Improved closed-loop stability for fixed-point controller realizations using the delta operator
✍ Scribed by Tinglun Song; Emmanuel G. Collins Jr.; Robert H. Istepanian
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 167 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1049-8923
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✦ Synopsis
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 "xed-point digital control processor due to the "nite word length (FWL) e!ects, 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 "xed-point performance of delta control laws with the performance of the corresponding forward-shift control laws quanti"es 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.