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

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LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad

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

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

Ali Karimpour Apr 2009 Lecture Mapping نگاشت s=

Ali Karimpour Apr 2009 Lecture Mapping نگاشت r=

Ali Karimpour Apr 2009 Lecture Mapping نگاشت 1 -2 r=

Ali Karimpour Apr 2009 Lecture Mapping نگاشت r=2.5

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

Ali Karimpour Apr 2009 Lecture Nyquist path Nyquist fundamental

Ali Karimpour Apr 2009 Lecture Nyquist path Nyquist plot Nyquist fundamental

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

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

Ali Karimpour Apr 2009 Lecture Nyquist path Nyquist plot Nyquist fundamental

Ali Karimpour Apr 2009 Lecture More study مطالعه بیشتر + -

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

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

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

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

Ali Karimpour Apr 2009 Lecture More study مطالعه بیشتر

Ali Karimpour Apr 2009 Lecture ٍ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)

Ali Karimpour Apr 2009 Lecture ٍ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)

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

Ali Karimpour Apr 2009 Lecture 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.

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