Shaping the Energy of Port-Hamiltonian Systems Without Solving PDE's

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.