Fractional order controllers have been used intensively
over the last decades in controlling different types of processes. The main
methods for tuning such controllers are based on a frequency domain approach
followed by optimization routine, generally in the form of the Matlab fminsearch, but also evolving to more
complex routines, such as the genetic algorithms. An alternative to these time
consuming optimization routines, a simple graphical method has been proposed.
However, these graphical methods are not suitable for all combinations of the
imposed performance specifications. To preserve their simplicity, but also to
make these graphical methods generally applicable, a modified graphical method
using a very straightforward and simple optimization routine is proposed within
the paper. Two case studies are presented, for tuning fractional order PI and
PD controllers.
References
[1]
C.A. Monje, Y. Chen, B. M. Vinagre, D. Xue and V. Feliu, “Fractional-order Systems and Controls: Fundamentals and Applications,” Springer, London, 2010. doi:10.1007/978-1-84996-335-0
[2]
C. I. Pop (Muresan), C. M. Ionescu, R. De Keyser, E. H. Dulf, “Robustness Evaluation of Fractional Order Control for Varying Time Delay Processes,” Signal, Image and Video Processing, Vol. 6, 2012, pp. 453-461. doi:10.1007/s11760-012-0322-4
[3]
A. Oustaloup,” La Commande CRONE: Commande Robust d’ordre non entiere,” Hermes, Paris, France, 1991
[4]
C. A. Monje, B. Vinagre, Y. Chen and V. Feliu, “On Fractional PIλcontrollers: Some Tuning Rules for Robustness to Plant Uncertainties,” Nonlinear Dynam, Vol. 38, 2004, pp. 369-381. doi:10.1007/s11071-004-3767-3
[5]
C. I. Muresan, E. H. Dulf, R. Both, A. Palfi and M. Caprioru, “Microcontroller Implementation of a Multivariable Fractional Order PI Controller,” The 9th International Conference on Control Systems and Computer Science (CSCS19-2013), 29-31 May, Bucharest, Romania, Vol. 1, 2013, pp. 44-51.
[6]
Y. Luo and Y. Chen, “Fractional Order Motion Controls,” John Wiley & Sons, 2012. doi:10.1002/9781118387726
[7]
Y. Luo, Y. Chen, C.Y. Wang and Y. G. Pi, “Tuning Fractional Order Proportional Integral Controllers for Fractional Order Systems,” Journal of Process Control, Vol. 20, 2010, pp. 823-831. doi:10.1016/j.jprocont.2010.04.011
[8]
C.A. Monje, B. Vinagre, Y. Chen and V. Feliu, “On Fractional PIλcontrollers: Some Tuning Rules for Robustness to Plant Uncertainties,” Nonlinear Dynam, Vol. 38, 2004, pp. 369-381. doi:10.1007/s11071-004-3767-3
[9]
Y. Q. Chen and K. L. Moore, “Discretization Schemes for Fractional-order Differentiators and Integrators,” IEEE T. Circuits.-I., Vol. 49, 2002, pp. 363-367.
[10]
Y. Q. Chen, H. Dou, B. M. Vinagre and C. A. Monje, “A Robust Tuning Method for Fractional Order PI Controllers,” Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, Portugal, 2006.
