Abstract
In this paper, the approach of a shifted Chebyshev series is proposed to solve the time-varying Takagi–Sugeno (TS) fuzzy-model-based dynamic equations. The new method simplifies the procedure of solving the time-varying TS-fuzzy-model-based dynamic equations into the successive solution of a system of recursive formulae only involving the matrix algebra. Based on the presented recursive formulae, an algorithm involving only straightforward algebraic computation is also proposed in this paper. The new proposed approach is non-iterative, non-differential, non-integral, straightforward, and well adapted to the computer implementation. The computational complexity can therefore be reduced remarkably. The first illustrated numerical example shows that the proposed method based on the shifted Chebyshev series can yield better and more satisfactory results than the Runge–Kutta method. The second illustrated example for the pendulum system with the vibration in the vertical direction on the pivot point is given to demonstrate the application of the proposed approach.
Acknowledgement
This work was supported by the National Science Council, Taiwan, Republic of China, under grant number NSC 91-2213-E327-001.
Wen-Hsien Ho received the B.S. degree in Marine Engineering from National Taiwan Ocean University, the B.S. degree in Industrial and Information Management from National Cheng-Kung University, and the M.S. degree in Mechanical and Automation Engineering from National Kaohsiung First University of Science and Technology, Taiwan, in June 1991, June 1998, and June 2002, respectively. He is currently a Ph.D. Candidate in Engineering Science and Technology at National Kaohsiung First University of Science and Technology, Taiwan. From September 1991 until present, he has been an Engineer of Design Department at China Shipbuilding Corporation, Taiwan. From August 2002 until present, he has also been an Adjunct Lecturer of Marine Engineering Department at National Kaohsiung Marine University, Taiwan. His research interests include intelligent systems and control, computational intelligence and methods, robust control, and quality engineering.
Jyh-Horng Chou received the B.S. and M.S. degrees in Engineering Science from National Cheng-Kung University, Taiwan, in June 1981 and June 1983, respectively, and the Ph.D. degree in Mechatronic Engineering from National Sun Yat-Sen University, Taiwan, in December 1988. He is currently a Professor and the Dean of Engineering College at National Kaohsiung First University of Science and Technology, Taiwan. From August 1983 to July 1986, he was a Lecturer of Mechanical Engineering Department at National Sun Yat-Sen University, Taiwan. From August 1986 to July 1991, he was an Associate Professor of Mechanical Engineering Department and the Director of the Center for Automation Technology at National Kaohsiung University of Applied Sciences, Taiwan. From August 1991 to July 1999, he was a Professor and the Chairman of Mechanical Engineering Department at National Yunlin University of Science and Technology, Taiwan. From August 1999 to September 2004, he was a Professor and Chairman of Mechanical and Automation Engineering Department at National Kaohsiung First University of Science and Technology, Taiwan. He has coauthored three books and published more than 145 refereed journal papers. He also holds two patents (one is in the technology area of automation, and the other is in the area of computational intelligence). His research and teaching interests include intelligent systems and control, computational intelligence and methods, robust control, and quality engineering.
Dr. Chou is a Senior Member of the Institute of Electrical and Electronic Engineers (IEEE). He received both the Research Award and the Excellent Research Award from the National Science Council of Taiwan 14 times. He also received the 2004 Excellent Project Outcome Award of the Educational Promotion Project on the Integrated Manufacturing and e-Commerce Technology from the Ministry of Education, Taiwan. He is currently an Editorial Member for the Journal of the Chinese Society of Mechanical Engineers, and an Associate Editor for the International Journal of Information and Systems Sciences.