Identifying a non-commensurable fractional transfer function from a frequency response

Abstract

This paper extends Levy's identification method to non-commensurable fractional models. This identification method allows finding a transfer function that models a frequency response. Explicit expressions for the calculations, using five different variations of the method, are given. A sensitivity analysis supports an empirical way of finding the orders involved. Two application examples, concerning the identification of a model for a viscoelastic material and a model the human arm, are given.

Continuous-Time Fractional Order Linear Systems Identification Using Chebyshev Wavelet

“…Simplified refined instrumental vari-able (SRIVC) method [14], subspace method [15] and set member method [16] have also been proposed for fractional order system identification. In frequency domain, the Levy's identification method was extended by Val´erio et al to identify fractional transfer function [17][18][19]. The commensurate and non-commensurate fractional transfer function were studied in [17] and [19], respectively.…”

Magnitude–frequency responses of fractional order systems: properties and subsequent results

“…More specifically, analysis of frequency responses plays a significant role in control systems engineering. For example, till now various frequency response based methods have been proposed for identification of real‐world plants by using fractional order models [31–33]. Frequency responses are frequently referred in stability analysis of fractional order control systems [34, 35].…”

Analytical design of fractional order PID controllers based on the fractional set-point weighted structure: Case study in twin rotor helicopter

“…The existence of the tunable order a in the structure of the fractional order pre-filters makes these filters more flexible in comparison with the classical pre-filters [7]. This is due to the fact that the fractional calculus has a great potential to improve the traditional methods in different fields of control systems; such as controller design [11][12][13][14][15][16][17][18][19][20] and system identification [21][22][23][24][25]. Fractional order concepts are employed in simple and advanced control methodologies; such as set-point weighted fractional order PID (SWFOPID) controller [11,19], phase lead and lag compensator [14,26], internal model based fractional order controller [27], Smith predictor based fractional order controller [18,21], optimal fractional order controller [28,29], robust fractional order control systems [30][31][32], fuzzy fractional order controller [33], fractional order sliding mode controller [34], fractional order switching systems [35], and adaptive fractional order controller [17,36].…”