Title: Modelling and robust stabilisation of a closed-link 2-dof inverted pendulum with gain scheduled control

Authors: C. Ishii, Y. Nishitani, H. Hashimoto

Addresses: Department of Engineering Science and Mechanics, College of Engineering, Shibaura Institute of Technology, 3-7-5, Toyosu, Koto-ku, Tokyo 135-8548, Japan. ' Department of Mechanical Engineering, Faculty of Engineering, Kogakuin University, 2665-1, Nakano-cho, Hachioji-shi, Tokyo 192-0015, Japan. ' Master's Program of Innovation for Design and Engineering, Advanced Institute of Industrial Technology, 1-10-40, Higashiooi, Shinagawa-ku, Tokyo 140-0011, Japan

Abstract: In this paper, modelling and stabilisation control of a closed-link driven 2-dof inverted pendulum system is discussed, which consists of two rotary robots and four closed linkages with holonomic constraint. A complete mathematical model derived by Lagrange|s equations is partially linear approximated around the operating point. Then, the modelling error is regarded as a structured perturbation and the controlled object is described as a slight non-linear model with structured additive perturbation. In order to facilitate a controller design, model reduction is performed by removing redundant dynamics. Then, the reduced order simplified model is described as a linear parameter variable (LPV) system with structured additive perturbation. Stabilisation controller with L₂-gain disturbance attenuation is designed to guarantee the stability of the controlled object robustly in the range of specified perturbation by applying gain scheduling control technique developed for the LPV system. Experimental works show the effectiveness of the proposed simplified model and the stabilisation controller.

Keywords: 2-dof inverted pendulum; robust stabilisation; L₂-gain attenuation; linear matrix inequalities; LMIs; gain scheduled control; mathematical modelling; stabilisation control; rotary robots; closed linkages; holonomic constraints.

DOI: 10.1504/IJMIC.2009.024739

International Journal of Modelling, Identification and Control, 2009 Vol.6 No.4, pp.320 - 332

Published online: 29 Apr 2009 *

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