Abstract
In this paper, a stabilization problem for the discrete nonlinear system with external disturbance, multiplicative noises and multiple constraints has been discussed in accordance with the definition of Lyapunov stability. Based on fuzzy modeling approach, the overall fuzzy model of a nonlinear plant is transformed into a class of linear systems. Applying a Sliding Mode Fuzzy Control (SMFC) scheme, the designed controller causes the closed-loop system converging to the sliding surface and achieving the required control performance. For the control performance, the concepts of stability, individual state variance and passivity constraints are introduced for the sliding mode fuzzy control system. To apply convex optimal programming algorithm, some sufficient conditions derived in this paper are reduced to Linear Matrix Inequality (LMI) problem. At last, two simulation examples are proposed to demonstrate the applicability and usefulness of the proposed design method. One of the examples is to discuss the conservatism of this paper. Another is to show that the discrete truck-trailer system controlled by sliding mode fuzzy controller can achieve stability constraints, individual state variance constraints and passivity constraints.
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Recommended by Associate Editor Sung Jin Yoo under the direction of Editor Jessie (Ju H.) Park. This paper was supported by the Ministry of Science and Technology of the Republic of China under Contract MOST105-2221-E-019-032.
Wen-Jer Chang received the B.S. degree from National Taiwan Ocean University, Taiwan, R.O.C., in 1986. He received the M.S. degree in the Institute of Computer Science and Electronic Engineering from the National Central University in 1990, and the Ph.D. degree from the Institute of Electrical Engineering of the National Central University in 1995. Since 1995, he has been with National Taiwan Ocean University, Keelung, Taiwan, R.O.C. He is currently the Dean of Academic Affairs, Director of General Education Center and a full Professor of the Department of Marine Engineering of National Taiwan Ocean University. He is now a life member of the CIEE, CACS, CSFAT and SNAME. Since 2003, Dr. Chang was listed in the Marquis Who’s Who in Science and Engineering. In 2003, he also won the outstanding young control engineers award granted by the Chinese Automation Control Society (CACS). In 2004, he won the universal award of accomplishment granted by ABI of USA. In 2005, he was selected as an excellent teacher of the National Taiwan Ocean University. Dr. Chang has over 220 publications including 110 journal papers. His recent research interests are fuzzy control, robust control, performance constrained control.
Feng-Ling Hsu received the M.S. degree from the Department of Marine Engineering of the National Taiwan Ocean University, Taiwan, R.O.C., in 2016. His research interests focus on fuzzy control and sliding mode control.
Cheung-Chieh Ku received the B.S. and M.S. degree from the Department of Marine Engineering of the National Taiwan Ocean University, Taiwan, R.O.C., in 2001 and 2006, respectively. He received the Ph.D. degree from the electrical engineering of the National Taiwan Ocean University, Taiwan R.O.C., in 2010. Since 1995, he has been with National Taiwan Ocean University, Keelung, Taiwan, R.O.C. He is current the Division Chief of Internship and Career and an Associate Professor of the Department of Marine Engineering of National Taiwan Ocean University. His research interests focus on fuzzy control, stochastic systems and passivity theory.
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Chang, WJ., Hsu, FL. & Ku, CC. Complex performance control using sliding mode fuzzy approach for discrete-time nonlinear systems via T-S fuzzy model with bilinear consequent part. Int. J. Control Autom. Syst. 15, 1901–1915 (2017). https://doi.org/10.1007/s12555-016-9404-3
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DOI: https://doi.org/10.1007/s12555-016-9404-3