New results on Control by Interconnection and Energy-Balancing Passivity-Based Control of port-hamiltonian systems

In this paper we present some new results on two energy-shaping controllers for port-Hamiltonian (pH) systems: Control by Interconnection (CbI) and Energy-Balancing Passivity-Based Control (EB-PBC). The work is motivated by two recent developments, first, the identification of a novel class of passive outputs for pH systems. Second, the observation that allowing the energy function of the controller used in CbI to depend on the state of the system to be controlled also generates new passive outputs. As shown here, using these passive outputs gives additional degrees of freedom for the design of CbI and EB-PBC to make both techniques more widely applicable. Another contribution of the paper is to provide an unified framework for the design of the various forms of CbI and EB-PBC reported in the literature, objective that is achieved viewing EB-PBC as a particular instance of CbI with regulated sources.