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Research Papers

Projected Phase-Plane Switching Curves for Vibration Reduction Filters With Negative Amplitudes

[+] Author and Article Information
Abhishek Dhanda

HGST, A Western Digital Company,
San Jose, CA 95136
e-mail: adhanda@stanfordalumni.org

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 15, 2010; final manuscript received March 7, 2014; published online July 9, 2014. Assoc. Editor: Marco P. Schoen.

J. Dyn. Sys., Meas., Control 136(5), 051014 (Jul 09, 2014) (9 pages) Paper No: DS-10-1097; doi: 10.1115/1.4027203 History: Received April 15, 2010; Revised March 07, 2014

In this paper, we extend the phase-plane based closed-loop scheme of implementing commands shaped with vibration-reduction filters. A generalized shaping filter is considered in this work which can have negative impulse intensities and different acceleration and deceleration limits. Switching conditions are derived in terms of the filter parameters for both convolution-based and closed-form based shaping techniques. Analytical expressions are provided for the switching curves and various schemes are discussed for selecting appropriate phase-planes and implementing shaped-commands on real-time servomechanisms.

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Copyright © 2014 by ASME
Topics: Vibration , Filters
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Figures

Grahic Jump Location
Fig. 1

Three impulse vibration reduction filter based on switching control. The impulse amplitudes and switching times are selected to cancel the flexible poles while maintaining the actuator limitations and unit DC gain.

Grahic Jump Location
Fig. 2

Comparison of convolution based and TS based schemes, (a) reference command, (b) control shaped with UM filter (impulse amplitudes [1, −1, 1]), and (c) closed-form control with TS filters designed for 0→1, 1→-1, and -1→0 transitions

Grahic Jump Location
Fig. 6

Switching curves in (e,v) projected phase plane for bang-bang command filtered with robust bang-bang transition shapers with γ = 0.8, ω = 1, and ζ = 0.1

Grahic Jump Location
Fig. 7

Switching curves in (y,v) projected phase plane for bang-bang command filtered with robust bang-bang transition shapers with γ = 0.8, ω = 1, and ζ = 0.1

Grahic Jump Location
Fig. 9

Size of dead-zone region for different actuator limits

Grahic Jump Location
Fig. 10

System response y and acceleration comparison for rest-to-rest motion subjected to XPTOS and commands shaped with ZV and ZVD TS filters

Grahic Jump Location
Fig. 8

Proposed control structure. Phase plane switching curves are generated based on the filter parameters. For small errors, the control is switched to a linear feedback controller. r, u, y, and v refer to the reference signal, control input, position output, and velocity, respectively.

Grahic Jump Location
Fig. 4

Switching curves in (e,v) projected phase plane for bang-bang command filtered with bang-bang transition shapers designed for γ = 0.8, ω = 1, and ζ = 0.1

Grahic Jump Location
Fig. 5

Switching curves in (y,v) projected phase plane for bang-bang command filtered with bang-bang transition shapers designed for γ = 0.8, ω = 1, and ζ = 0.1

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