Tracking Control of Marine Craft in the port-Hamiltonian Framework: A Virtual Differential Passivity Approach

In this work we propose a virtual contraction-based control (v-CBC) design approach to the tracking problem in marine craft modeled as port-Hamiltonian (pH) systems. The design method consists of three main steps: i) construct a virtual control system which has all the original marine craft pH model's solutions embedded; ii) design a control law that makes the virtual control system contracting with a desired steady-state trajectory; iii) close the loop of the original marine craft pH model with above controllers. Due to the rigid body nature of marine craft, two v-CBC schemes are proposed; one in a body frame and another in an inertial frame. We show how the intrinsic structure of pH models and their workless forces can be exploited to construct virtual control systems for marine craft in both frames. The closed-loop system's performance is evaluated on simulations.

[1]  Arjan van der Schaft,et al.  On Differential Passivity , 2013, NOLCOS.

[2]  A. Schaft,et al.  Variational and Hamiltonian Control Systems , 1987 .

[3]  Rodolphe Sepulchre,et al.  A Differential Lyapunov Framework for Contraction Analysis , 2012, IEEE Transactions on Automatic Control.

[4]  Nathan van de Wouw,et al.  Convergent Systems: Nonlinear Simplicity , 2017 .

[5]  Mohammad Javad Yazdanpanah,et al.  Trajectory tracking for a class of contractive port Hamiltonian systems , 2017, Autom..

[6]  Tristan Perez,et al.  Trajectory tracking passivity-based control for marine vehicles subject to disturbances , 2017, J. Frankl. Inst..

[7]  Asgeir J. Sørensen,et al.  Design of ride control system for surface effect ships using dissipative control , 1995, Autom..

[8]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[9]  Naomi Ehrich Leonard,et al.  Stabilizing underwater vehicle motion using internal rotors , 2002, Autom..

[10]  Dong Eui Chang,et al.  Controlled Lagrangian and Hamiltonian systems , 2002 .

[11]  Thor I. Fossen,et al.  A Tutorial on Incremental Stability Analysis using Contraction Theory , 2010 .

[12]  Arjan van der Schaft,et al.  On differential passivity of physical systems , 2013, 52nd IEEE Conference on Decision and Control.

[13]  Jean-Jacques E. Slotine,et al.  On Contraction Analysis for Non-linear Systems , 1998, Autom..

[14]  Tristan Perez,et al.  Dynamic positioning of marine craft using a port-Hamiltonian framework , 2012, Autom..

[15]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[16]  Suguru Arimoto,et al.  Stability and robustness of PID feedback control for robot manipulators of sensory capability , 1984 .

[17]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[18]  Bayu Jayawardhana,et al.  Tracking Control of Fully-actuated port-Hamiltonian Mechanical Systems via Sliding Manifolds and Contraction Analysis , 2017 .

[19]  Jana Fuhrmann,et al.  Guidance And Control Of Ocean Vehicles , 2016 .

[20]  Thor I. Fossen,et al.  Nonlinear vectorial backstepping design for global exponential tracking of marine vessels in the presence of actuator dynamics , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[21]  Diana Bohm,et al.  L2 Gain And Passivity Techniques In Nonlinear Control , 2016 .

[22]  Leigh McCue,et al.  Handbook of Marine Craft Hydrodynamics and Motion Control [Bookshelf] , 2016, IEEE Control Systems.

[23]  Eduardo Sontag.  Contractive Systems with Inputs , 2010 .

[24]  Jean-Jacques E. Slotine,et al.  On partial contraction analysis for coupled nonlinear oscillators , 2004, Biological Cybernetics.