An adaptive fractional-order controller

This paper deals with a possible adaptation algorithm for the fractional order controllers. Suggested adaptation is based on the heuristic principle, where the controller gain and the fractional order could be adapted. The fractional order controller is presented in discrete form together with implementation algorithm. An illustrative example is presented in order to show the main advantage of such kind of the controllers. Some additional comments and proposals are presented as well.

[1]  Samir Ladaci,et al.  On Fractional Adaptive Control , 2006 .

[2]  A. Oustaloup.  La dérivation non entière , 1995 .

[3]  Ivo Petráš,et al.  Tuning and implementation methods for fractional-order controllers , 2012 .

[4]  YangQuan Chen,et al.  Fractional order control - A tutorial , 2009, 2009 American Control Conference.

[5]  YangQuan Chen,et al.  Fractional-order systems and control : fundamentals and applications , 2010 .

[6]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[7]  Y. Q. Chen,et al.  Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control , 2002 .

[8]  YangQuan Chen,et al.  A Fractional Adaptation Scheme for Lateral Control of an AGV , 2008 .

[9]  YangQuan Chen,et al.  Tuning and auto-tuning of fractional order controllers for industry applications , 2008 .

[10]  Jaroslav Marsík,et al.  Application of identification-free algorithms for adaptive control , 1989, Autom..

[11]  Tore Hägglund,et al.  Advanced PID Control , 2005 .

[12]  YangQuan Chen,et al.  UBIQUITOUS FRACTIONAL ORDER CONTROLS , 2006 .

[13]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[14]  A. J. Calderón,et al.  Fractional PID Controllers for Industry Application. A Brief Introduction , 2007 .

[15]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[16]  Y. Chen,et al.  Fractional order adaptive feedforward cancellation , 2011, Proceedings of the 2011 American Control Conference.

[17]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[18]  W. Marsden.  I and J , 2012 .

[19]  Ivo Petras,et al.  Fractional-Order Nonlinear Systems , 2011 .

[20]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[21]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[22]  S. Manabe.  The non-integer integral and its application to control systems. , 1961 .

[23]  R. Magin.  Fractional Calculus in Bioengineering , 2006 .

[24]  F. Mainardi.  Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[25]  Yangquan Chen,et al.  Two direct Tustin discretization methods for fractional-order differentiator/integrator , 2003, J. Frankl. Inst..

[26]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[27]  Y. Chen,et al.  Fractional Order Motion Controls , 2012 .

[28]  Reza Ghaderi,et al.  Adaptive Fractional PID Controller for Robot Manipulator , 2012, ArXiv.

[29]  José António Tenreiro Machado,et al.  Time domain design of fractional differintegrators using least-squares , 2006, Signal Process..

[30]  I. Petráš.  Fractional Order Systems , 2011 .

[31]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[32]  I. Podlubny.  Fractional differential equations , 1998 .

[33]  V. Strejc,et al.  Applications of Identification-Free Algorithms for Adaptive Control , 1987 .