Ripple-free robust output regulation and tracking for multirate sampled-data control

Abstract

The problem of the robust continuous-time asymptotic tracking and disturbance rejection for a multivariable multirate sampled-data system is studied. The necessity of a continuous-time internal model of the exogenous signals (except for the constant ones, if any) for obtaining a ripple-free zero error response, is proven. The conditions are given for the existence of a hybrid control system (including, possibly, a continuous-time subcompensator) for which the exponential stability and a continuous-time convergence to zero of the tracking error are guaranteed at least in a neighbourhood of the nominal parameters. This, in particular, both for when the dead-beat convergence of the state free response and the continuous-time error response is required at the nominal parameters, and for when an exponential convergence with a prescribed rate of decay is required (including design procedures of the continuous-time and the discrete-time subcompensators); both for when the available description of the plant has a known dependence on some`physical' parameters, and for when the only nominal description of the plant is available, and independent perturbations of the entries of (some of) the matrices characterizing the plant representation are assumed.

Robust semiclassical internal model based regulation for a class of hybrid linear systems

“…The proposed compensator has many conceptual similarities with the ones proposed many years ago for ripplefree control of sampled-data systems, e.g., by Yamamoto [1994], Grasselli et al [1996Grasselli et al [ , 2002, in the sense that, here and there, the internal model is provided by a continuous-time component (here called the flow internal model, needed to ensure output regulation during flows, and possibly obtained through the use of generalized hold functions), and a discrete-time component (here called the jump internal model, needed to ensure output regulation at periodically sampled time instants). A quite surprising novelty here with respect to the mentioned results is that, due to the rich class of uncertainties taken into account (affecting both the flow and the jump dynamics), the jump internal model must contain as many copies of the equivalent discrete-time dynamics of the exosystem as the sum of the dimensions of the states of the observable dynamics of the plant and of the flow internal model; on the other hand, the flow internal model must contain only as many copies of the flow dynamics of the exosystem as the number of regulated outputs.…”