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Title: Conditions for forced and subharmonic oscillations in relay and quantized feedback systems
Keywords: Relay Feedback, Forced Oscillations, Subharmonic Oscillations, Quantized Feedback, Limit Cycles, Dither
Issue Date: 19-Jan-2009
Citation: LIM LI HONG IDRIS (2009-01-19). Conditions for forced and subharmonic oscillations in relay and quantized feedback systems. ScholarBank@NUS Repository.
Abstract: This thesis contributes to control literature in the following three topics: (1) Forced and subharmonic oscillation (FO and SO, respectively) in relay feedback systems (RFS), (2) Design of sinusoidal dither in RFS, and (3) Limit cycles in quantized feedback systems (QFS). Firstly, the necessary and sufficient conditions for FO and SO are analyzed. It is shown that FO of any frequency will always occur if and only if the amplitude of the external forcing signal is larger than Rmin, determined by graphical/numerical approaches. The amplitude and the range of frequencies where SO can exists are also determined. Secondly, the phenomenon of FO is also applied to design a dither signal which results in reduced oscillation amplitudes in RFS. The minimum required dither frequency, fmin, is determined. Analytical expressions for fmin are obtained and the identification of fmin using the Tsypkin loci is shown. Lastly, further extension of the limit cycle conditions in RFS to QFS reveals the existence of stable self oscillations. Local stability is assessed by Poincaré map. The bounds on the quantization resolution for self oscillation in a second order system are also identified.
Appears in Collections:Ph.D Theses (Open)

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