Characteristic ratio assignment in fractional order systems

Design and implementation of fractional order pole placement controller to control the magnetic flux in Damavand tokamak

“…Two most important methods to relate polynomial coefficients and transient time response of integer and fractional order systems are CDM 14 and generalized CRA, 16 respectively. These methods are useful for higher order transfer functions.…”

“…Considering a 0 and having γ i and τ, the coefficients M α (s) are determined uniquely 16 M α (s) = 1 a n s nλ + a n−1 s (n−1)λ + · · · + a 1 s λ + a 0 ,…”

“…For various practical physics studies, it is necessary to have different time responses in the control system of the magnetic flux. In this sub-section, to provide this facility, at first, two desired closed loop reference models are presented based on the technical specifications in the plant by using CDM method 14 for two different rise times of t r = 3.5 and 1 ms. Then, a desired closed loop reference model is presented for the plant by means of generalized CRA method 16 for the rise time t r = 1 ms. After that, FOPPC is designed and implemented for tracking these reference models.…”

“…To investigate a faster response request, an integer secondorder with the rise time of 1 ms and maximum overshoot 2% is designed using open loop model G 3n10 in (16). The same characteristic of response γ = [2.5, 2] is demanded with a different speed.…”

“…The aim of this paper is to use the CDM method 14 and generalized CRA method 16 The overall structure of the paper is as follows: In Sec. II, a brief introduction in fractional order calculation is presented.…”