Journal article
Stability of adaptive delta modulators with forgetting factor and constant inputs
International journal of adaptive control and signal processing, Vol.25(8), pp.723-739
08/2011
DOI: 10.1002/acs.1238
Abstract
Motivated by applications to feedback control over communication networks where the actuation and feedback signals are transmitted over communication channels, we study the stability of Adaptive Delta Modulators (ADM) when the coded signal is a constant. The importance of such a setting arises because a common control task is to track a dc input. It is known that a standard accumulator-based ADM has the following highly undesirable characteristic: virtually all combinations of the algorithm parameters result in 4-cycles, and the avoidance of 4-cycles requires a nongeneric initialization. Further, the steady state oscillations that generically arise in the course of these cycles can have amplitudes that can be arbitrarily close to the initial error. Consequently, we study the use of a forgetting factor in the ADM loop, and provide a detailed stability analysis and design guidelines. Intuitively, adding a forgetting factor to the classical ADM algorithm prevents 4-periodic cycles from occurring by damping them. In particular, we show that for suitably chosen design parameters, the ADM with forgetting factor can track a constant signal arbitrarily closely under mild assumptions. We provide simulations to demonstrate how much better the modified algorithm performs relative to the original ADM algorithm in a remote control setting.
Details
- Title: Subtitle
- Stability of adaptive delta modulators with forgetting factor and constant inputs
- Creators
- Sandra H Dandach - Center for Control, Dynamical Systems and Computation, University of California at Santa Barbara, Santa Barbara, CA 93106, U.S.ASoura Dasgupta - Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA 52242, U.S.ABrian D. O Anderson - Research School of Information Sciences and Engineering, Australian National University and National ICT Australia Ltd, Locked Bag 8001, Canberra ACT 2601, Australia
- Resource Type
- Journal article
- Publication Details
- International journal of adaptive control and signal processing, Vol.25(8), pp.723-739
- Publisher
- John Wiley & Sons, Ltd
- DOI
- 10.1002/acs.1238
- ISSN
- 0890-6327
- eISSN
- 1099-1115
- Number of pages
- 17
- Language
- English
- Date published
- 08/2011
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984083256202771
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