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Discrete IDA-PBC Design for 2D Port-Hamiltonian Systems

Abstract : We address the discrete-time passivity-based control laws synthesis within port-Hamiltonian framework. We focus on IDA-PBC design for canonical port-Hamiltonian systems with separable energy being quadratic in momentum. For this class of systems, we define a discrete Hamiltonian dynamics that exactly satisfies a discrete energy balance. We then derive a discrete controller following the IDA-PBC procedure. The proposed methodology relies on an energy discretization scheme with suitable discrete conjugate port variables. The main result is illustrated on two examples: a nonlinear pendulum in order to compare with some simulation results of the literature, and the impact oscillator which requires robust discretization scheme.
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https://hal.archives-ouvertes.fr/hal-00999667
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Submitted on : Tuesday, June 3, 2014 - 9:25:02 PM
Last modification on : Monday, September 13, 2021 - 2:44:03 PM

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Saïd Aoues, Damien Eberard, Wilfrid Marquis-Favre. Discrete IDA-PBC Design for 2D Port-Hamiltonian Systems. 9th IFAC Symposium on Nonlinear Control Systems, Sep 2013, Toulouse, France. pp.134-139, ⟨10.3182/20130904-3-FR-2041.00088⟩. ⟨hal-00999667⟩

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