A constructive procedure for energy shaping of port-Hamiltonian systems

Abstract : Equilibrium stabilization of nonlinear systems via energy shaping is a well-established, robust, passivity-based controller design technique. Unfortunately, its application is often stymied by the need to solve partial differential equations, which is usually a difficult task. In this paper a new, fully constructive, procedure to shape the energy for a class of port-Hamiltonian systems that obviates the solution of partial differential equations is proposed. Proceeding from the well-known passive, power shaping output we propose a nonlinear static state-feedback that preserves passivity of this output but with a new storage function. A suitable selection of a controller gain makes this function positive definite, hence it is a suitable Lyapunov function for the closed-loop. The resulting controller may be interpreted as a classical PI—connections with other standard passivity-based controllers are also identified.
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Luis Pablo Borja Rosales, R. Cisneros, Roméo Ortega. A constructive procedure for energy shaping of port-Hamiltonian systems. Automatica, Elsevier, 2016, 72, pp.230-234. 〈10.1016/j.automatica.2016.05.028 〉. 〈hal-01633793〉

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