This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.
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
Slotine JE, Li W (1991) Applied Nonlinear Control. Prentice-Hall, NJ
Podlubny I (1999) Fractional Differential Equations. Academic, San Diego, CA
Duarte F, Machado JA (2006) Fractional Dynamics in the Describing Function Analysis of Nonlinear Friction. In: 2nd IFAC Workshop on Fractional Differentiation and Its Applications, Porto, Portugal
Azenha A, Machado JA (1996) Limit Cycles Prediction of Robot Systems with Nonlinear Phenomena in the Joints. In: 27th International Symposium on Industrial Robots, Milan, Italy, 1996, pp 1003–1008
Armstrong B, Dupont B, de Wit C (1994) A Survey of Models, Analysis Tools and Compensation Methods for the Machines with Friction. Automatica 30:1083–1183
Armstrong B, Amin B (1996) PID Control in the Presence of Static Friction: A Comparison of Algebraic and Describing Function Analysis. Automatica 32:679–692
Haessig DA, Friedland B (1991) On the Modelling and Simulation of Friction. ASME Journal of Dynamic Systems, Measurement and Control 113:354–362
Karnopp D (1985) Computer Simulation of Stick-Slip Friction in Mechanical Dynamic Systems. ASME Journal of Dynamic Systems, Measurement and Control 107:100–103
Cox CS (1987) Algorithms for Limit Cycle Prediction: A Tutorial Paper. International Journal of Electrical Engineering Education 24:165–182
Azenha A, Machado JA (1998) On the Describing Function Method and Prediction of Limit Cycles in Nonlinear Dynamical Systems. System Analysis-Modelling-Simulation 33:307–320
Barbosa R, Machado JA (2002) Describing Function Analysis of Systems with Impacts and Backlash. Nonlinear Dynamics 29:235–250
Barbosa R, Machado JA, Ferreira I (2003) Describing Function Analysis of Mechanical Systems with Nonlinear Friction and Backlash Phenomena. In: 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, Sevilla, Spain, 2003, pp 299–304
Duarte F, Machado JA (2005) Describing Function Method in Nonlinear Friction. In: IEEE, 1st International Conference on Electrical Engineering, Coimbra, Portugal, 2005
Atherton DP (1975) Nonlinear Control Engineering. IEEE, 1st International Conference on Electrical Engineering, Van Nostrand Reinhold Company, London
Dupont PE (1992) The Effect of Coulomb Friction on the Existence and Uniqueness of the Forward Dynamics Problem. In: Proceedings of the IEEE International Conference on Robotics and Automation, Nice, France, pp 1442–1447
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
Duarte, F.B.M., Machado, J.A.T. (2009). Fractional Describing Function of Systems with Nonlinear Friction. 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_22
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8678-6_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8677-9
Online ISBN: 978-1-4020-8678-6
eBook Packages: Computer ScienceComputer Science (R0)