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Particle swarm optimization for time-optimal control design

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Abstract

In this paper, a particle swarm optimization (PSO) based method is proposed to obtain the time-optimal bang-bang control law for both linear and nonlinear systems. By introducing a penalty function, the method can be modified to deal with systems with constraints. Compared with existing computational methods, the proposed method can be implemented in a straightforward manner. The convergent solutions can be achieved by selecting suitable PSO parameters regardless of the initial guess of the switching times. A double integrator and a third-order nonlinear system are used to demonstrate the effectiveness and robustness of the proposed method. The method is applied to obtain the time-optimal control law for a high performance linear motion positioning system. The results show the practicality of the proposed algorithm.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Yiqiang Li & Xing Zhang

  2. Department of Electrical and Computer Engineering, Indiana University-Purdue University at Indianapolis (IUPUI), Indianapolis, IN, 46202, USA

    Yaobin Chen

  3. School of Engineering, China Agricultural University, Beijing, 100083, China

    Huixing Zhou

Authors
  1. Yiqiang Li
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  2. Xing Zhang
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  3. Yaobin Chen
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  4. Huixing Zhou
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Corresponding author

Correspondence to Yiqiang Li.

Additional information

This work was partly supported by the China Scholarship Council (No. 2007103188).

Yiqiang LI received his Ph.D. degree in Mechanical Engineering from China Agricultural University, Beijing, China in 2010. He was a joint-training Ph.D. candidate with the department of Electrical and Computer Engineering, Purdue University at Indianapolis (IUPUI), USA, from September 2007 to September 2009. Since 2010, Dr. Li has been a postdoctoral researcher with the department of Engineering Mechanics, Tsinghua University. Dr. Li’s current research interests are wind energy and power systems, renewable energy technology and its applications, modeling and control, linear motor, and optimization. He has published 8 technical papers in refereed journals and conference proceedings. He is a member of IEEE.

Xing ZHANG received his Ph.D. degree in Power Engineering and Engineering Thermophysics from Tsinghua University, Beijing, China in 1988. From 1991 to 2005, he was an assistant professor and associate professor respectively, Kyushu University, Fukuoka, Japan. Since 2005, Dr. Zhang has been with the School of Aerospace, Tsinghua University, where he is currently Professor and Director of Institute of Engineering Thermophysics. Dr. Zhang’s currently research interests are thermophysical properties, efficient use of wind/solar energy, energy conservation technology, and heat transfer enhancements. He has published more than 300 technical papers in refereed journals and conference proceedings, and has given invited/keynote lectures at international conferences. He is the IOC Chairmen of Asian Thermophysical Properties Conference, and on the editorial board of several journals. He received several Best Paper Awards of international conference and technical society. He was awarded First Class Award in Natural Science in 2007.

Yaobin CHEN received his M.S. and Ph.D. degrees from Rensselaer Polytechnic Institute, Troy, New York, in 1986 and 1988 respectively, all in Electrical Engineering. From 1988 to 1990, Dr. Chen was with the Faculty of Electrical Engineering and Computer Science at George Washington University, Washington, DC. Since 1990, Dr. Chen has been with the Purdue School of Engineering and Technology, Indiana University-Purdue University Indianapolis (IUPUI), where he is currently Professor and Chair of Electrical and Computer Engineering. Dr. Chen’s current research interests are modeling, control, optimization, and simulation of advanced transportation and vehicle systems, energy and power systems, computational intelligence and its applications. He has published more than 110 technical papers in refereed journals and conference proceedings. He received a National Science Foundation Research Initiation Award in 1991. He is a senior member of IEEE, and a member of SAE and ASEE.

Huixing ZHOU received his B.E. degree in Engineering from Dalian University of Technology, Dalian, China, and the Ph.D. degree in Mechanical Engineering from Tsinghua University, Beijing, China, in 1983 and 1998, respectively. Currently, he is a professor in the College of Mechanical Engineering, China Agricultural University, Beijing, China. He is also the technical director of Winner- Motor Co. and the director of precision engineering center of CAU. His research interests include linear motor and actuator, precision motion control and mechatronics. Professor Zhou is a senior member of CMES, member of IMechE and a chartered engineer.

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Li, Y., Zhang, X., Chen, Y. et al. Particle swarm optimization for time-optimal control design. J. Control Theory Appl. 10, 365–370 (2012). https://doi.org/10.1007/s11768-012-0060-8

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  • DOI: https://doi.org/10.1007/s11768-012-0060-8

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