Model reduction approach for digital PID control based on generalized holds

This paper explores the use of a discretization procedure based on multirate sampling called generalized sample-data hold function (GSHF) for modeling and control purposes. Within this framework, the designer is allowed to use the degrees of freedom provided by the GSHF to deliberately cause stable pole-zero cancellations and, thus, obtaining reduced-order discrete-time models from linear continuous-time ones. This methodology is used for controller design purposes, concretely, proportional-integral-derivative (PID) control. In this way, a continuous-time process that is not suitable for PID control is discretized by means of a GSHF allowing a double benefit: complex dynamics of the continuous-time plant are removed in order to make PID control adequate and, for the reason that the order of the model is reduced, more simple tuning procedures can be used. Simulation examples have shown the applicability of the proposed approach and its usefulness providing good asymptotic tracking and smooth inter-sample behavior both in the perfectly known system and under parametric uncertainty.