Anti-disturbance stabilization for a hybrid system of non-uniform elastic string |
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| Institution: | 1. School of Mathematics, Tianjin University, Tianjin 300354, PR China;2. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, PR China;1. School of Mathematics, Shandong University, Jinan 250100, China;2. School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo 255000, China;1. School of Electrical Engineering and Computer Science, Washington State University, Pullman WA, USA;2. College of Information Science and Engineering, Northeastern University, Shenyang, China;3. Department of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, the Netherlands;1. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, 150006, PR China;2. Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA;1. Department of Mathematics, PSGR Krishnammal College for Women, Coimbatore 641004, India;2. Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India;1. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;2. Information and Control Institute, Hangzhou Dianzi University, Hangzhou 310018, China;3. Department of Chemical and Biological Engineering, Hong Kong University of Science and Technology, Hong Kong, China |
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| Abstract: | This paper is concerned with the anti-disturbance boundary feedback stabilization for a hybrid system coupling a non-uniform elastic string with a rigid body at one end by the active disturbance rejection control technology. An infinite-dimensional disturbance estimator and a Luenberger state observer are designed to estimate the disturbance and state of the system, respectively, based on which, a boundary output feedback control is further proposed to stabilize the system. The control consists of two parts: one part is for the stabilization of system without external disturbance, and the other part is for the rejection of the disturbance by virtue of the disturbance estimator. The well-posedness and exponential stability of the closed-loop system are proved by employing the semigroup theories and frequency domain method. Besides, all the signals of the closed-loop system are shown to be uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed control strategy. |
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