Robust continuous-time tracking for multi-rate digital control systems

Abstract

Rhe robust ripple-free tracking and regulation problem is solved for multi-rate sampled-data systems, whose state-space description depends on some unknown “physical” parameters. The used control system includes a periodic discrete-time subcompensator and, possibly, a continuous-time subcompensator. The conditions for the existence of a solution are found for two different convergence requirements: a prescribed rate of continuous-time exponential convergence of the error response and the free state response (to be obtained at least in a neighborhood of the nominal parameters), or a continuous-time dead-beat error and free state response at the nominal parameters (together with a continuous-time exponential convergence with any rate of convergence in some neighborhood of the nominal parameters). For both of them, the necessity of a wholly continuous-time internal model of the exogenous signals is proven, and a design procedure is proposed.