Bode diagram

bode diagram

1. Control system Bode diagram Copyright © 2014 A ddaani

2. Group names: A/ rizak mohamed ahmed ……31 A/ kadir A/ llahi adan …………34 Abukar Hassan Takow ………38 Ahmed A/ aziiz yasiin …………64 Lecturer : ENG- mahamuud A/ qadir Copyright © 2014 Addaani

3. Outline part: one Introduction to frequency response Amplitude ratio and phase part: two Introduction to bode diagram System analysis using bode diagram Copyright © 2014 Addaani

4. Frequency response System response to sinusoidal input is known us frequency response Range of frequency used Used for system identification Used for stability analysis Copyright © 2014 Addaani

5. Frequency response System behavior determined from the steady state response to sinusoidal input in the form R =Asine ᾢ t Sine wave used : Easy to analyse Easy to generate Easy to measure experimentally Copyright © 2014 Addaani

6. Cont …… Sinusoidal applied to linear system: Output will be sinusoidal Output amplitude is proportional to input Harmonic input produces harmonic output at same frequency Variation amplitude and phase Function of frequency Copyright © 2014 Addaani

7. CONT…… Copyright © 2014 Addaani If output flows input is known lag system

8. BODE DIAGRAM PART :TWO BODE DIAGRAM Copyright © 2014 Addaani

9. INTRODUCTION Hendrik Wade Bode (1905–1982), while working at Bell Labs in the United States in the 1930s, devised a simple but accurate method for graphing gain and phase-shift plots . These bear his name, Bode gain plot and Bode phase plot . Copyright © 2014

10. What is Bode plot? The Bode plot is the frequency response plot of the transfer function of a system. Bode plot consists of two graphs: One is the plot of magnitude of sinusoidal transfer function versus log . The other is a plot of the phase angle of a sinusoidal function versus log  . Copyright © 2014 Addaani

11. BODE DIAGRAM Copyright © 2014 Addaani

12. BODE PLOTS A Bode plot is a standard format for plotting frequency response of LTI systems . Becoming familiar with this format is useful because: It is a standard format, so using that format facilitates communication between engineers. Many common system behaviors produce simple shapes (e.g. straight lines) on a Bode plot, so it is easy to either look at a plot and recognize the system behavior, or to sketch a plot from what you know about the system behavior. Copyright © 2014 Addaani

13. cont That format is a log frequency scale on the horizontal axis and, on the vertical axis, phase in degrees and magnitude in decibels . Thus, we begin with a review of decibels: Decibels Definition : for voltages or other physical variables (current, velocity, pressure, etc .) (Since power is proportional to voltage squared (or current, velocity, pressure, etc., squared) Copyright © 2014 Addaani

14. Constructing bode diagram Section of TF can be represented as straight lines =asymptotic approximation Example: Copyright © 2014 Addaani Constructing bode diagram

15. Phase Copyright © 2014 Addaani

16. Cont ….. Phase plot :this has three asymptotes A LF horizontal asymptote at 0 A HF horizontal asymptote at -45 A mid –frequency asymptote that intersects between HF and LF asymptote -90 Copyright © 2014 Addaani

17. Cont ….. Each of TF has certain type of frequency response: Building blocks: Gain Differentiator Integrator First order/second order Copyright © 2014 Addaani

18. Gain……… K Constant terms such as K contribute a straight horizontal line of magnitude 20 log10( K ) A positive constant, K has no effect on phase Copyright © 2014 Addaani

19. Differentiator…….. | j | A zero at the origin occurs when there is an s or j? multiplying the numerator. Each occurrence of this causes a positively sloped line passing through ? = 1 with a rise of 20 db over a decade. Copyright © 2014 Addaani

20. Cont ……. Effect of Zeros at the origin on Phase Angle: Zeros at the origin, s , cause a constant +90 degree shift for each zero. Copyright © 2014 Addaani

21. Integrator………1/s or 1/ jw A pole at the origin occurs when there are s or j? multiplying the denominator. Each occurrence of this causes a negatively sloped line passing through ? = 1 with a drop of 20 db over a decade. Copyright © 2014 Addaani

22. Cont …… Effect of Poles at the origin on Phase Angle: Poles at the origin , s -1 , cause a constant -90 degree shift for each pole. Copyright © 2014 Addaani

23. first order lead Copyright © 2014 Addaani

24. 1’s order lag Copyright © 2014 Addaani

25. Rules for Making Bode Plots Copyright © 2014 Addaani

26. Bode plots Where do the Bode diagram lines comes from ? Determine the Transfer Function of the system : 2) Rewrite it by factoring both the numerator and denominator into the standard form where the z s are called zeros and the p s are called poles . Copyright © 2014 Addaani

27. Con……. 3) Replace s with j? . Then find the Magnitude of the Transfer Function . If we take the log10 of this magnitude and multiply it by 20 it takes on the form of Copyright © 2014 Addaani

28. Example 1: For the transfer function given, sketch the Bode log magnitude diagram which shows how the log magnitude of the system is affected by changing input frequency. ( TF=transfer function ) Step 1: Repose the equation in Bode plot form : Copyright © 2014 Addaani

29. Con…….. Copyright © 2014 Addaani

30. Example 2: Your turn. Find the Bode log magnitude plot for the transfer function , Start by simplifying the transfer function form : Copyright © 2014 Addaani

31. Technique to get started: Copyright © 2014 Addaani

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