GENERALIZED ALGORITHM FOR ESTIMATING NON-COMMENSURATE FRACTIONAL-ORDER MODELS A. Taskinen, T. Roinila, M. Vilkko ABSTRACT The dynamics of real systems are often of fractional-order but typically approximated using integer-order models for simplicity. Due to the major improvements in the area of fractional-order calculus during the last years, the fractional-order methods may be used more efficientl thus providing more accurate and realistic models. This paper presents an algorithm to estimate non-commensurate fractional-order models from frequency response data. Compared to the traditional method where only commensurate models are estimated, the presented technique provides more accurate models. The theory behind the method is shown and the results are illustrated by experimental measurements from a viscous elastic component, made from Polydimethylsiloxane (PDMS), a silicon-based organic polymer. Key Words: Fractional Dynamics, Non-Commensurate Order, Frequency Response I. INTRODUCTION A wide range of real world-phenomena exhibit fractional-order dynamics. Before the last years, the fiel has not gained too much popularity. This is likely because the basic principles starting from multiple definition of fractional differential operator seem at firs sight quite complex. This has been, however, changed due to the rapidly increasing development of computing power and level of understanding. To date fractional-order systems have gained popularity in various field of engineering such as in stability analysis [1], system identificatio [2, 3], system approximation [4], control [5, 6], and analysis [5, 7]. It may be obvious, that utilizing a fractional-order model instead of an integer-order model provides more accurate model and hence more valuable design tool whenever a system exhibits fractional dynamics. Thus, more efficien results can be obtained for any model- based applications such as simulation or prediction. Manuscript received--. The authors are with the Department of Automation Science and Control, Tampere University of Technology, Tampere, Finland, P.O. Box 692, FIN-33101, e-mail: first name.lastname@tut.fi Another advantage of fractional-order modeling lies behind the fact that in some cases the model can be significantl simpler than corresponding integer- order model. One such case is modeling of long electric transmission lines where an infinit number of resistors and capacitors can be modeled as a single half- integrator [8]. The fractional-order dynamics are typically stud- ied applying commensurate models, meaning that both the numerator and denominator polynomials consist of powers with common basis, allowed to be any rational number. Hence, the identificatio procedure becomes more complex. The importance of fractional- order identificatio has been well stated in previous studies. According to [9], system identificatio by applying fractional-order computation was initiated by the authors in [10–12]. They proposed two different approaches; equation error (ER)-based and output error- based approaches. Both methods are well studied for integer-order models. Since then, the development in the fiel of fractional-order identificatio has been rapid. Practical challenges have also been considered; various filte methods have been proposed for fractional-order models [13, 14], and time-delay issues have been considered [9]. Many of the proposed c  The published version is 1 page shorter