several simulations are carried out, the effectiveness of self-tuning MC-ADRC is verified, and the proposed soft-switching PTOC shows better performance compared with MC-ADRC.