Sliding Mode Controller for Near-Surface Motion Model of the Submarine with Static Catastrophe

In this paper, a static catastrophe problem for submarines is considered, where the near-surface motion model is studied. At the equilibrium points, center manifold theory is used to reduce the motion equations to a lower layer system which contains all dynamic properties of the original system. Then, transcritical bifurcation and static catastrophe are determined. To suppress nonlinear phenomena, a sliding surface is proposed for the linearization system derived by feedback linearization of submarine near-surface model. Based on exponential tendency law, a sliding mode control law is developed. In the end, the simulation results show the effectiveness of the control law.