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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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References

Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Control, Prentice-Hall, Englewood Cliffs, NJ.
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Reed,  J. S., and Ioannou,  P. A., 1989, “Instability Analysis and Robust Adaptive Control of Robotic Manipulators,” IEEE Trans. Rob. Autom., 5, pp. 381–386.
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Tomei,  P., 1999, “Robust Adaptive Control of Robots With Arbitrary Transient Performance and Disturbance Attenuation,” IEEE Trans. Autom. Control, 44, pp. 654–658.
Pagilla,  P. R., Yu,  B., and Pau,  K. L., 2000, “Adaptive Control of Time-Varying Mechanical Systems: Analysis and Experiments,” Mechatronics, 5, pp. 410–418.
Tsakalis, K. S., and Ioannou, P. A., 1993, Linear Time-Varying Systems: Control and Adaptation, Prentice-Hall, Englewood Cliffs, NJ.
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Figures

Grahic Jump Location
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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