A hybrid controller design for bi-axial inverted pendulum system

Long Hong Chang, An-Chen Lee*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This study presents the use of Tustin's friction model and a disturbance observer (DOB) to improve the steady-state error (SSE) of a bi-axial inverted pendulum-cart system (IPCS). Furthermore, a hybrid controller contains a feedback linearization control for pendulum angle in the region of 3-12° to enlarge the angle of operation and an H control using loop shaping design procedure (LSDP) for cart position and pendulum angle in the region of 0-3° to stabilize the IPCS, respectively. Experimental results reveal that the pendulum maximum angle of operation is improved from 7 to 12°; the SSE of the angle of the pendulum is reduced from 0.85 to 0.1°, and the SSE of the position of the cart is reduced from 10 to 1.4 mm. Experimental results are illustrated and films are provided at the web site http://hinfinity.myweb.hinet.net to show the effectiveness and robustness of the hybrid controller with Tustin's friction model and DOB compensation.

Original languageEnglish
Pages (from-to)512-531
Number of pages20
JournalInternational Journal of Robust and Nonlinear Control
Issue number5
StatePublished - 25 Mar 2009


  • Disturbance observer
  • Friction compensation
  • H
  • Inverted pendulum
  • Loop shaping design procedure

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