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An Adaptive Algorithm for Estimating the Frequency and Damping Factor of Damped Sinusoidal Signal: Analysis and Design

Jahvani, Mohammad | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40155 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Karimi, Masoud; Mojiri, Mohsen
  7. Abstract:
  8. Disturbance rejection is one of the most important criteria that should be considered when designing control systems. The problem has been widely investigated and studied when the parameters of disturbance signal is known. However, there are still ongoing researches in the field when the parameters of disturbance signals are uncertain and/or varying with time. In some applications the disturbance signal can be modelled by special dynamics, e.g., step type disturbances with unknown magnitude, sinusoidal disturbances with unknown magnitude and frequency, and damped sinusoidal disturbances with unknown magnitude, frequency and damping factor. In such cases, an adaptive scheme for estimating the unknown parameters can be augmented to the control system. Motivated by this idea, two adaptive algorithms are proposed in this thesis to estimate the frequency and damping factor of a damped sinusoidal signal. The convergence feature of each algorithm is analytically investigated. The proposed algorithms are highly nonlinear since the problem of estimating parameters of a damped sinusoidal signal is intrinsically nonlinear. The algorithms are developed by extending the concept of adaptive notch filters which have been used in frequency estimation. Adaptive nature of the algorithms enables them to estimate the parameters and track their changes. Various aspects of the proposed algorithms are comprehensively studied by means of computer simulations. A method for tuning the parameters of the algorithms is also proposed in this research. The simulation studies show that the algorithms are robust with respect to perturbations in the tuning parameters. Moreover, the studies verify that both algorithms are highly immune to noise and show fast convergence features for any initial conditions within a range
  9. Keywords:
  10. Parameter Estimation ; Averaging Method ; Damped Sinusoidal Signal ; Adaptive Notch Filter ; Integral Manifold of Slow Adaptation

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