Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems

摘要

The Interconnection and Damping Assignment\udPassivity-Based Control (IDA-PBC) problem for port-controlled\udHamiltonian systems is revisited. We propose a methodology that\udexploits the novel notion of algebraic solution of the so-called\udmatching equation. This notion is instrumental for the construction\udof an energy function, defined on an extended state-space,\udwhich does not rely upon the solution of any partial differential\udequation. This yields, differently from the classical solution, a\uddynamic state feedback that stabilizes a desired equilibrium point.\udIn addition, conditions that allow to preserve the port-controlled\udHamiltonian structure in the extended closed-loop system are\udprovided. The theory is validated on two physical systems: the\udmagnetic levitated ball and a third order food-chain system. A\uddynamic control law is constructed for both these systems by\udassigning a damping factor that cannot be assigned by the classical\udIDA-PBC.