A Frequency criterion for analysis of stability of systems with fractional-order derivatives

Abstract

Based on an analysis of the influence of the roots of a characteristic polynomial on the increment of the argument of the frequency characteristic of the system, the frequency criterion of stability of a system with fractional-order derivatives has been suggested. The boundaries of the zone of location of the roots of the characteristic polynomial of a stable system have been determined in a complex plane when the index α of the basis of the characteristic polynomial changes.

Formation of Characteristic Polynomials on the Basis of Fractional Powers j of Dynamic Systems and Stability Problems of Such Systems

“…In particular, no single method has been developed to form a characteristic polynomial taking into account the features of fractional order ACS, defining the concept of its order, stability criteria of such a fractional control system, and other theory provisions that describe the dynamic properties of fractional systems as for integer ACS. One of the first works, where the task of stability research of fractional systems in the frequency domain and the frequency criterion of stability is offered, is work [8].…”

“…Nevertheless, the analysis of a number of works [1][2][3][4][5][6][7][8][9][10] devoted to the stability of fractional order systems does not allow us to say unequivocally how best to form a characteristic polynomial. It is possible on the basis of a wide range of possible values of the fractional degree j, some one, or on the basis of bringing different values of the fractional degrees of the elements of the fractional characteristic polynomial to a common denominator.…”

Control Techniques for a Class of Fractional Order Systems

“…The control of multi-system architectures defined by FOS models is discussed in [29][30][31]. Frequency criteria for the control of Linear FOS are presented in [32][33][34]. A comprehensive review of literature related to the industrial use and integration of FOPID control is presented in [35].…”