Adaptive SMC based on the dynamic containment of the sliding variable |
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| Authors: | Luis Ibarra Antonio Rosales Pedro Ponce Arturo Molina |
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| Affiliation: | 1. School of Engineering and Sciences, Tecnologico de Monterrey, Puente 222, Tlalpan Mexico city, 14380, Mexico;2. Department of Applied Physics and Electronics, Umeå University, Umeå 901 87, Sweden;1. School of Electronics Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea;2. School of Architecture and Civil Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea;3. Department of Control and Instrumentation Engineering, Pukyong National University, 45 Yongsoro, Namgu, Busan 48513, Republic of Korea;1. School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong 250353, PR China;2. Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan, Shandong 250014, PR China;3. Shandong Provincial Key Laboratory of Computer Networks, Jinan, Shandong 250014, PR China;4. School of Electrical Engineering and Automation, HeFei University of Technology, Hefei, Anhui 230009, PR China;5. Department of Automation, University of Science and Technology of China, Hefei, Anhui 230027, PR China;6. School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, NSW 2751, Australia;7. Department of Computer Science and Technology, Shandong University of Finance and Economics, Jinan, Shandong250014, PR China;1. School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China;2. Department of Earth and Space Science and Engineering, York University, 4700 Keele St., Toronto M3J 1P3, Canada;1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China;2. Frontier Institute of Science and Technology Innovation, Beihang University, Beijing 100191, PR China;3. School of Electronic and Information Engineering, Beihang University, Beijing 100191, PR China;1. School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China;2. Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering, Beijing 100190, China |
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| Abstract: | Conventional Sliding Mode Controllers (SMCs) exhibit a robust performance against matched bounded uncertainties and disturbances by containing them under a fixed controller’s effort. Consequently, the controller is commonly found excessive, leading to chattering and straining the actuator. As a solution, the variable-gain SMCs adapt to the instantaneous system requirements, thus attenuating the aforesaid effects and keeping the SMC’s benefits. However, the reported adaptive laws underlying such behavior commonly require arbitrary design considerations and do not consider practical implementation. Unlikely, in this work, a hysteresis-based adaptability law to drive the sliding variable to a boundary layer around zero is proposed. The sliding boundary—hysteresis’ width—will consistently “bounce” over the sliding variable, trying to shrink against it while preserving the sliding mode. This behavior finds its steady-state once the sliding variable and the sliding boundary’s dynamics are synchronized, with no need of subjective or arbitrary adjustments. The close-loop tuning can be derived from the system’s parameters alone, and its steady-state performance can be quantitatively predicted. Furthermore, a method to adjust the sliding surface parameters according to the system’s desired behavior is provided, all in a closed, analytical way. Finally, the physical actuator limits are taken into account and never exceeded, and the discrete nature of the devices normally used for SMC implementation is incorporated throughout. Two examples are studied to portray the proposal’s advantages. |
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