Variable structure controller design for linear systems with bounded inputs

Abstract

This paper studies the design of variable structure systems with saturation inputs. Sliding mode domain, reaching domain, and unescapable reaching domain of linear systems with variable structure are defined and investigated. When the state matrix of the linear system is Hurwitz, the stability of the variable structure systems is proven by using passivity theory. Moreover, variable structure systems with novel nonlinear switching surfaces are proposed for second order systems. Two strategies for designing variable structure control for high order linear systems are also proposed, such as stepby-step variable structure control and moving-surface variable structure control, which were found to guarantee that the reaching condition of the variable structure control is always satisfied. Finally, an illustrative example pertaining to the attitude control of a flexible spacecraft demonstrates the effectiveness of the proposed methods.

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Correspondence to Pinhas Ben-Tzvi.

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Recommended by Editor Jae Weon Choi.

Shengjian Bai received his B.S. degree in Mechatronics Engineering from Northeastern University, P. R. China in 2003, and his M.S. degree in Control Science and Engineering from National University of Defense Technology (NUDT), P. R. China in 2005. Since 2006 he has been a Ph.D. student in the Mechatronics Engineering Department at NUDT. His current research interests include dynamics of multibody systems, variable structure control, and fuzzy control.

Pinhas Ben-Tzvi received his B.S. degree Summa Cum Laude from the Technion — Israel Institute of Technology, Haifa, Israel, in 2000, and his M.S. and Ph.D. degrees from the University of Toronto, Toronto, Canada, in 2004 and 2008, respectively, both in Mechanical Engineering. Dr. Ben-Tzvi is currently an Assistant Professor in the department of Mechanical and Aerospace Engineering and the Director of the Robotics and Mechatronics Laboratory at the George Washington University. His areas of research and academic interests are focused on the advanced mechanics and control of robotic and mechatronic systems, the design of intelligent autonomous systems, medical robotics, and the development of novel smart sensors and actuators for biomedical and miniature mechatronic and microrobotic systems. He is a member of the American Society of Mechanical Engineers (ASME) and the Institute of Electrical and Electronics Engineers (IEEE).

Qingkun Zhou received his B.S. degree in Mechatronics Engineering from Hunan Normal University, China in 2003, and his M.S. degree in Mechatronics Engineering from National University of Defense Technology (NUDT), P. R. China in 2005. Since 2006 he has been a Ph.D. student in the Mechatronics Engineering Department at NUDT. From 2008 to 2009, he won a scholarship from the Chinese Scholarship Council as a Joint Ph.D. Student in the Department of Mechanical and Industrial Engineering at the University of Toronto, Canada, where he joined the Robotics and Automation Laboratory (RAL) under the supervision of his co-supervisors Professor A.A. Goldenberg and Professor F. Ben Amara. His current research interests include mechatronics, dynamics of multibody systems, and compliant mechanisms.

Xinsheng Huang received his B.S. degree in Controls Engineering from Xi’an Jiaotong University, P. R. China in 1982, and his M.S. degree in Systems Engineering from Huazhong Science and Technology University, P. R. China in 1986. He is currently a Professor at the National University of Defense Technology, China. His current research interests include dynamics of multibody systems, nonlinear control, and image processing.

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Bai, S., Ben-Tzvi, P., Zhou, Q. et al. Variable structure controller design for linear systems with bounded inputs. Int. J. Control Autom. Syst. 9, 228 (2011). https://doi.org/10.1007/s12555-011-0204-5

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Keywords

  • Bounded inputs
  • linear systems
  • nonlinear switching surface
  • passivity theory
  • variable structure control