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Research Papers

Dynamics and Control of Supercavitating Vehicles

[+] Author and Article Information
Guojian Lin

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland, College Park, MD 20742linguoji@eng.umd.edu

Balakumar Balachandran

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742balab@eng.umd.edu

Eyad H. Abed

Department of Electrical and Computer Engineering and the Institute for Systems Research, University of Maryland, College Park, MD 20742abed@eng.umd.edu

J. Dyn. Sys., Meas., Control 130(2), 021003 (Feb 29, 2008) (11 pages) doi:10.1115/1.2837307 History: Received April 27, 2006; Revised June 12, 2007; Published February 29, 2008

Analytical and numerical investigations into the dynamics and control of dive-plane dynamics of supercavitating vehicles are presented. Dominant nonlinearities associated with planing forces are taken into account in the model. Two controllers are proposed to realize stable inner-loop dynamics, a linear state feedback control scheme and a switching control scheme. Through numerical simulations and estimation of the region of attraction, it is shown that effective feedback schemes can be constructed. In comparison to existing control schemes, the feedback schemes proposed in this work can stabilize a supercavitating vehicle with a large region of attraction around the trim condition instead of just stabilization around the limit cycle motion. In particular, the achieved stability is robust to modeling errors in the planing force. This robustness is especially important for supercavitating vehicles because the underlying planing force physics is complicated and not yet fully understood. Compared to the linear feedback control scheme, the switching control scheme is seen to increase the region of attraction with reduced control effort, which can be useful for avoiding saturation in magnitude. Analytical tools, including the describing function method and the circle criterion, are applied to facilitate understanding of the closed-loop system dynamics and assist in the controller design. This work provides a basis for interpreting the tail-slap phenomenon of a supercavitating body as a limit cycle motion and for developing control methods to achieve stable inner-loop dynamics in the full model.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A supercavitating body with an envelope surrounding it

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Figure 2

System form for DFM analysis and application of circle criterion

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Figure 3

Planing force term versus the vertical speed w

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Figure 4

Motions initiated from trivial initial conditions in the uncontrolled case

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Figure 5

Motions initiated from trivial initial conditions in the controlled case (controller I)

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Figure 6

Illustration of tail-slap phenomenon (cavity exaggerated for clarity)

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Figure 7

Motions initiated from [z,w,θ,q]=[0,1.8,0,0] in the controlled case (controller IIa)

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Figure 8

Motions initiated from [z,w,θ,q]=[0,1.8,0,0] in the controlled case (controller IIb)

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Figure 9

Motions initiated from [z,w,θ,q]=[0,3,0,0] in the controlled case (controller IIb)

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Figure 10

Motions initiated from [z,w,θ,q]=[0,3,0,0] in the controlled case (controller IIc)

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Figure 11

ROA estimation using the circle criterion

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Figure 12

Nyquist diagram of G(s) and the straight line of Re[s]=−1∕β

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Figure 13

Switching control design

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Figure 14

Motions initiated from [z,w,θ,q]=[0,1.8,0,0] in the controlled case (controller IIIa)

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Figure 15

Motions initiated at [z,w,θ,q]=[0,1.8,0,0] in the controlled case (controller IIIb)

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Figure 16

Motions initiated from [z,w,θ,q]=[0,3,0,0] in the controlled case (controller IIIb)

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Figure 17

Motions initiated from [z,w,θ,q]=[0,3,0,0] in the controlled case (controller IIIc)

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