On the limit cycle of the underwater vehicle control system

Underwater vehicle control systems usually experience the limit cycle due to inherent nonlinear properties. Two major nonlinearities existing in such a system are the fluid drag force and the thruster dynamics. Solution of the limit cycle for the underwater vehicle control system using the describing function approach is presented in this paper. It appears that the proportional controller gain to excite the limit cycle has a lower bound. Simulation study is conducted to investigate characteristics of the limit cycle for an underwater vehicle position control system. Prediction performance of the limit cycle using the proposed method is evaluated by comparing with actual amplitude and frequency of the limit cycle measured from step responses of a complete dynamics model. Simulation results demonstrate excellent performance of prediction. Effect of model linearization on the limit cycle will also be examined