Research On Stabilization Control Of Underactuated Surface Vessels

Nowadays, the hot issue that scholars dedicated to research and solve is how to use fewer control inputs to control the object with multiple degree which can be called underactuated system. That means the underactuated system is the one that the number of control inputs is less than that of generalized coordinate variables (or degrees of freedom) of system. And the significance of the research about underactuated surface vessel can not only reduce the cost of the ship, but also decrease the weight of the ship with fewer controllers.Our research focuses on the stabilization control of underactuated surface vessel, mainly considering about the underactuated symmetric surface vessel and underactuated asymmetric surface vessel. The general ship only has front and back symmetry, not left and right symmetry. This means in the mathematical model the non-diagonal elements that in the matrix of inertia parameters M, and the matrix of damping D(v) are non-zero. However, a large number of existing stabilization control research literatures about ship, treat the ship as front-back and left-right symmetry. That is to ignore the non-diagonal elements, and weak the coupling characteristics of movement states. In light of the surface vessel with only propeller and steering gear (that is, underactuated surface vessel), the stabilization of symmetric and asymmetric ships are studied.The focused object is surface vessel. The dynamic characteristics of surface vessel with three degrees of freedom are introduced by two aspects from kinematics and dynamics. And the mathematical model of the three degrees of freedom for symmetrical and asymmetrical ships are established. And different diffeomorphism transformation are made for them. It has been proved that as long as one subsystem can be asymptotically stable, the whole system can be asymptotically stable. And one research of global exponential stabilization of underactuated asymmetrical surface vessel is introduced, which provides analytical methods and ideas for the research of stabilization of underactuated asymmetrical surface vessel.Based on the theory of backstepping and cascaded nonlinear systems, the mathe-matical model of underactuated surface vessel is divided into two series subsystems. Firstly, one subsystem is stabilized by the controller with Lyapunov function, and then the underactuated surface vessel can achieve asymptotically global uniform stability to the equilibrium point with backstepping method.Finally, the Simulink simulation has been built to verify the controllers which are designed by Backstepping method. Simulation results show that the effect of this controller is really ideal, and each state of the system can converge to the equilibrium point. And backstepping stabilization is more simple and direct than exponential stabilization. By comparing the simulations of symmetrical and asymmetrical ships, it has been seen that non-diagonal elements will affect the results of stabilization.