A constructive procedure for energy shaping of port—Hamiltonian systems. (October 2016)

• Record Type: Journal Article
• Authors: Borja, Pablo; Cisneros, Rafael; Ortega, Romeo
• Is Part Of: Automatica. Volume 72(2016)
• Page Start: 230
• Page End: 234
• Publication Date: 2016-10
• Subjects: Passivity -- Nonlinear systems -- Passivity-based control -- Hamiltonian systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.05.028
• Languages: English
• ISSNs: 0005-1098

Abstract

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.