Presentation is loading. Please wait.

Presentation is loading. Please wait.

LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad.

Similar presentations


Presentation on theme: "LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad."— Presentation transcript:

1 LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad

2 Ali Karimpour Apr 2009 Lecture 24 2 Nyquist stability criteria. Topics to be covered include: Nyquist stability criteria.

3 Ali Karimpour Apr 2009 Lecture 24 3 Mapping نگاشت b' b d c a a' c' d' 2 4

4 Ali Karimpour Apr 2009 Lecture 24 444 Mapping نگاشت s=0.5 1 -2 0.2

5 Ali Karimpour Apr 2009 Lecture 24 555 Mapping نگاشت r=0.5 1 -2

6 Ali Karimpour Apr 2009 Lecture 24 666 Mapping نگاشت 1 -2 r=0.5 -5 7

7 Ali Karimpour Apr 2009 Lecture 24 77 1 -2 Mapping نگاشت r=2.5

8 Ali Karimpour Apr 2009 Lecture 24 8 1+kf(s)=0 : تعداد قطبهای RHP، 1+kf(s) Nyquist path Nyquist fundamental : تعداد صفرهای RHP، 1+kf(s)

9 Ali Karimpour Apr 2009 Lecture 24 99 Nyquist path Nyquist fundamental

10 Ali Karimpour Apr 2009 Lecture 24 10 Nyquist path Nyquist plot Nyquist fundamental

11 Ali Karimpour Apr 2009 Lecture 24 11 Example 1: Check the stability of the following system by Nyquist method. مثال 1 : پایداری سیستم را توسط روش نایکوئیست بررسی کنید. + -

12 Ali Karimpour Apr 2009 Lecture 24 12 Example 1: Check the stability of the following system by Nyquist method. مثال 1 : پایداری سیستم را توسط روش نایکوئیست بررسی کنید. + -

13 Ali Karimpour Apr 2009 Lecture 24 13 Nyquist path Nyquist plot Nyquist fundamental

14 Ali Karimpour Apr 2009 Lecture 24 14 More study مطالعه بیشتر + -

15 Ali Karimpour Apr 2009 Lecture 24 15 + - Very important Example 2: Check the stability of following system by Nyquist method. مثال 2 : پایداری سیستم را توسط روش نایکوئیست بررسی کنید.

16 Ali Karimpour Apr 2009 Lecture 24 16 Example 2: Check the stability of following system by Nyquist method. پایداری سیستم را توسط روش نایکوئیست بررسی کنید. + - Very important How to calculate?

17 Ali Karimpour Apr 2009 Lecture 24 17 Example 2: Check the stability of following system by Nyquist method. پایداری سیستم را توسط روش نایکوئیست بررسی کنید. + -

18 Ali Karimpour Apr 2009 Lecture 24 18 Example 2: Check the stability of following system by Nyquist method. پایداری سیستم را توسط روش نایکوئیست بررسی کنید. + -

19 Ali Karimpour Apr 2009 Lecture 24 19 + - More study مطالعه بیشتر

20 Ali Karimpour Apr 2009 Lecture 24 20 + - ٍExample 3: Check the stability of following system from the given Nyquist plot. مثال 3 : پایداری سیستم را با توجه به منحنی نایکوئیست داده شده بررسی کنید. d(s) is a polynomial. System is unstable( 1 RHP zero) System is stable System is unstable( 2 RHP zero) System is unstable( 1 RHP zero)

21 Ali Karimpour Apr 2009 Lecture 24 21 + - ٍExample 3: Check the stability of following system from the given Nyquist plot. مثال 3 : پایداری سیستم را با توجه به منحنی نایکوئیست داده شده بررسی کنید. d(s) is a polynomial. System is unstable( 1 RHP zero) System is stable System is unstable( 2 RHP zero) System is unstable( 1 RHP zero)

22 Ali Karimpour Apr 2009 Lecture 24 22 Exercises تمرینها 1- Assume the following control system Find the value of k which make the system stable. Answer: k>1 + - + - R(s)C(s) 2- Consider the following control system Find the value of k which make the system stable. + G(s) - K

23 Ali Karimpour Apr 2009 Lecture 24 23 Exercises تمرینها 3- Polar plot of an open loop transfer function is shown in the following: W=0 -1+j0 Discuss about the stability of system. Answer: It is unstable and it has 4 unstable poles.

24 Ali Karimpour Apr 2009 Lecture 24 24 Exercises تمرینها 4- Discuss the stability of following system by Nyquist criteria.. + + -


Download ppt "LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad."

Similar presentations


Ads by Google