Shaping the energy of port-Hamiltonian systems without solving PDE's

Luis Pablo Borja Rosales (1) , Rafael Cisneros (1) , Roméo Ortega (1)

1 L2S - Laboratoire des signaux et systèmes

Equilibrium stabilisation 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. 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. This function contains some tuning gains used to ensure it is positive definite, hence a suitable Lyapunov function for the closed-loop. Connections with other standard passivity-based controllers are indicated and it is shown that the new controller design is applicable to two benchmark examples.

Domaines: Automatique; Automatique / Robotique

Luis Pablo Borja Rosales, Rafael Cisneros, Roméo Ortega. Shaping the energy of port-Hamiltonian systems without solving PDE's. 54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. ⟨10.1109/cdc.2015.7403116⟩. ⟨hal-01262402⟩