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Introduction to Frequency Analysis

Introduction to Frequency Analysis. Response of a system to sinusoidal input. S&C, p44. Transient. non -Transient. The frequency of the input = frequency of the output The output includes both transient and non-transient terms non-Transient term

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Introduction to Frequency Analysis

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  1. BAE 3023 Introduction to Frequency Analysis

  2. Response of a system to sinusoidal input BAE 3023 S&C, p44 Transient non -Transient • The frequency of the input = frequency of the output • The output includes both transient and non-transient terms • non-Transient term • The non-transient term has different magnitude than the input • The non-transient term has a phase lag compared to the input

  3. Frequency Analysis(Bode Analysis) BAE 3023

  4. Frequency Analysis(Bode Analysis) BAE 3023

  5. Frequency Analysis(Bode Analysis) BAE 3023

  6. Frequency Analysis(Bode Analysis) BAE 3023

  7. If measured is subtracted from error! BAE 3023

  8. Frequency Analysis BAE 3023 • Conditions for Instable system determined by frequency analysis • 1800 phase lag occurs at some frequency • Gain at this point is more than 1 • Method for determining stability by Frequency Analysis • Plot Open Loop Magnitude Ratio (loop gain, K=1) and • Plot phase lag for system • Determine if above condition occurs

  9. Calculating Magnitude Response BAE 3023 Use the fortunate result that substituting iw for s in the transfer function and plotting magnitude and phase of the result yields non-transient frequency response Example:

  10. Calculating Phase Response BAE 3023

  11. Plotting Frequency response BAE 3023

  12. Plotting Frequency response BAE 3023

  13. Plotting Frequency response BAE 3023

  14. Adding terms of Frequency Response BAE 3023 We can simply add terms on the Bode Magnitude plot and on the Bode Phase plot to get total response

  15. Frequency Analysis(Bode Analysis) BAE 3023 Conventional 2nd Order system w/ Proportional Controller

  16. Bode Magnitude Plot BAE 3023 Kc = 1

  17. Bode Phase Plot BAE 3023

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