Time Optimal Swing-Up Control of Single Pendulum

[+] Author and Article Information
Yongcai Xu

ESS Tech. Inc., Feemont Ca

Masami Iwase, Katsuhisa Furuta

School of Science and Engineering, Department of Computers and Systems Engineering, Tokyo Denki University, Saitama, Japan

J. Dyn. Sys., Meas., Control 123(3), 518-527 (Feb 11, 2000) (10 pages) doi:10.1115/1.1383027 History: Received February 11, 2000
Copyright © 2001 by ASME
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Grahic Jump Location
Illustration of Furuta Pendulum: a pendulum is hinged to a rotating arm connected to a direct-drive motor
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Relation between input amplitude vin and torque τ of the motor. vd is the threshold of the dead zone
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Comparison of time optimal control using nonlinear optimization (NO) and linear programming (LP): The upper shows the optimal input, and the lower shows the angle of the pendulum, where the solid line is of NO case and the dotted line is of LP case
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Verification of necessary condition using simplified pendulum model: the upper is the angle as a result of optimal swing-up control, and the lower shows the optimal input (dotted line) and the corresponding switching function (solid line)
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Verification of necessary condition using real pendulum model (8): the upper shows the angles of the pendulum (θ1: solid line) and the arm (θ0: dotted line) in Fig. 1. The lower shows the optimal input (dotted line) and the switching function (dashed line).
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Design of time optimal swing-up control of Furuta Pendulum: the upper is the designed input for swing-up, and the lower shows angles of the pendulum (θ1: solid line) and the arm (θ0: dashed line) in swing-up motion
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Result of experiment: the dotted line shows the computed trajectory of the pendulum angle θ1. The dashed line is of the experimental result.
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Result of experiment: the dotted line shows the computed trajectory of the arm rotation angle θ0. The dashed line is of the experimental result.
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Optimal input used in experiment: the dotted line shows the designed input. The dashed line shows the input used in experiment.
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Photos of swing-up control of Furuta Pendulum
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Simulation result of swing-up control based on energy-based approach: the upper shows the angle of pendulum, and the lower shows the input
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Result of swing-up control of the perturbed pendulum: the lower is the same control input as Fig. 6. The upper shows the angle of the pendulum (θ1: solid line) and the arm (θ0: dotted line)



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