Research On Stabilization Control Of Underactuated Surface Vessels

The underactuation of mechanical systems means that the dimension of the control vectors of systems is less than that of the configuration vector of systems. It implies that underactuated mechanical systems can reduce the cost and the weight of systems. Moreover, the idea of underactuation can be used to control systems in which some components are failed during operation. Therefore, the more and more attention has been paid on underactuated mechanical systems in recent years.The focused object is surface vessel. It is pointed out that underactuated characteristic is emerged under special control aims. So stabilization problem of underactuated surface vessel is addressed in this paper. The dynamical model of surface vessels with three degrees of motion is introduced. The property of the kinematics and dynamics is described respectively. The controllability, nonholonomy and equilibrium points proper of the systems is analysed.For underactuated surface vessel is small time locally controllable from any equilibrium, a discontinuous control approach with two stage control laws switched on at given time is proposed. The system is divided into two subsystems. A feedback controller is designed for one subsystem to control its converge rate. Then nonlinear sliding mode method is used to stable another subsystem. So the whole system is made to stabilization by the discontinuous controller.Based on property of cascaded nonlinear systems, the mathematical model of underactuated surface vessels is divided into two series subsystems. A period time-varying control law is proposed in two steps with the aid of the well-known backstepping technique. All states of the system global identical asymptotic stability to the equilibrium point are guaranteed by the designed smooth period time-varying feedback stabilization law.The main methods of researching on stabilization of underactuated surface vessels areσ-transformation, homogeneity, backstepping and so on. In this paper,σ-transformation, homogeneity and the designed methods are carried out by Simulink Toolbox of Matlab. Simulink results account for that every state of the system can converge to the equilibrium point by designed controller. The effect is perfect. Moreover, controller with the aid of the well-known backstepping technique guarantees the states of the underactuated system stability to the equilibrium point without oscillating.