أعضاء هيئة التدريس - جامعة بنها
Fundamentals of fractional-order LTI circuits and systems: number of poles, stability, time and frequency responses
International Journal of Circuit Theory and Application • 2016
معلومات البحث
المؤلفون
M. S. Semary; A. G. Radwan; Hany. N. Hassan
الكلمات المفتاحية
Fractional-order systems; stability analysis; control; poles; physical-plane; filters; time
invariant; linear system
المجلة العلمية
International Journal of Circuit Theory and Application
الناشر
Not Available
المجلد
Not Available
العدد
Not Available
الصفحات
Not Available
publication.type
International
رابط البحث
Not Available
المواد المرفقة
Not Available
الملخص
This paper investigates some basic concepts of fractional-order linear time invariant systems related to their
physical and non-physical transfer functions, poles, stability, time domain, frequency domain, and their rela-
tionships for different fractional-order differential equations. The analytical formula that calculates the number
of poles in physical and non-physical s-plane for different orders is achieved and verified using many practical
examples. The stability contour versus the number of poles in the physical s-plane for different fractional-order
systems is discussed in addition to the effect of the non-physical poles on the steady state responses. Moreover,
time domain responses based on Mittag-Leffler functions for both physical and non-physical transfer functions
are discussed for different cases, which confirm the stability analysis. Many fractional-order linear time invari-
ant systems based on fractional-order differential equations have been discussed numerically in both time and frequency domains to validate the previous fundamentals.
physical and non-physical transfer functions, poles, stability, time domain, frequency domain, and their rela-
tionships for different fractional-order differential equations. The analytical formula that calculates the number
of poles in physical and non-physical s-plane for different orders is achieved and verified using many practical
examples. The stability contour versus the number of poles in the physical s-plane for different fractional-order
systems is discussed in addition to the effect of the non-physical poles on the steady state responses. Moreover,
time domain responses based on Mittag-Leffler functions for both physical and non-physical transfer functions
are discussed for different cases, which confirm the stability analysis. Many fractional-order linear time invari-
ant systems based on fractional-order differential equations have been discussed numerically in both time and frequency domains to validate the previous fundamentals.