Direct discrete-time control of port controlled Hamiltonian systems

The direct discrete time control of Port Controlled Hamiltonian Systems (PCHS) in the sense of energy shaping and damping injection is considered. In order to give a direct discrete time design method for PCHS, firstly an appropriate discrete gradient is proposed, which enables the derivation of a discrete time equation corresponding to the discrete time counterpart of Hamiltonian Systems. Using this proposed discrete-time model, the discrete-time counterpart of Passivity Based Control (PBC) technique is developed for n-degreesof- freedom mechanical systems. The discrete-time control rules which correspond to the energy shaping and damping assignment are obtained directly using the discrete time model of the desired system and the discrete time model of the open loop systems. To illustrate the effectiveness of the proposed method, two non-separable and under actuated examples are investigated and the simulation results are given.