Design of a fractional - Order controller for the setpoint ramp tracking problem

It is well known that a classical PI controller cannot accurately follow a ramp setpoint. A real world situation which shows this behavior could be a system composed of a direct current motor whose input setpoint is an acceleration/deceleration ramp. In this paper, we propose the design of a fractional PIλ controller, with a fractional-order parameter λ > 1, as a well suited approach to solve this problem. The design methodology is frequency-based, which allows finding the corresponding fractional controller parameters in order to guarantee stability, robustness and zero steady-state error.

[1]  María Luisa Cuadrado Ebrero,et al.  Temas de variable compleja , 1989 .

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

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

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

[5]  S. Westerlund,et al.  Capacitor theory , 1994 .

[6]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[7]  José António Tenreiro Machado,et al.  Effect of fractional orders in the velocity control of a servo system , 2010, Comput. Math. Appl..

[8]  J. A. Tenreiro Machado,et al.  New Trends in Nanotechnology and Fractional Calculus Applications , 2010 .

[9]  Alain Oustaloup,et al.  Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench , 2004 .

[10]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[11]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[12]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[13]  Ivo Petráš,et al.  FRACTIONAL – ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

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

[15]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[16]  J. A. Tenreiro Machado,et al.  Special Issue on “Discontinuous and Fractional Dynamical Systems” , 2008 .

[17]  Duarte Valério,et al.  NINTEGER: A NON-INTEGER CONTROL TOOLBOX FOR MATLAB , 2004 .

[18]  Rafael Arnay,et al.  Towards a Multiagent Approach for the VERDINO Prototype , 2009, IWANN.

[19]  Ivo Petraÿs,et al.  FRACTIONAL - ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

[20]  José António Tenreiro Machado,et al.  Fractional differentiation and its applications I , 2013, Comput. Math. Appl..

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

[22]  Yangquan Chen,et al.  Matrix approach to discrete fractional calculus II: Partial fractional differential equations , 2008, J. Comput. Phys..

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