An innovative fixed-pole numerical approximation for fractional order systems. (May 2016)

• Record Type: Journal Article
• Authors: Wei, Yiheng; Tse, Peter W.; Du, Bin; Wang, Yong
• Is Part Of: ISA transactions. Volume 62(2016:May)
• Page Start: 94
• Page End: 102
• Publication Date: 2016-05
• Subjects: Fractional order systems -- Numerical approximation -- Identification -- Caputo derivative -- Fixed-pole -- Non-zero initial conditions; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2016.01.010
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: A novel numerical approximation scheme is proposed for fractional order systems by the concept of identification. An identical equation is derived firstly, from which one can obtain the exact state space model of fractional order systems. It reveals the nature of the approximation problem, and then provides an effective scheme to obtain the desired model. This research project also focuses on solving a knotty but crucial issue, i.e., the initial value problem of fractional order systems. The results generated by the study prove that it can reduce to the Caputo case by selecting some specific initial values. A careful simulation study is reported to illustrate the effectiveness of the proposed scheme. To exhibit the superiority clearly, the results are compared with that of the published fixed-pole finite model method. Abstract : Highlights: The nature of such a class of approximation problem is revealed. The concept of identification is applied and the poles extend to be complex. The fixed-pole approach is adopted. The approximate model is discussed in detail. The initial condition problem is studied finally.