Inertia Shaping Techniques for Marine Vessels Using Acceleration Feedback

The concept of energy based Lyapunov control is extended to marine vessels with a nonsymmetric system inertia matrix. Acceleration feedback is used as the main tool to symmetrize the nonsymmetric part of the system inertia matrix. The main reason for a nonsymmetric mass distribution is hydrodynamic added mass which depend on the forward speed of the vessel and the frequency of the incoming waves. This is a well known phenomenon for marine vessels moving at positive speed in waves while low-speed applications like dynamic positioning systems are fairly well described with a symmetric system inertia matrix. The main contribution of the paper is a new Lyapunov-based design technique incorporating acceleration feedback to shape the kinetic energy of the system. Acceleration feedback is implemented in conjuncture with a nonlinear PID-controller derived from vectorial backstepping. The result is a uniformly globally asymptotically stable (UGAS) closed-loop control system applicable to marine vessels with nonsymmetric system inertia matrices. Typical applications are ships in maneuvering situations, vessels in transit and high speed craft where nonsymmetric added mass e¤ects must be compensated for. Copyright c °2002 IFAC