A fast terminal fractional-order backstepping sliding mode control for ball-balancing robots

Minh Duc Pham, Cong Minh Pham, Phuong Thao Dao, Thu Giang Do, Nhat Minh Nguyen, Van Trong Dang and Tung Lam Nguyen

International Journal of Industrial and Systems Engineering, 2026, vol. 53, issue 2, 265-281

Abstract: In this paper, we construct a robust controller of the 2D ballbot model with one input and two desired outputs. The combination of back-stepping, fast terminal sliding mode, and fractional calculus becomes fast terminal fractional-order back-stepping sliding mode control (FTFBSMC) to accomplish both the tracking task and balancing task of the ballbot. Moreover, we have analyzed and proved the stability in the finite approach of the controller without zero dynamics of outputs. Numerical simulation results are also used to determine and analyze the efficiency of the control law. Sliding mode control and fast terminal fractional order back-stepping sliding mode control are compared to evaluate the main improvement of the proposed controller in different scenarios.

Keywords: sliding mode control; SMC; back-stepping technique; fractional-order; finite approach; ball-balancing robot. (search for similar items in EconPapers)
Date: 2026
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