ROBOTICA & MANAGEMENT - Vol. 23, No. 2, December 2018, pp. 37-41

PD Controller for Bicycle Model Balancing

Anh Khoa Vo *, Minh Tam Nguyen *, Thanh Nguyen Nguyen **, Thien Van Nguyen ***, Van Khanh Doan ***, Hoang Chinh Tran *, Van Dong Hai Nguyen *


* Ho Chi Minh city University of Technology and Education (HCMUTE)
Vo Van Ngan street, 01, Ho Chi Minh city, Vietnam
** Ton Duc Thang University (TDTU)
Nguyễn Hữu Thọ street, No. 19 Tân Phong ward, District 7, Ho Chi Minh city, Vietnam
E-mail: 41403135(at)
*** “Politehnica” University of Bucharest (UPB)
Splaiul Independenţei nr. 313, Sector 6, Bucharest, Romania
E-mail:; jamberry129(at)

Abstract: Bicycle is a conventional vehicle and it cannot self-balance. An equivalent model is required to be supplied in order to base a control structure for this under-actuated system. Thence, in this paper, authors infer a balancing model of bicycle which is based on re-action wheel pendulum (body of the model can be regarded as a pendulum). PD controller, a popular linear control method, is examined for this model. A structure of this control method is designed for this under-actuated system. Then, through trial and error test, a set of control parameters are selected.  In both simulation and experiment, PD controller is proved to stabilize bicycle well.
Keywords: Re-action wheel pendulum, bicycle, self-balance, PD controller, under-actuated system, linear control.

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