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

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