| Abstract: | A stable discrete‐time control system may achieve a lower than predicted performance or even become unstable when the discrete‐time control law is implemented with a fixed‐point digital control processor due to the finite word length (FWL) effects, which depends on the control law state‐space realization and the discrete‐time operator (e.g., the delta operator or the forward‐shift operator) used to represent the control law. To improve the closed‐loop stability (and as a byproduct, performance) when the control law is implemented, a state‐space approach that selects the control law realization to optimize a stability‐related objective function is developed using the delta operator. Analytical and numerical comparison of the fixed‐point performance of delta control laws with the performance of the corresponding forward‐shift control laws quantifies the improved closed‐loop stability of the delta realizations over those of the corresponding forward‐shift realizations. It is also shown that there exists a simple mapping between the optimal FWL forward‐shift control law realizations and the optimal FWL delta control law realizations. The results are illustrated by delta and forward‐shift control law realizations of a discrete‐time H∞ control law designed for a teleoperation motion‐scaling system. Copyright © 2001 John Wiley & Sons, Ltd. |
