A new and simple method to construct root locus of general fractional-order systems

Patil, Mukesh D.; Vyawahare, Vishwesh A.; K.Bhole, Manisha

doi:10.1016/j.isatra.2013.09.002

Cited by 30 publications

(9 citation statements)

References 13 publications

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“…In Table III (case a < 0, K > 1), the system oscillates when 0:25π ¼ sec À1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1:25 þ p osc p , then the value of p osc = 0.75. Figure 6(b) shows the number of unstable poles function against p, where the system moves from unstable to stable behavior when p = 0.75, and the frequency response is shown in Figure 6(c), which is consistent with [37].…”

Section: Conditionssupporting

confidence: 76%

“…which can be written in the form D s ð Þ ¼ 0:8s 22α þ 0:5s 9α þ 1 þ p; α ¼ 0:1: (66) Figure 6(d) shows the number of unstable poles function against p, where the system switches from stable to unstable behavior when p = 1.316, which is consistent with [37].…”

Section: Conditionssupporting

confidence: 73%

“…In Tables II and III, the number of physical poles functions (N*) when a = À 1is Example (3): [37,38]: Consider the following characteristic equation: D s ð Þ ¼ s 2 À 3s 1:5 À 2s þ 2 þ p ð Þs 0:5 þ 12 À p; p ≥ 0: (61) This example can be written in the form D s ð Þ ¼ s 4α À 3s 3α À 2s 2α þ 2 þ p ð Þs α þ 12 À p; α ¼ 0:5: (62) Figure 6(a) shows the number of unstable poles function (40) against p, where the system is always unstable, which is consistent with [37,38]. In Tables II and III, the number of physical poles functions (N*) when a = À 1is Example (3): [37,38]: Consider the following characteristic equation: D s ð Þ ¼ s 2 À 3s 1:5 À 2s þ 2 þ p ð Þs 0:5 þ 12 À p; p ≥ 0: (61) This example can be written in the form D s ð Þ ¼ s 4α À 3s 3α À 2s 2α þ 2 þ p ð Þs α þ 12 À p; α ¼ 0:5: (62) Figure 6(a) shows the number of unstable poles function (40) against p, where the system is always unstable, which is consistent with [37,38].…”

Section: Conditionsmentioning

confidence: 99%

“…Example (5): [37]: Consider the following characteristic equation: D s ð Þ ¼ 0:8s 2:2 þ 0:5s 0:9 þ 1 þ p; p ≥ 0;…”

Section: Conditionsmentioning

confidence: 99%

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Fundamentals of fractional‐order LTI circuits and systems: number of poles, stability, time and frequency responses

Semary

Radwan

Hassan

2016

Circuit Theory & Apps

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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 relationships 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 invariant systems based on fractional-order differential equations have been discussed numerically in both time and frequency domains to validate the previous fundamentals.

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Section: Conditionssupporting

confidence: 76%

Section: Conditionssupporting

confidence: 73%

Section: Conditionsmentioning

confidence: 99%

“…Example (5): [37]: Consider the following characteristic equation: D s ð Þ ¼ 0:8s 2:2 þ 0:5s 0:9 þ 1 þ p; p ≥ 0;…”

Section: Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

Fundamentals of fractional‐order LTI circuits and systems: number of poles, stability, time and frequency responses

Semary

Radwan

Hassan

2016

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…There is a method to construct the root locus of a fractional order control system [71,72] . Based on the root locus, one can perform an analysis of the system.…”

Section: Other Work On Fractional Pid Controllermentioning

confidence: 99%