Research Papers

Data-Driven Backstepping Control of Underactuated Mechanical Systems

[+] Author and Article Information
Jingwen Huang, Tingting Zhang

Beijing University of Chemical Technology,
Beijing 100029, China

Jian-Qiao Sun

Fellow ASME
Department of Mechanical Engineering,
School of Engineering,
University of California, Merced,
Merced, CA 95343

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received November 20, 2018; final manuscript received March 7, 2019; published online April 9, 2019. Assoc. Editor: Xuebo Zhang.

J. Dyn. Sys., Meas., Control 141(9), 091003 (Apr 09, 2019) (7 pages) Paper No: DS-18-1522; doi: 10.1115/1.4043154 History: Received November 20, 2018; Revised March 07, 2019

This paper studies control problems of underactuated mechanical systems with model uncertainties. The control is designed with the method of backstepping. The first-order low-pass filters are used to estimate the unknown quantities and to avoid the “explosion of terms.” A novel method is also proposed to implement the control without the knowledge of the control coefficient, which makes the whole process of backstepping control data-driven. The stability of the proposed control in the Lyapunov sense is studied. It is numerically and experimentally validated, and compared with the well-known model-based linear quadratic regulator (LQR) control. The data-driven backstepping control is found to provide comparable performances to that of the LQR control with the advantage of being model-free and robust.

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Fig. 1

The design procedure of the proposed data-driven backstepping control

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Fig. 2

The hardware of the flexible rotating beam by Quanser

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Fig. 3

Comparison of the proposed backstepping control (solid line) with the standard LQR control (dashed line)

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Fig. 4

Effect of the coefficient η on the control performance. Two values of η are considered: 1012 (red solid line) and 1014 (blue dashed line).

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Fig. 5

The comparison of square wave tracking experiments by the LQR control and the proposed control. LQR: Black lines. Proposed control: Red lines.

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Fig. 6

The comparison of square wave tracking experiments by the LQR control with noisy state estimator, and the proposed control. LQR: Black lines. Proposed control: Red lines.

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Fig. 7

Experimental study of effect of the coefficient η on the control performance corresponding to the results in Fig. 4. Two values of η are considered: 1012 (red solid line) and 1014 (blue dashed line).



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