Skip to main content
SpringerLink
Log in

Boundary control of coupled nonlinear three dimensional marine risers

  • Research Paper
  • Published:
Journal of Marine Science and Application Aims and scope Submit manuscript

Abstract

This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser’s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser’s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Balas MJ (1978). Active control of flexible systems. Journal of Optimization Theory and Application, 25(3), 415–436.

    Article  MathSciNet  MATH  Google Scholar 

  • Cavallo A, De Maria G (1999). Robust active control of flexible systems with second order sliding. Proc. of the 1999 IEEE/ASME Conference on Advanced Intelligent Mechatronics, Atlanta, USA, 162–166.

    Google Scholar 

  • Do KD, Pan J (2008). Boundary control of transverse motion of marine risers with actuator dynamics. Journal of Sound and Vibration, 318(4–5), 768–791.

    Article  Google Scholar 

  • Do KD, Pan J (2009). Boundary control of three-dimensional inextensible marine risers. Journal of Sound and Vibration, 327(3–5), 299–321.

    Article  Google Scholar 

  • Fard MP, Sagatun SI (2001). Exponential stabilization of a transversely vibrating beam via boundary control. Journal of Sound and Vibration, 240(4), 613–622.

    Article  MathSciNet  MATH  Google Scholar 

  • Fung R, Liao C (1995). Application variable structure control in the nonlinear string system. International Journal of Mechanical Sciences, 37(9), 985–993.

    Article  MATH  Google Scholar 

  • Ge SS, Lee TH, Zgu G, Hong F (2001). Variable structure control of a distributed-parameter flexible beam. Journal of Robotic Systems, 18(1), 17–27.

    Article  MATH  Google Scholar 

  • Ge SS, He W, How BVE, Choo YS (2010). Boundary control of a coupled nonlinear flexible marine riser. IEEE Transactions on Control Systems Technology, 18(5), 1080–1091.

    Article  Google Scholar 

  • He W, Ge SS, How BE (2011). Robustadaptive boundary control of a flexible marine riser with vessel dynamics. IEEE Transactions on Control Systems Technology, 47(4), 722–732.

    MathSciNet  MATH  Google Scholar 

  • How BVE, Ge SS, Choo YS (2009). Active control of flexible marine risers. Journal of Sound and Vibration, 320(4–6), 758–776.

    Article  Google Scholar 

  • Kim D, Jung IH (2011). Some boundary feedback control of a nonlinear string equation of kirchhoff-carrier type. 11th International Conference on Control, Automation and Systems, Gyeonggi-do, Korea, 254–257.

    Google Scholar 

  • Krstic M, Siranosian AA, Smyshlyaev A (2006a). Backstepping boundary controllers and observers for the slender timoshenko beam: Part I—design. American Control Conference, Minneapolis, USA, 2412–2417.

    Google Scholar 

  • Krstic M, Siranosian AA, Smyshlyaev A (2007). Control of string and flexible beams by backstepping boundary control. American Control Conference, New York, USA, 2007, 882–887.

    Google Scholar 

  • Krstic M, Siranosian AA, Smyshlyaev A, Bement M (2006b). Backstepping boundary controllers and observers for the slender timoshenko beam: Part II—stability and simulations. Conference on Decision and Control, San Diego, USA, 3938-3943.

  • Niedzwecki JM, Liagre PYF (2003). System identification of distributed-parameter marine riser model. Ocean Engineering, 30(11), 1387–1415.

    Article  Google Scholar 

  • Queiroz MSD, Dawson M, Nagarkatti S, Zhang F (2000). Lyapunov-based control of mechanical systems. Birkhauser, Boston.

    Book  MATH  Google Scholar 

  • Shahruz SM, Narasimha CA (1997). Suppression of vibration in stretched strings by the boundary control. Journal of Sound and Vibration, 204(5), 835–840.

    Article  MathSciNet  MATH  Google Scholar 

  • Shahruz SM, Krishna LG (1996). Boundary control of a nonlinear string. Journal of Sound and Vibration, 195(1), 169–174.

    Article  MathSciNet  MATH  Google Scholar 

  • Shahruz SM, Kurmaji DA (1997). Vibration suppression of a nonlinear axially moving string by boundary control. Journal of Sound and Vibration, 201(1), 145–152.

    Article  MathSciNet  MATH  Google Scholar 

  • Tanaka N, Iwanmoto H (2007). Active boundary control of an euler-bernoulli beam for generating vibration-free state. Journal of Sound and Vibration, 304(3–5), 570–586.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, WA, 6009, Australia

    T. L. Nguyen

  2. Department of Mechanical Engineering, Curtin University, Crawley, WA, 6102, Australia

    K. D. Do

  3. School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, WA, 6009, Australia

    J. Pan

Authors
  1. T. L. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. D. Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. L. Nguyen.

Additional information

Tung Lam Nguyen received his B.S. degree in Electrical Engineering from Hanoi University of Science and Technology, Vietnam, in 2005. He received his M.S. degree in 2007 from Asian Institute of Technology, Thailand and is currently a Ph.D. Candidate in the School of Mechanical and Chemical Engineering at the University of Western Australia. His research interests are in the areas of nonlinear control, flexible sytems.

Khac Duc Do received M.E. and Ph.D. degrees (with Distinction) in mechanical engineering from The University of Wollongong, Wollongong, Australia, and The University of Western Australia, Crawley, Australia, in 1999 and 2003, respectively. Before 2012, he was a research professor with the School of Mechanical Engineering, The University of Western Australia. He is currently with the Department of Mechanical Engineering, Curtin University of Technology. His research interests include control of nonlinear systems, control of multiple agents, control of land, air, and ocean vehicles, and control of systems governed by partial differential equations.

Jie Pan obtained a BSc in physics and acoustics from Nanjing University in China. He completed his PhD on sound and structural interaction at Adelaide University under the supervision of David Bies and his postdoctoral work on active noise and vibration under Colin Hansen. He joined the University of Western Australia in 1991 and he is now the Winthrop professor in the School of Mechanical and Chemical Engineering and director of Center for Acoustics, Dynamics and Vibration of UWA. He has authored and co-authored more than 300 journals and conference papers, one book and an eBook based on his research in acoustics and control. His H-index is 28, i10-index is 95. Professor Pan also contributed to WA ship building, mining and power industries through his consulting activities. Jie has several patents and a couple of them have been successfully implemented in WA marine, mining and power industries.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nguyen, T.L., Do, K.D. & Pan, J. Boundary control of coupled nonlinear three dimensional marine risers. J. Marine. Sci. Appl. 12, 72–88 (2013). https://doi.org/10.1007/s11804-013-1175-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11804-013-1175-8

Keywords

Search

Navigation