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TECHNICAL PAPERS

Adaptive Control of Mechanical Systems With Time-Varying Parameters and Disturbances

[+] Author and Article Information
Prabhakar R. Pagilla, Yongliang Zhu

School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078-5016

J. Dyn. Sys., Meas., Control 126(3), 520-530 (Dec 03, 2004) (11 pages) doi:10.1115/1.1789538 History: Received March 12, 2003; Revised June 23, 2003; Online December 03, 2004
Copyright © 2004 by ASME
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Figures

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Local approximation of a continuous function. Each fi(t) can be approximated by a polynomial in time using Taylor’s formula.
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Picture of the two-link robot
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The time-varying inertia, I(t) (top plot), and the time-varying disturbance, d(t) (bottom plot) are shown. I(t) and d(t) are computed by using the experimental data of q2(t),q̇2(t),q̇1(t) in (47) and (48). The data from zero to 16 s corresponds to τ2=4 N-m and the data from 16 to 30 s corresponds to τ2=3 N-m.
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Tracking error of the base link [e1(t), top plot] and the angular velocities of the base link and elbow link [q̇1(t) and q̇2(t), bottom plot] are shown
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Motor control torques of base link [τ1(t), top plot] and elbow link [τ2(t), bottom plot] are shown
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Estimated disturbance parameters d⁁0(t) and d⁁1(t) are shown in the top plot. The estimate of the disturbance d⁁(t)=d⁁0(t)+(t−t0)d⁁1(t) is shown in the bottom plot.
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Estimated inertia parameters I⁁0(t) and I⁁1(t) are shown in the top plot. The estimate of the inertia I⁁(t)=I⁁0(t)+(t−t0)I⁁1(t) is shown in the bottom plot.
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Estimated friction parameters f⁁v(t) and f⁁c(t) are shown
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Experimental results from the ideal nonadaptive robust controller given by (51) and (53). Tracking error of the base link [e1(t), top plot], motor control torques of the base link [τ1(t), middle plot] and the elbow link [τ2(t), bottom plot] are shown.

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