Skip to main content
Log in

Robust sampled-data \({\varvec{H}}_{\varvec{\infty }}\) control for offshore platforms subject to irregular wave forces and actuator saturation

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper presents a robust sampled-data \({H_\infty }\) control scheme for vibration attenuation of offshore platforms subject to irregular wave forces and actuator saturation. When a digital computer is used to sample and quantize the measurement signal, a discrete-time control input signal will be produced. At the same time, the actuator is usually saturated due to the physical or technological constraints. In view of these, a sampled-data \({H_\infty }\) controller is designed to attenuate the wave-induced vibration of the offshore platform, thereby improving the control performance of the system. It is shown through simulation results that the proposed control scheme is effective to suppress the vibration of the offshore platform in the presence of actuator saturation.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Terro, M.J., Mahmoud, M.S., Abdel-Rohman, M.: Multi-loop feedback control of offshore steel jacket platforms. Comput. Struct. 70(2), 185–202 (1999)

    Article  MATH  Google Scholar 

  2. Zribi, M., Almutairi, N., Abdel-Rohman, M., Terro, M.: Nonlinear and robust control schemes for offshore steel jacket platforms. Nonlinear Dyn. 35(1), 61–80 (2004)

    Article  MATH  Google Scholar 

  3. Li, H.J., Hu, S.L.J., Jakubiak, C.: \({H_2}\) active vibration control for offshore platform subjected to wave loading. J. Sound Vib. 263(4), 709–724 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ma, H., Tang, G.Y., Zhao, Y.D.: Feedforward and feedback optimal control for offshore structures subjected to irregular wave forces. Ocean Eng. 33(8), 1105–1117 (2006)

    Article  Google Scholar 

  5. Luo, M., Zhu, W.Q.: Nonlinear stochastic optimal control of offshore platforms under wave loading. J. Sound Vib. 296(4), 734–745 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ma, H., Tang, G.Y., Hu, W.: Feedforward and feedback optimal control with memory for offshore platforms under irregular wave forces. J. Sound Vib. 328(4), 369–381 (2009)

    Article  Google Scholar 

  7. Zhang, B.L., Han, Q.L.: Network-based modelling and active control for offshore steel jacket platform with TMD mechanisms. J. Sound Vib. 333(25), 6796–6814 (2014)

    Article  Google Scholar 

  8. Zhang, X.M., Han, Q.L., Han, D.: Effects of small time-delays on dynamic output feedback control of offshore steel jacket structures. J. Sound Vib. 330(16), 3883–3900 (2011)

    Article  Google Scholar 

  9. Zhang, B.L., Hu, Y.H., Tang, G.Y.: Stabilization control for offshore steel jacket platforms with actuator time-delays. Nonlinear Dyn. 70(2), 1593–1603 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, B.L., Tang, G.Y.: Active vibration \({H_\infty }\) control of offshore steel jacket platforms using delayed feedback. J. Sound Vib. 332(22), 5662–5677 (2013)

    Article  Google Scholar 

  11. Zhang, B.L., Han, Q.L., Huang, Z.W.: Pure delayed non-fragile control for offshore steel jacket platforms subject to non-linear self-excited wave force. Nonlinear Dyn. 77(3), 491–502 (2014)

    Article  MATH  Google Scholar 

  12. Zhang, B.L., Han, Q.L., Zhang, X.M., Yu, X.: Integral sliding mode control for offshore steel jacket platforms. J. Sound Vib. 331(14), 3271–3285 (2012)

    Article  Google Scholar 

  13. Zhang, B.L., Ma, L., Han, Q.L.: Sliding mode \({H_\infty }\) control for offshore steel jacket platforms subject to nonlinear self-excited wave force and external disturbance. Nonlinear Anal. Real World Appl. 14(1), 163–178 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, B.L., Han, Q.L., Zhang, X.M., Yu, X.: Sliding mode control with mixed current and delayed states for offshore steel jacket platforms. IEEE Trans. Control Syst. Technol. 22(5), 1769–1783 (2014)

    Article  Google Scholar 

  15. Chen, T., Francis, B.: Optimal Sampled-Data Control Systems. Springer, London (1995)

    Book  MATH  Google Scholar 

  16. Fridman, E., Seuret, A., Richard, J.P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8), 1441–1446 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  17. Naghshtabrizi, P., Hespanha, J.P., Teel, A.R.: Exponential stability of impulsive systems with application to uncertain sampled-data systems. Syst. Control Lett 57(5), 378–385 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Suh, Y.S.: Stability and stabilization of nonuniform sampling systems. Automatica 44(12), 3222–3226 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lei, J.: Optimal vibration control for uncertain nonlinear sampled-data systems with actuator and sensor delays: application to a vehicle suspension. J. Dyn. Syst. Measur. Control 135(2), 021021–021033 (2013)

    Article  Google Scholar 

  20. Ankireddi, S., Yang, H.T.Y.: Sampled-data \({H_2}\) optimal output feedback control for civil structures. Earthq. Eng. Struct. Dyn. 28(9), 921–940 (1999)

    Article  Google Scholar 

  21. Zhao, Y.: Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay. J. Sound Vib. 329(21), 4335–4353 (2010)

    Article  Google Scholar 

  22. Gao, H., Sun, W., Shi, P.: Robust sampled-data \({H_\infty }\) control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 18(1), 238–245 (2010)

    Article  Google Scholar 

  23. Du, H., Zhang, N., Samali, B., Naghdy, F.: Robust sampled-data control of structures subject to parameter uncertainties and actuator saturation. Eng. Struct. 36, 39–48 (2012)

    Article  Google Scholar 

  24. Du, H., Zhang, N., Naghdy, F.: Actuator saturation control of uncertain structures with input time delay. J. Sound Vib. 330(18–19), 4399–4412 (2011)

    Article  Google Scholar 

  25. Ding, Y.C., Weng, F.L., Yu, Z.A.: Actuator saturation and control design for buildings structural systems with improved uncertainty description. Shock Vib. 20(2), 297–308 (2013)

    Article  Google Scholar 

  26. Da Silva Jr., J.M.G., Tarbouriech, S.: Anti-windup design with guaranteed regions of stability: an LMI-based approach. IEEE Trans. Automat. Control. 50(1), 106–111 (2005)

    Article  MathSciNet  Google Scholar 

  27. Xie, L.: Output feedback \({H_\infty }\) control of systems with parameter uncertainty. Int. J. control 63(4), 741–750 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  28. Chen, W.H., Zheng, W.X.: An improved stabilization method for sampled-data control systems with control packet loss. IEEE Trans. Automat. Control 57(9), 2378–2384 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 61273120, and the Postgraduate Innovation Project of Jiangsu Province (Grant No. KYLX-0372).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhengrong Xiang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, S., Cai, M. & Xiang, Z. Robust sampled-data \({\varvec{H}}_{\varvec{\infty }}\) control for offshore platforms subject to irregular wave forces and actuator saturation. Nonlinear Dyn 88, 2705–2721 (2017). https://doi.org/10.1007/s11071-017-3404-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3404-6

Keywords

Navigation