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Discontinuous H control of underactuated mechanical systems with friction and backlash

Abstract

Nonlinear H -control is extended to discontinuous mechanical systems with degree of underactuation one, where nonlinear phenomena such as Coulomb friction and backlash are considered. The problem in question is to design a feedback controller via output measurements so as to obtain the closed-loop system in which all trajectories are locally ultimate bounded, and the underactuated link is regulated to a desired position while also attenuating the influence of external perturbations and nonlinear phenomena. It is considered that positions are the only measurements available for feedback in the system. Performance issues of the discontinuous H -regulation controller are illustrated in an experimental study made for a rectilinear plant with friction modified to have a gap in the point of contact between bodies.

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Correspondence to Raúl Rascón.

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Recommended by Associate Editor Nam H. Jo under the direction of Editor Hyouk Ryeol Choi.

Raúl Rascón received his Ph.D. degree in Electronics and Telecommunications from Centro de Investigación Científica y de Educación Superior de Ensenada CICESE, Baja California, México, in 2012. He is currently a full time professor and researcher at Universidad Autónoma de Baja California UABC. His research interests include robust control, nonlinear control, observers and its applications to mechanical systems.

Joaquin Alvarez was born in Tampico, Mexico, in 1953. He received the Engineering degree in Communications and Electronics from the School of Electrical and Mechanical Engineering of the National Polytechnic Institute (IPN) of Mexico, in 1975. He is MSc by the Advanced Studies and Research Center of IPN (CINVESTAV), in Mexico (1976) and Doctor in Engineering in Automatic Control by the National School of Electrotechnical Engineering of the National Polytechnic Institute of Grenoble, France (1979). He held a professorial position at the Electrical Engineering Department of the CINVESTAV. Since 1990, he has been working as a full-time professor at the Electronics and Telecommunications Department of the Scientific Research and Advanced Studies Center of Ensenada (CICESE). At present, his research interests are in the fields of nonlinear control, discontinuous systems, chaos control and synchronization, with applications to mechanical systems and electronic circuits.

Luis T. Aguilar received his Industrial Electronics Engineer diploma from Instituto Tecnologico de Tijuana, in 1994. He received his MSc degree in Digital Systems from Centro de Investigacion y Desarrollo de Tecnologia Digital (CITEDIIPN), Tijuana, Mexico and his PhD degree in Electronics and Telecommunications from CICESE Research Center, Ensenada, Mexico, in 1998 and 2003, respectively. He is currently a full professor at the CITEDI-IPN Research Center. His current research interests include variable structure systems, nonlinear H-infinity control, and control of electromechanical systems. He has authored over 30 referred journal and conference papers in the above areas as well as two research monographs.

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Rascón, R., Alvarez, J. & Aguilar, L.T. Discontinuous H control of underactuated mechanical systems with friction and backlash. Int. J. Control Autom. Syst. 14, 1213–1222 (2016). https://doi.org/10.1007/s12555-014-0498-1

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  • DOI: https://doi.org/10.1007/s12555-014-0498-1

Keywords

  • Backlash
  • discontinuous H control
  • friction
  • mechanical systems