Fractional order modelling of dynamic backlash

Mechatronics

Volumn 23, Issue 7, 2013, Pages 741-745

  Tenreiro Machado, J A ^a  

^a INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

Author keywords

Backlash; Fractional calculus; Fractional derivatives; Impacts; Modelling

Indexed keywords

MECHANICAL ENGINEERING; MECHATRONICS; MODELS;

BACKLASH; DYNAMICAL EFFECTS; DYNAMICAL PROPERTIES; FRACTIONAL CALCULUS; FRACTIONAL DERIVATIVES; FRACTIONAL MODEL; FRACTIONAL ORDER; IMPACTS;

CALCULATIONS;

EID: 84886285450     PISSN: 09574158     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechatronics.2013.01.011     Document Type: Article

References (44)

1. A. Azenha, and J.T. Machado On the describing function method and the prediction of limit cycles in nonlinear dynamical systems J Syst Anal Modell Simul 33 3 1998 307 320
2. D. Baleanu About fractional quantization and fractional variational principles Commun Nonlinear Sci Numer Simul 14 6 2009 2520 2523
3. D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo Fractional calculus: models and numerical methods 2012 World Scientific Boston (Mass, USA)
4. R.S. Barbosa, and J.T. Machado Describing function analysis of systems with impacts and backlash Nonlinear Dyn 29 1-4 2002 235 250
5. Y.Q. Chen, and K.L. Moore Discretization schemes for fractional-order differentiators and integrators IEEE Trans Circ Syst - I: Fundam Theory Appl 49 3 2002 363 367
6. Y.S. Choi, and S.T. Noah Periodic response of a link coupling with clearance ASME J Dyn Syst Measur Control 111 2 1989 253 259
7. N.G. Dagalakis, and D.R. Myers Adjustment of robot joint gear backlash using the robot joint test excitation technique Int J Rob Res 4 2 1985 65 79
8. F. Duarte, and J.T. Machado Describing function of two masses with backlash Nonlinear Dyn 56 4 2009 409 413
9. R. Hilfer Application of fractional calculus in physics 2000 World Scientific Singapore
10. Hovland G, Hanssen S, Gallestey E, Moberg S, Brogrdh T, Gunnarsson S, Isaksson M. Nonlinear identification of backlash in robot transmissions. In: Proc. of the 33rd int. symposium on robotics, Stockholm, Sweden; 2002.
11. C.M. Ionescu Phase constancy in a ladder model of neural dynamics Trans Syst Man Cyber Part A - Syst Humans 42 6 2012 1543 1551
12. C.M. Ionescu, and R. De Keyser Relations between fractional-order model parameters and lung pathology in chronic obstructive pulmonary disease IEEE Trans Biomed Eng 56 4 2009 978 987
13. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and applications of fractional differential equations North-Holland mathematics studies vol. 204 2006 Elsevier Amsterdam
14. Y. Li, Y.Q. Chen, and I. Podlubny Mittag-Leffler stability of fractional order nonlinear dynamic systems Automatica 45 8 2009 1965 1969
15. M.F.M. Lima, J.T. Machado, and M. Crisóstomo Filtering method in backlash phenomena analysis Math Comput Modell 49 4 2009 1494 1503
16. M.F.M. Lima, J.T. Machado, and M. Crisóstomo Experimental backlash study in mechanical manipulators Robotica 29 2 2011 211 219
17. Ying Luo, and YangQuan Chen Fractional order motion controls 2012 Wiley Chichester
18. Ma C, Hori Y. The application of fractional order control to backlash vibration suppression. In: Proc. of American control conference, Boston (Massachusetts, USA); 2004. p. 2901-6.
19. J.A. Tenreiro Machado Analysis and design of fractional-order digital control systems Syst Anal Modell Simul 27 2-3 1997 107 122
20. J.A. Tenreiro Machado Discrete-time fractional-order controllers Fract Calc Appl Anal 4 1 2001 47 66
21. J.T. Machado, and A.M.S. Galhano Fractional dynamics: a statistical perspective ASME J Comput Nonlinear Dyn 3 2 2008 021201-1 021201-5
22. R.L. Magin Fractional calculus in bioengineering 2006 Begell House Inc. Redding
23. F. Mainardi Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models 2010 Imperial College Press London
24. Merzouki R, Davila JA, Cadiou JC, Fridman L. Backlash phenomenon observation and identification. In: Proc. of American Control Conference, France; 2006. p. 3322-7.
25. K.S. Miller, and B. Ross An introduction to the fractional calculus and fractional differential equations 1993 John Wiley and Sons New York
26. C.A. Monje, Y. Chen, B.M. Vinagre, D. Xue, and V. Feliu Fractional-order systems and controls: fundamentals and applications 2010 Springer London
27. M. Nordin and P. Gutman, Non-linear speed control of elastic systems with backlash. In: Proc. 39th IEEE conf. on decision and control, Sydney (Australia); 2000. p. 4060-5.
28. M. Nordin, and P. Gutman Controlling mechanical systems with backlash - a survey Automaticas 38 10 2002 1633 1649
29. K.B. Oldham, and J. Spanier The fractional calculus: theory and application of differentiation and integration to arbitrary order 1974 Academic Press New York
30. Oustaloup A. La commande CRONE: commande robuste d'ordre non entier. Hermès (Paris, France); 1991.
31. I. Podlubny Fractional differential equations An introduction to fractional derivatives, fractional differential equations, to methods of their solution, mathematics in science and engineering vol. 198 1998 Academic Press San Diego
32. μ-controllers IEEE Trans Autom Control 44 1 1999 208 213
33. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional integrals and derivatives: theory and applications 1993 Gordon and Breach Science Publishers Amsterdam
34. N. Sarkar, R.E. Ellis, and T.N. Moore Backlash detection in geared mechanisms: modeling, simulation, and experimentation Mech Syst Signal Process 11 3 1997 391 408
35. D.R. Seidl, S. Lam, J.A. Putman, and R.D. Lorenz Neural network compensation of gear backlash hysteresis in position-controlled mechanisms IEEE Trans Ind Appl 31 6 1995 1475 1483
36. H. Sheng, Y. Chen, and T. Qiu Fractional processes and fractional-order signal processing: techniques and applications 2012 Springer London
37. Stein JL, Wang C. Automatic detection of clearance in mechanical systems: theory and simulation. In: Proc. American control conference, Seattle (Washington, USA); 1995. p. 1737-45.
38. Y. Stepanenko, and T.S. Sankar Vibro-impact analysis of control systems with mechanical clearance and its application to robotic actuators ASME J Dyn Syst Measur Control 108 1 1986 9 16
39. C. Su, M. Oya, and H. Hong Stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash-like hysteresis IEEE Trans Fuzzy Syst 11 1 2003 1 8
40. V.E. Tarasov Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media 2010 Springer New York
41. I. Trendafilova, and H. Van Brussel Non-linear dynamics tools for the motion analysis and condition monitoring of robot joints Mech Syst Signal Process 15 6 2001 1141 1164
42. B. West, M. Bologna, and P. Grigolini Physics of fractal operators 2003 Springer New York
43. S. Westerlund, and L. Ekstam Capacitor theory IEEE Trans Dielectrics Electr Insulat 1 5 1994 826 839
44. G.M. Zaslavsky Hamiltonian chaos and fractional dynamics 2005 Oxford University Press Oxford