Discrete-time Control by Interconnection Using Energy-Preserving Collocation Methods

The energy-preserving collocation methods combine a high order of accuracy with an exact discrete-time energy balance equation when discretizing port-Hamiltonian systems. We show how they can be used to translate Control by Interconnection to the discrete-time setting. We set up the discrete-time plant and controller model and compute the discrete-time inputs for which the desired equilibrium of the continuous-time closed-loop system becomes a stable equilibrium of the discrete-time models. To obtain a continuous-time control signal for the plant system in the sampling interval, these discrete inputs are then interpolated by a polynomial. The advantages of the proposed approach at large sampling times are illustrated in simulations using the example of the controlled pendulum.