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

Optimizing stability bounds of finite-precision controller structures for sampled-data systems in the delta operator domain
Optimizing stability bounds of finite-precision controller structures for sampled-data systems in the delta operator domain
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.
1350-2379
517-526
Chen, S.
ac405529-3375-471a-8257-bda5c0d10e53
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Istepanian, R. H.
b71b8b46-cb69-4fcd-8253-d2e7a93079ea
Chu, J.
08744087-3532-4f12-9d8a-5c8e5d79be0e
Whidborne, J. F.
4ab1bd73-64f5-4c7c-97da-31c8758352a0
Chen, S.
ac405529-3375-471a-8257-bda5c0d10e53
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Istepanian, R. H.
b71b8b46-cb69-4fcd-8253-d2e7a93079ea
Chu, J.
08744087-3532-4f12-9d8a-5c8e5d79be0e
Whidborne, J. F.
4ab1bd73-64f5-4c7c-97da-31c8758352a0

Chen, S., Wu, J., Istepanian, R. H., Chu, J. and Whidborne, J. F. (1999) Optimizing stability bounds of finite-precision controller structures for sampled-data systems in the delta operator domain. Control Theory and Applications, IEE Proceedings, 146 (6), 517-526.

Record type: Article

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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Published date: November 1999
Organisations: Southampton Wireless Group

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Local EPrints ID: 251071
URI: http://eprints.soton.ac.uk/id/eprint/251071
ISSN: 1350-2379
PURE UUID: deb60e9f-8658-495f-8df4-68034b2d8970

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Date deposited: 29 Jan 2000
Last modified: 23 Apr 2020 16:54

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