Fractional calculus (FC) is widely used in most areas of science and engineering, being recognized its ability to yield a superior modeling and control in many dynamical systems. In this perspective, this article illustrates two applications of FC in the area of control systems. Firstly, is presented a methodology of tuning PID controllers that gives closed-loop systems robust to gain variations. After, a fractional-order PID controller is proposed for the control of an hexapod robot with three dof legs. In both cases, it is demonstrated the system's superior performance by using the FC concepts.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Oldham, K. B. and Spanier, J. (1974) The Fractional Calculus. Academic, New York
Podlubny, I. (1999) Fractional Differential Equations. Academic, San Diego, CA
Podlubny, I., Dorcak, L. and Kostial, I. (1997) On Fractional Derivatives, Fractional-Order Dynamics Systems and PIλD¼-Controllers. In: 36th IEEE Conference on Decision and Control. San Diego, CA
Podlubny, I. (1999) Fractional-Order Systems and PIλD¼-Controllers. IEEE Transactions on Automatic Control 44(1):208–214
Bode, H. W. (1945) Network Analysis and Feedback Amplifier Design. Van Nostrand, New York
Miller, K. S. and Ross, B. (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York
Barbosa, R. S., Machado, J. A. T., and Ferreira, I. M. (2004) PID Controller Tuning Using Fractional Calculus Concepts. Journal of Fractional Calculus and Applied Analysis 7(2):119–134
Barbosa, R. S., Machado, J. A. T., and Ferreira, I. M. (2004) Tuning of PID Controllers Based on Bode's Ideal Transfer Function. Nonlinear Dynamics 38(1–4):305–321
Silva, M. F., Machado, J. A. T. and Lopes, A. M. (2003) Comparison of Fractional and Integer Order Control of an Hexapod Robot. In: Proceedings of VIB 2003 – ASME International 19th Biennial Conference on Mechanical Vibration and Noise. USA
Silva, M. F., Machado, J. A. T. and Jesus, I. S. (2006) Modelling and Simulation of Walking Robots With 3 dof Legs. In: MIC 2006 – The 25th IASTED International Conference on Modelling, Identification and Control. Lanzarote, Spain
Silva, M. F., Machado, J. A. T. (2006) Fractional Order PDα Joint Control of Legged Robots. Journal of Vibration and Control - Special Issue on Modeling and Control of Artificial Locomotion Systems 12(12):1483–1501
Silva, M. F., Machado, J. A. T. (2003) Position/Force Control of a Walking Robot. MIROC — Machine Intelligence and Robot Control 5:33–44
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Barbosa, R.S., Silva, M.F., Machado, J.A.T. (2009). Tuning and Application of Integer and Fractional Order PID Controllers. In: Machado, J.A.T., Pátkai, B., Rudas, I.J. (eds) Intelligent Engineering Systems and Computational Cybernetics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8678-6_21
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8678-6_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8677-9
Online ISBN: 978-1-4020-8678-6
eBook Packages: Computer ScienceComputer Science (R0)