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LINEAR CONTROL SYSTEMS

LINEAR CONTROL SYSTEMS. Ali Karimpour Associate Professor Ferdowsi University of Mashhad. Topics to be covered include : Frequency domain analysis of control systems. Frequency domain specification. Peak of resonance and resonance frequency . Bandwidth. Nyquist stability criteria.

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LINEAR CONTROL SYSTEMS

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  1. LINEAR CONTROL SYSTEMS Ali Karimpour Associate Professor Ferdowsi University of Mashhad

  2. Topics to be covered include: Frequency domain analysis of control systems. Frequency domain specification. Peak of resonance and resonance frequency. Bandwidth. Nyquist stability criteria. Lecture 18 Nyquist stability criteria.

  3. One degree-of-freedom configuration T(s) S(s) T(s) S(s) is : Sensitivity Function Why? T(s) is : Complementary Sensitivity Function Since S+T=1

  4. One degree-of-freedom configuration Where T(s) and S(s) are How to derive command tracking How to derive disturbance rejection How to derive noise attenuation

  5. One degree-of-freedom configuration Derive command tracking and disturbance rejection

  6. Derive command tracking and disturbance rejection One degree-of-freedom configuration How to derive noise attenuation

  7. Ideal |T| for command tracking, disturbance rejection and noise attenuation Ideal |L| for command tracking, disturbance rejection and noise attenuation Actual |T| for command tracking, disturbance rejection and noise attenuation Actual |L| for command tracking, disturbance rejection and noise attenuation One degree-of-freedom configuration

  8. + e c r - c r Frequency (rad/s) A prototype second order system. یک سیستم نمونه درجه 2

  9. Peak of resonance ( ) Resonance frequency ( ) Frequency domain specification

  10. Closed-loop bandwidth ( ) Open - loop bandwidth ( ) Gain crossover frequency ( ) Frequency domain specification -3

  11. Peak of resonance ( ) + Resonance frequency ( ) e c r c r - Introducing a prototype second order system.

  12. + Closed-loop bandwidth ( ) e c r c r - -3 Introducing a prototype second order system.

  13. + e c r c r - Introducing a prototype second order system.

  14. Mapping نگاشت c' d c 4 2 a a' d' b b'

  15. Mapping نگاشت s=0.5 0.2 -2 1 15 15

  16. Mapping نگاشت r=0.5 1 -2 16 16

  17. r=0.5 Mapping نگاشت -2 -5 1 7 17 17

  18. Mapping نگاشت r=2.5 1 -2 18

  19. Nyquist fundamental 1+kf(s)=0 : تعداد صفرهای RHP، 1+kf(s) Nyquist path :تعداد قطبهای RHP، 1+kf(s)

  20. Nyquist fundamental Nyquist path 20

  21. Nyquist fundamental Nyquist path Nyquist plot 21

  22. Example 1: Check the stability of the following system by Nyquist method. + - -1 مثال 1: پایداری سیستم را توسط روش نایکوئیست بررسی کنید. 22

  23. + - -1 Example 1: Check the stability of the following system by Nyquist method. مثال 1: پایداری سیستم را توسط روش نایکوئیست بررسی کنید. 23

  24. Nyquist fundamental Nyquist path Nyquist plot 24

  25. مطالعه بیشتر More study + - -1 25

  26. + K G(s) - R(s) C(s) + + - - Exercises تمرینها 1- Assume the following control system Find the value of k which make the system stable. Answer: k>1 2- Consider the following control system Find the value of k which make the system stable.

  27. W=0 -1+j0 Exercises تمرینها 3- Polar plot of an open loop transfer function with two RHP poles is shown in the following: Discuss about the stability of system. Answer: It is unstable and it has 4 unstable poles.

  28. + + + + - - Exercises تمرینها 4- Discuss the stability of following system by Nyquist criteria. 5- Discuss the stability of following system by Nyquist criteria by use of following Nyquist path(Final 1391).

  29. + - -1 Example 2: Check the stability of following system by Nyquist method. مثال 2: پایداری سیستم را توسط روش نایکوئیست بررسی کنید. Very important Very important 29

  30. Example 2: Check the stability of following system by Nyquist method. + - -1 Very important پایداری سیستم را توسط روش نایکوئیست بررسی کنید. How to calculate? 30

  31. + - -1 Example 2: Check the stability of following system by Nyquist method. پایداری سیستم را توسط روش نایکوئیست بررسی کنید. 31

  32. + - -1 Example 2: Check the stability of following system by Nyquist method. پایداری سیستم را توسط روش نایکوئیست بررسی کنید. 32

  33. + - -1 مطالعه بیشتر More study 33

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