Title: Stabilising the triple inverted pendulum by variable gain linear quadratic regulator

Authors: Yongli Zhang; Zhihong Miao; Hongxing Li; Fuzhong Nian

Addresses: School of Automation and Electrical Engineering, TianJin Key Laboratory of Information Sensing & Intelligent Control, Tianjin University of Technology and Education, Tianjin 300222, China. ' Department of Fire Protection Engineering, The Chinese People's Armed Police Force Academy, Langfang Hebei 065000, China. ' Department of Fire Protection Engineering, The Chinese People's Armed Police Force Academy, Langfang Hebei 065000, China. ' Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian Liaoning 116024, China

Abstract: A variable gain linear quadratic regulator (VGLQR) for multivariable non-linear control systems is designed. This control scheme, which can be viewed as a novel gain scheduling controller, consists of linearising the non-linear system to a family of time-invariant systems about sampling points and using LQR method to obtain optimal feedback gain in every sampling interval. In addition, a fast algorithm based on Schur method for online solving the algebraic Riccati equation is discussed in detail, and a software package, which is used to solve algebraic Riccati equation at each sampling point, is developed during the present research. A triple inverted pendulum is stabilised by using the VGLQR method and the results of simulation and physical experiments are displayed. The results of experiments demonstrate that the present control scheme is of good stability and robustness.

Keywords: variable gain LQR; linear quadratic regulator; VGLQR; nonlinear control; algebraic Riccati equation; triple inverted pendulum; experiments.

DOI: 10.1504/IJSCC.2012.048616

International Journal of Systems, Control and Communications, 2012 Vol.4 No.3, pp.208 - 223

Published online: 21 Aug 2012 *

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