Optimizing stability bounds of finite-precision controller structures for sampled-data systems in the delta operator domain

Abstract

The paper derives a tractable closed-loop stability related measure for controller structures, realized using the $\delta$ operator and digitally implemented with finite-word-length (FWL). The optimal realizations of the general finite-precision controller are defined as those that maximize this measure and are shown to be the solutions of a constrained nonlinear optimization problem. For the special case of digital PID controllers, the constrained problem can be decoupled into two simpler unconstrained optimization problems. A global optimization strategy based on the adaptive simulated annealing (ASA) is adopted to provide an efficient method for solving this complex optimal realization problem. Two numerical examples are presented to illustrate the design procedure, and the simulation results confirm that the optimal FWL realizations of the $\delta$-operator based controller have better closed-loop stability margins than those of the usual shift-operator based controller, especially under fast sampling conditions.

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