Robust tracking control for linear vibrating mechanical systems

Authors

DOI:

https://doi.org/10.17533/udea.redin.n75a20

Keywords:

mass-spring-damper systems, multiple degrees-of-freedom mechanical systems, active vibration control, mechanical vibration systems

Abstract

A novel output feedback tracking control approach is proposed for underactuated linear mass-spring-damper vibrating mechanical systems of multiple degrees of freedom. The presented control design methodology considers robustness against unmodeled dynamics and external forces. The proposed control scheme only requires measurements of the position output variable. Tracking error integral compensation is properly used to avoid real-time disturbance estimation. Analytical and numerical results prove the effectiveness of the introduced active vibration control scheme for resonant and chaotic vibration attenuation on the output variable response.

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Author Biography

Francisco Beltrán-Carbajal, Metropolitan Autonomous University

Research Professor, Department of Energy.

References

J. Han. “From PID to Active Disturbance Rejection Control”. IEEE Transaction on Industrial Electronics. Vol. 56. 2009. pp. 900-906.

Z. Gao. Active Disturbance Rejection Control: A Paradigm Shift in Feedback Control System Design. Proceedings of the American Control Conference. Minneapolis, USA. 2006. pp. 2399-2405.

M. Fliess, C. Join. “Model-free control”. International Journal of Control. Vol. 86. 2013. pp. 2228-2252.

B. Korenev, L. Reznikov. Dynamic Vibration Absorbers. 1st ed. Ed. John Wiley & Sons. Chichester, England. 1993. pp. 1-296.

F. Beltrán. “Variable frequency harmonic vibration suppression using active vibration absorption”. Rev. Fac. Ing. Univ. Ant. N.º 73. 2014. pp. 144-156.

F. Beltrán, G. Silva. “Adaptive-Like Vibration Control in Mechanical Systems with Unknown Parameters and Signals”. Asian J. Control. Vol. 15. 2013. pp. 1613- 1626.

F. Beltrán, G. Silva. “Active Vibration Control in Duffing Mechanical Systems Using Dynamic Vibration Absorbers”. Journal of Sound and Vibration. Vol. 333. 2014. pp. 3019-3030.

S. Zhou, J. Shi. “Active balancing and vibration control of rotating machinery: a survey”. Shock and Vibration Digest. Vol. 33. 2001. pp. 361-371.

J. Vance, F. Zeidan, B. Murphy. Machinery Vibratin and Rotordynamics. 1st ed. Ed. John Wiley & Sons. New Jersey, USA. 2010. pp. 71-114.

F. Beltrán, G. Silva, M. Arias. “Active Unbalance Control of Rotor Systems Using On-Line Algebraic Identification Methods”. Asian J. Control. Vol. 15. 2013. pp. 1627-1637.

K. Byung, R. Seung, P. Jong. “Development of a 3-axis desktop milling machine and a CNC system using advanced modern control algorithms”. International Journal of Precision Engineering and Manufacturing. Vol. 11. 2010. pp. 39-47.

F. Beltrán, E. Chavez, A. Favela, R. Vazquez. “Active Perturbation Rejection in Motion Control of Milling Machine Tools”. Rev. Fac. Ing. Univ. Ant. N.° 69. 2013. pp. 193-204.

E. Chavez, F. Beltrán, A. Valderrabano, A. Favela. “Active Vibration Control of Vehicle Suspension Systems Using Sliding Modes, Differential Flatness and Generalized Proportional-Integral Control”. Rev. Fac. Ing. Univ. Ant. N.° 61. 2011. pp. 104-113.

S. Rao. Mechanical Vibrations. 5th ed. Ed. Prentice Hall. New Jersey, USA. 2011. pp. 10-13.

S. Braun, D. Ewins, S. Rao. Encyclopedia of Vibration. 1st ed. Ed. Academic Press. London, UK. 2002. pp. 1-26.

A. Piersol, T. Paez. Harris’s Shock and Vibration Handbook. 6th ed. Ed. McGraw-Hill. Columbus, USA. 2010. pp. 6.1-6.33.

H. Sira, F. Beltrán, A. Blanco. “A Generalized Proportional Integral Output Feedback Controller for the Robust Perturbation Rejection in a Mechanical System”. Sciences et Technologies de l’Automatique. Vol. 5. 2008. pp. 24-32.

F. Beltrán, G. Silva, H. Sira. Active Vibration Absorbers Using Generalized PI and Sliding-Mode Control Techniques. Proceedings of the American Control Conference. Denver, USA. 2003. pp. 791-796.

M. Fliess, R. Marquez, E. Delaleau, H. Sira. “Correcteurs Proportionnels-Intégraux Généralisés”. ESAIM: Control, Optimization and Calculus of Variations. Vol. 7. 2002. pp. 23-41.

M. Fliess, J. Lévine, P. Martin, P. Rouchon. “Flatness and defect of nonlinear systems: introductory theory and examples”. International Journal of Control. Vol. 61. 1995. pp. 1327-1361.

H. Chen. “Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping”. Journal of Sound and Vibration. Vol. 255. 2002. pp. 719-740.

H. Khalil. Nonlinear Systems. 3rd ed. Ed. Prentice Hall. New Jersey, USA. 2002. pp. 126-130.

W. Rugh. Linear System Theory. 2nd ed. Ed. Prentice Hall. New Jersey, USA. 1996. pp. 203-216.

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Published

2015-05-19

How to Cite

Beltrán-Carbajal, F. (2015). Robust tracking control for linear vibrating mechanical systems. Revista Facultad De Ingeniería Universidad De Antioquia, (75), 211–221. https://doi.org/10.17533/udea.redin.n75a20