Fractional Control With a Smith Predictor

The advantageous use of fractional calculus (FC) in the modeling and control of many dynamical systems has been recognized. In this paper, we study the control of a heat diffusion system based on the application of the FC concepts. Several algorithms are investigated and compared, when integrated within a Smith predictor control structure. Simulations are presented assessing the performance of the proposed fractional algorithms.

[1]  Yun Li,et al.  Performance indices in evolutionary CACSD automation with application to batch PID generation , 1999, Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404).

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

[3]  José António Tenreiro Machado,et al.  Application of Fractional Calculus in the Control of Heat Systems , 2007, J. Adv. Comput. Intell. Intell. Informatics.

[4]  Y. Chen,et al.  Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review , 2004 .

[5]  D. P. Atherton,et al.  Automatic tuning of optimum PID controllers , 1993 .

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

[7]  I. S. Jesus,et al.  Fractional control of heat diffusion systems , 2008 .

[8]  B. Vinagre Practical application of digital fractional-order controller to temperature control , 2002 .

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

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

[11]  J. Machado,et al.  Smith Predictor Embedded With Fractional Algorithms for the Control of a Heat Diffusion System , 2009 .

[12]  On the Fractional Order Control of Heat Systems , 2009 .

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

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

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

[16]  Kevin L. Moore,et al.  Relay feedback tuning of robust PID controllers with iso-damping property , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[17]  William S. Levine,et al.  The Control Handbook , 2010 .

[18]  John Crank,et al.  The Mathematics Of Diffusion , 1956 .

[19]  J. A. Tenreiro Machado,et al.  Tuning of PID Controllers Based on Bode’s Ideal Transfer Function , 2004 .

[20]  Hilbert,et al.  Methods of Mathematical Physics, vol. II. Partial Differential Equations , 1963 .

[21]  J.A.T. Machado,et al.  Strategies for the Control of Heat Diffusion Systems Based on Fractional Calculus , 2006, 2006 IEEE International Conference on Computational Cybernetics.

[22]  J. Battaglia,et al.  Solving an inverse heat conduction problem using a non-integer identified model , 2001 .

[23]  Curtis F. Gerald,et al.  APPLIED NUMERICAL ANALYSIS , 1972, The Mathematical Gazette.