0
Research Papers

Stability Analysis and Control of Supercavitating Vehicles With Advection Delay

[+] Author and Article Information
Munther A. Hassouneh

Department of Mechanical Engineering and the Institute for Systems Research,
University of Maryland,
College Park, MD, 20742
e-mail: munther@umd.edu

Vincent Nguyen

Department of Mechanical Engineering,
University of Maryland,
College Park, MD, 20742
e-mail: vince1@umd.edu

Balakumar Balachandran

ASME Fellow
Department of Mechanical Engineering,
University of Maryland,
College Park, MD, 20742
e-mail: balab@umd.edu

Eyad H. Abed

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

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 26, 2011; final manuscript received April 23, 2012; published online July 23, 2012. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 8(2), 021003 (Jul 23, 2012) (10 pages) Paper No: CND-11-1077; doi: 10.1115/1.4006835 History: Received May 26, 2011; Revised April 23, 2012

A pitch-plane model of a supercavitating vehicle is developed to account for the time delay in the propagation of the cavitator action from the vehicle nose to the vehicle aft. This time delay is an advection delay, which is on the order of the vehicle length divided by its speed. Unlike previous models with time-delay effects, in the present model, the effect of cavity rotation during forward motion is incorporated. Stability analyses and feedback control designs are carried out using this model. It is found that the open-loop system with and without the time delay is unstable. Feedback control laws that stabilize the delay-free system model are found to be ineffective in the presence of the time delay. The authors show that the delay leads to destabilization of the supercavitating vehicle dynamics in the sense that an operation at a stable trim condition is replaced by a stable limit-cycle motion that is commonly referred to as tail-slap. Feedback control designs are carried out by taking into account the time delay, and it is demonstrated that the supercavitating vehicle can be stabilized at trim conditions inside and outside the cavity. By using numerical studies of the nonlinear delay-dependent pitch-plane model of the supercavitating vehicle, the effectiveness of the new control designs are demonstrated.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

A supercavitating vehicle body with an envelope surrounding it

Grahic Jump Location
Fig. 2

Forces acting on a supercavitating vehicle

Grahic Jump Location
Fig. 3

Depiction of immersion depth

Grahic Jump Location
Fig. 4

Closed-loop system response for delay dependent system with initial condition (w0,q0,θ0,z0)=(2.4,0,0.03,0) and δc=-0.3q-30θ+15z, δe=0. Here, V=80 m/s.

Grahic Jump Location
Fig. 5

Planing force as a function of time for the closed-loop delay-free system with δc=-0.3q-30θ+15z, δe=0

Grahic Jump Location
Fig. 6

Closed-loop system response for delay dependent system with initial condition (w0,q0,θ0,z0)=(2.4,0,0.03,0) and δc=-0.3q-30θ+15z, δe=0. Here, V=80 m/s.

Grahic Jump Location
Fig. 7

Planing force as a function of time for the closed-loop delay dependent system with δc=-0.3q-30θ+15z, δe=0

Grahic Jump Location
Fig. 8

Closed-loop system response for delay-free model with zero initial condition and δc=-0.3q-30θ+15z, δe=0. Here, V=87 m/s.

Grahic Jump Location
Fig. 9

Effect of delay on stable equilibrium point. Delay is increased from 0 to 0.025s in steps of 0.00001s. The stable equilibrium point looses stability and a limit cycle is born around τ=0.0013s.

Grahic Jump Location
Fig. 10

Closed-loop system response for delay-dependent system with control δc=-0.3q-10θ+130z, δe=-0.1 (stabilization outside cavity). Here, V=87 m/s.

Grahic Jump Location
Fig. 11

Cavitator and elevator deflection angles as a function of time for the closed-loop system with control δc=-0.3q-10θ+130z, δe=-0.1 (stabilization outside cavity). Here, V=87 m/s.

Grahic Jump Location
Fig. 12

Planing force as a function of time for the closed-loop system with control δc=-0.3q-10θ+130z, δe=-0.1 (stabilization outside cavity). Here, V=87 m/s. Note that the value of the (normalized) planing force approaches a nonzero constant.

Grahic Jump Location
Fig. 13

Closed-loop system response for delay-dependent system with initial condition (w0,q0,θ0,z0)=(-1,0,-0.012,0) and δc=-0.3q-30θ+15z, δe=0.1 (stabilization inside cavity). Here, V=87 m/s.

Grahic Jump Location
Fig. 14

Cavitator and elevator deflection angles as a function of time for the closed-loop system with δc=-0.3q-30θ+15z, δe=0.1 (stabilization inside cavity). Here, V=87 m/s.

Grahic Jump Location
Fig. 15

Planing force as a function of time for the closed-loop system with δc=-0.3q-30θ+15z, δe=0.1 (stabilization inside cavity). Here, V=87m/s. Note that the value of the (normalized) planing force approaches zero in steady state.

Grahic Jump Location
Fig. 16

Cylindrical cavity used for planing force

Grahic Jump Location
Fig. 17

Cavity and vehicle centerlines for the delayed case

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In