Stabilize the planar single inverted pendulum based on LQR

Author

Liu Feng ; Tang Yongchuan ; Qi Qian

Author_Institution

Coll. of Comput. & Inf. Sci., Southwest Univ., Chongqing, China

fYear

2011

fDate

15-16 Aug. 2011

Firstpage

238

Lastpage

242

Abstract

This paper firstly analyses the physical model of planar single inverted pendulum system, then builds the mathematical model of this system based on Lagrangian mechanics. These characteristics: multi-parameter, less-driven, strong coupling and highly nonlinearity make it difficult to stabilize the planar inverted pendulum system. But nearby the upright equilibrium of this system, the nonlinear mathematical model of the system can be linearized and get decoupled in X-axis and Y-axis. Then two LQR controllers are designed for each linear inverted pendulum in each axis respectively, and they are almost the same. At last, the simulation experiments in MATLAB test and verify the mathematical model is right and the control policy is effective.

Keywords

control nonlinearities; control system synthesis; linear quadratic control; linearisation techniques; multivariable control systems; nonlinear control systems; pendulums; stability; LQR controller design; Lagrangian mechanics; MATLAB; control policy; linear inverted pendulum; multiparameter characteristics; nonlinear mathematical model linearization; planar single inverted pendulum stabilization; strong coupling; system nonlinearity; Acceleration; MATLAB; Mathematical model; Potential energy; Presses; Rails; Transmission line matrix methods; LQR; Lagrangian Mechanics; Planar Inverted Pendulum;

fLanguage

English

Publisher

ieee

Conference_Titel

Automation and Logistics (ICAL), 2011 IEEE International Conference on

Conference_Location

Chongqing

ISSN

2161-8151

Print_ISBN

978-1-4577-0301-0

Electronic_ISBN

2161-8151

Type

conf

DOI

10.1109/ICAL.2011.6024720

Filename

6024720