Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.


    Access

    Access via TIB

    Check availability in my library


    Export, share and cite



    Title :

    Control of Initialized Fractional-Order Systems


    Contributors:

    Publication date :

    2002-03-01


    Type of media :

    Report


    Type of material :

    No indication


    Language :

    English




    Control of Initialized Fractional-Order Systems

    T. T. Hartly / C. F. Lorenzo | NTIS | 2002


    Optimal Rendezvous Trajectories Initialized with Analytical Radial Thrust Solutions

    Vedantam, Mihir / Kaki, Siddarth / Akella, Maruthi | AIAA | 2024


    Initialized Design Knowledge Model Constructing for Complex Structural Components

    Jia, L. / Hong, J. / Qiu, Z. | British Library Online Contents | 2008


    A Particle Swarm Optimization Algorithm with Initialized Adaptive Inertia Weights

    Du, J. / Zhang, F. / Li, J. et al. | British Library Online Contents | 2012


    Fractional-Order Control for TITO Systems

    Copot, Cosmin / Ionescu, Clara Mihaela / Muresan, Cristina I. | Springer Verlag | 2020