Abstract
Dither is a high-frequency signal introduced into a nonlinear system to improve the system performance. A nonlinearity with memory (backlash, hysteresis) is considered in this paper; a dither of a given amplitude is being injected at the input of the nonlinearity. The dither can effectively eliminate memory of the nonlinearity. The significance of the dither frequency lies in its effect on the deviation of the dithered system from its corresponding model, the smoothed system, in which the nonlinearity is a smooth function. The deviation amount can be improved as the dither frequency increases. If the dither has a sufficiently high frequency, the outputs of the smoothed system and the dithered system can be made as close as desired. This enables us to predict the stability of the dithered system by establishing the stability of the smoothed system.
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Hsiao, F.H., Hwang, J.D. Optimal Controller for Dithered Systems with Backlash or Hysteresis. Journal of Optimization Theory and Applications 94, 87–113 (1997). https://doi.org/10.1023/A:1022607619198
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DOI: https://doi.org/10.1023/A:1022607619198