Dither in linear systems with memoryless nonlinearity and optimal control

The injection of a high-frequency signal, commonly called dither, into a nonlinear system may improve its performance. Stability of the dithered system is related to that of its corresponding model - the smoothed system, of which the nonlinear element N/sub s/ (smoothed nonlinearity) is the convolut...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 1997-05, Vol.44 (5), p.412-421
Main Authors: HSIAO, F.-H, HWANG, J.-D
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Convolution
Cutoff frequency
Exact sciences and technology
Feedback control
Linear systems
Low pass filters
Nonlinear systems
Optimal control
Robust control
Robust stability
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Summary:The injection of a high-frequency signal, commonly called dither, into a nonlinear system may improve its performance. Stability of the dithered system is related to that of its corresponding model - the smoothed system, of which the nonlinear element N/sub s/ (smoothed nonlinearity) is the convolution of the dither distribution and the original nonlinearity N. The dither amplitude, but not its frequency affects the sector of N/sub s/. The importance of dither frequency is found in its effect on the deviation of the smoothed system from the dithered system, and the deviation can be improved as dither frequency increases. The dither with a sufficiently high frequency may result in the smoothed system's output and the dithered system's output as close as desired. An optimal controller and a dither, as an auxiliary of the controller, are simultaneously introduced to make the stability more robust, no matter whether the controlled plant is stable or not. The main characteristic of this paper is that an algorithm is proposed to find a lower bound on dither amplitude to stabilize the nonlinear feedback system.
ISSN:1057-7122
1558-1268
DOI:10.1109/81.572337