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Research Papers

Uncertainty and Disturbance Estimator-Based Backstepping Control for Nonlinear Systems With Mismatched Uncertainties and Disturbances

[+] Author and Article Information
Jiguo Dai

Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: jiguo.dai@ttu.edu

Beibei Ren

Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: beibei.ren@ttu.edu

Qing-Chang Zhong

Department of Electrical & Computer
Engineering,
Illinois Institute of Technology,
Chicago, IL 60616
e-mail: zhongqc@ieee.org

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 9, 2016; final manuscript received June 19, 2018; published online July 23, 2018. Assoc. Editor: Manish Kumar.

J. Dyn. Sys., Meas., Control 140(12), 121005 (Jul 23, 2018) (11 pages) Paper No: DS-16-1591; doi: 10.1115/1.4040590 History: Received December 09, 2016; Revised June 19, 2018

This paper proposes an uncertainty and disturbance estimator (UDE)-based controller for nonlinear systems with mismatched uncertainties and disturbances, integrating the UDE-based control and the conventional backstepping scheme. The adoption of the backstepping scheme helps to relax the structural constraint of the UDE-based control. Moreover, the reference model design in the UDE-based control offers a solution to address the “complexity explosion” problem of the backstepping approach. Furthermore, the strict-feedback form condition in the conventional backstepping approach is also relaxed by using the UDE-based control to estimate and compensate “disturbance-like” terms including nonstrict-feedback terms and intermediate system errors. The uniformly ultimate boundedness of the closed-loop system is analyzed. Both numerical and experimental studies are provided.

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Figures

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Fig. 1

Structure of the UDE-based backstepping control

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Fig. 2

Compact invariant set

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Fig. 3

Numerical control results of the systems (59) and (60)

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Fig. 4

Effect of different parameters

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Fig. 5

A rotary inverted pendulum

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Fig. 6

Stabilization of a rotary inverted pendulum

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Fig. 7

A coupled water tank system

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Fig. 8

Dead zone of the pump voltage

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Fig. 9

Level control for a coupled water tank

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