Hung-Tuan-Anh Tran ¹, Trung-Hieu Le ²*, Thi-Hong-Lam Le ¹, Thi-Ngoc-Thao Nguyen ¹, Thi-Ngoc-Hieu Phu ¹, Hoang-Lam Le ¹, Phong-Luu Nguyen ¹, Thanh-Binh Nguyen ¹

¹ Ho Chi Minh City University of Technology and Engineering (HCM-UTE), Ho Chi Minh City (HCMC), Vietnam
Vo Van Ngan Str., No. 01, Thu Duc ward, HCMC, Vietnam
² Avery Dennison RBIS Long An Company
Suare E.01, Trung Tam Str., Can Giuoc ward, Tay Ninh province, Vietnam
* Corresponding author. E-mail: hieu.t.le@ap.averydennison.com

Robotica & Management, Vol. 31, No. 1, pp. 38-43
DOI: https://doi.org/10.24193/rm.2026.1.7

Abstract: This paper presents a hybrid LQR–Backstepping control approach for the ball-and-beam system, a nonlinear and inherently unstable system. The proposed method combines the optimal performance of LQR with the nonlinear stability of Backstepping to enhance both stabilization and trajectory tracking. Simulation results under fixed-point stabilization and sinusoidal tracking scenarios demonstrate fast response, low overshoot, and good tracking accuracy, confirming the effectiveness of the proposed approach for nonlinear control applications.
Keywords: Ball-and-beam system; LQR; Backstepping control; Hybrid control; Trajectory tracking.

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