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Research Papers

Optimized Input-Shaped Model Reference Control on Double-Pendulum System

[+] Author and Article Information
Daichi Fujioka

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: gtg369q@gatech.edu

William Singhose

The George W. Woodruff School
of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332-0405
e-mail: Singhose@gatech.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received July 9, 2017; final manuscript received March 16, 2018; published online May 2, 2018. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 140(10), 101004 (May 02, 2018) (9 pages) Paper No: DS-17-1345; doi: 10.1115/1.4039786 History: Received July 09, 2017; Revised March 16, 2018

This paper presents an optimized input-shaped model reference control (OIS-MRC) for limiting oscillation of multimode flexible systems. The controller is analyzed by using it to control an uncertain, time-varying double pendulum using a linear single-pendulum reference model. Single- and double-pendulum dynamics are presented, and the significant natural frequency ranges of the double pendulum are calculated. A Lyapunov control law using only the first mode states of the plant is obtained. An optimization technique is used to obtain the OIS-MRC controller parameters that realizes the shortest time duration, while meeting a set of design constraints. The oscillation suppression, control effort reduction, and disturbance rejection performances of the proposed OIS-MRC controller are tested via numerical simulations and experiments. The OIS-MRC achieves a robust oscillation suppression performance, while reducing the rise time.

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Figures

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Fig. 1

Input-shaped MRC block diagram with external disturbance

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Fig. 2

Model of a single pendulum

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Fig. 3

Model of a double pendulum

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Fig. 4

Small-scale bridge crane experimental setup

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Fig. 5

ω1 as a function of L1 and L2

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Fig. 6

Amplitude ratio as a function of L1 and L2

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Fig. 7

ω2 as a function of L1 and L2

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Fig. 8

Hook responses during hoist-up motion

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Fig. 9

Payload responses during hoist-up motion

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Fig. 10

Control signal during hoist-up motion

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Fig. 11

Maximum hook oscillation versus hoist-up distance

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Fig. 12

Maximum payload oscillation versus hoist-up distance

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Fig. 13

Maximum control effort versus hoist-up distance

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Fig. 14

External disturbance rejection of the crane moved by trapezoidal command

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Fig. 15

External disturbance rejection of the crane moved by SI2M-MRC

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Fig. 16

External disturbance rejection of the crane moved by OIS-MRC

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