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Research Papers

The Design of Input Shapers Which Eliminate Nonzero Initial Conditions

[+] Author and Article Information
Daniel Newman

Department of Mechanical Engineering,
University of Louisiana at Lafayette,
Lafayette, LA 70503

Seong-Wook Hong

Professor
Kumoh National Institute of Technology,
Gumi 730-701, Gyeongbuk, South Korea

Joshua E. Vaughan

Assistant Professor
Department of Mechanical Engineering,
University of Louisiana at Lafayette,
Lafayette, LA 70503
e-mail: joshua.vaughan@louisiana.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 14, 2017; final manuscript received March 2, 2018; published online May 2, 2018. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 140(10), 101005 (May 02, 2018) (9 pages) Paper No: DS-17-1620; doi: 10.1115/1.4039668 History: Received December 14, 2017; Revised March 02, 2018

Input shaping is widely used in the control of flexible systems due to its effectiveness and ease of implementation. Due to its open-loop nature, it is often overlooked as a control method in systems where parametric uncertainty or force disturbances are present. However, if the disturbances are known and finite in duration, their effect on the flexible mode can be approximated by formulating an initial condition control problem. With this knowledge, an input shaper can be designed, which cancels the initial oscillation, resulting in minimal residual vibration. By incorporating Specified Insensitivity robustness constraints, such shapers can be designed to ensure good performance in the presence of modeling uncertainty. This input shaping method is demonstrated through computer and experimental methods to eliminate vibration in actuator bandwidth-limited systems.

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Figures

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Fig. 1

Convolution of a reference input with a series of impulses

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Fig. 2

Initial condition impulse cancellation

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Fig. 3

Response characteristics of an impulse versus a pulse

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Fig. 4

Vector diagram of an input shaper subject to actuator limitations

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Fig. 5

Phase shift of a pulse response relative to an impulse response

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Fig. 6

Amplitude shift of a pulse response relative to an impulse response

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Fig. 7

Sensitivity of a ZV-IC shaper to Ae and θe

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Fig. 8

Sensitivity of a ZV-IC shaper to modeling error: (a) sensitivity of a ZV-IC shaper to θe and ωn/ωm and (b) sensitivity of a ZV-IC shaper to Ae and ωn/ωm

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Fig. 9

Sensitivity of an SI-IC shaper to modeling error: (a) sensitivity of an SI-IC shaper θe and ωn/ωm and (b) sensitivity of an SI-IC shaper to Ae and ωn/ωm

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Fig. 10

Zero vibration, initial condition shaped pulse response

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Fig. 11

Specified insensitivity, initial condition shaped pulse response

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Fig. 12

Sensitivity curves of a ZV-IC and SI-IC shaper

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Fig. 13

Planar boom crane model

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Fig. 14

Example shaped response of a boom crane with nonzero initial conditions

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Fig. 15

Benchmark experimental system

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Fig. 16

Typical unshaped response

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Fig. 17

Zero vibration, initial condition shaped response at the designed frequency

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Fig. 18

Specified insensitivity, initial condition shaped response at the designed frequency

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Fig. 19

Experimental results: (a) 1. ZV-IC shaper (b) SI-IC shaper (I = 0.2)

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Fig. 20

Absolute vibration amplitude of each command

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