Skip to main content

LPV Approaches for Varying Sampling Control Design: Application to Autonomous Underwater Vehicles

  • Chapter
Robust Control and Linear Parameter Varying Approaches

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 437))

Abstract

This chapter deals with the robust control of an Autonomous Underwater Vehicle (AUV) subject to computation or communication constraints. The aim is the design of a gain-scheduled varying sampling controller using non periodic measurements, where the varying sampling rate is considered as a known parameter. First a Linear Parameter Varying (LPV) model of the AUV is developed to keep some non-linearities of the plant in the model, thus enlarging the model’s domain of validity around nominal conditions. The weighting templates are also made bandwidth dependent to take into account the dependencies between the achievable control performances and the sampling interval. From this model a LPV controller is synthesized in continuous time and then discretized over the range of predefined sampling rates. The approach is applied to the altitude control of an AUV, where depth measurements are asynchronously supplied by acoustic sensors.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Apkarian, P., Gahinet, P.: A convex characterisation of gain-scheduled \(\mathcal{H}_{\infty}\) controllers. IEEE Transaction on Automatic Control 40, 853–864 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Apkarian, P., Gahinet, P., Becker, G.: Self-scheduled \(\mathcal{H}_\infty\) control of linear parameter-varying systems: a design example. Automatica 31(9), 1251–1261 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bokor, J., Balas, G.: Detection filter design for LPV systems–a geometric approach. Automatica 40(3), 511–518 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Briat, C., Sename, O., Lafay, J.F.: Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays. Systems and Control Letters 59(8), 451–459 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Feng, Z., Allen, R.: Reduced order \(\mathcal{H}_{\infty}\) control of an autonomous underwater vehicle. Control Engineering Practice 12, 1511–1520 (2004)

    Article  Google Scholar 

  6. Fossen, T.I.: Guidance and Control of Ocean Vehicles. John Wiley & Sons (1994)

    Google Scholar 

  7. Gaspar, P., Szabo, Z., Bokor, J.: LPV design of fault-tolerant control for road vehicles. In: 2010 Conference on Control and Fault-Tolerant Systems (SysTol), pp. 807–812 (October 2010)

    Google Scholar 

  8. Healey, A.J., Lienard, D.: Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles. Oceanic Engineering 18(3), 327–339 (1993)

    Article  Google Scholar 

  9. Heemels, W.P.M.H., Daafouz, J., Millerioux, G.: Observer-based control of discrete-time LPV systems with uncertain parameters. IEEE Transactions on Automatic Control 55(9), 2130–2135 (2010)

    Article  MathSciNet  Google Scholar 

  10. Hetel, L., Kruszewski, A., Perruquetti, W., Richard, J.-P.: Discrete and intersample analysis of systems with aperiodic sampling. IEEE Transactions on Automatic Control 56(7), 1696–1701 (2011)

    Article  MathSciNet  Google Scholar 

  11. Leveille, E.A.: Analysis, redesign and verification of the iver2 autonomous underwater vehicle motion controller. Master’s thesis, University of Massachusetts Dartmouth (2007)

    Google Scholar 

  12. Lofberg, J.: YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei, Taiwan (2004)

    Google Scholar 

  13. Miyamaoto, S., Aoki, T., Maeda, T., Hirokawa, K., Ichikawa, T., Saitou, T., Kobayashi, H., Kobayashi, E., Iwasaki, S.: Maneuvering control system design for autonomous underwater vehicle. In: MTS/IEEE Conference and Exhibition, vol. 1, pp. 482–489 (November 2001)

    Google Scholar 

  14. Opderbecke, J.: Description of the scientific mission scenario(s) to be investigated for the marine application. deliverable D08.01, FeedNetBack project (2009), http://feednetback.eu/public-deliverables/public-deliverables-pdf/ploneexfile.2009-12-09.1317343148/

  15. Pellanda, P.C., Apkarian, P., Tuan, H.D., Alazard, D.: Missile autopilot design via a multi-channel LFT/LPV control method. In: 15th IFAC World Congress, Barcelona, Spain (2002)

    Google Scholar 

  16. Poussot-Vassal, C., Sename, O., Dugard, L., Gáspár, P., Szabó, Z., Bokor, J.: Attitude and handling improvements through gain-scheduled suspensions and brakes control. Control Engineering Practice 19(3), 252–263 (2011)

    Article  Google Scholar 

  17. Poussot-Vassal, C., Sename, O., Dugard, L., Gáspár, P., Szabó, Z., Bokor, J.: A new semi-active suspension control strategy through LPV technique. Control Engineering Practice 16(12), 1519–1534 (2008)

    Article  Google Scholar 

  18. Robert, D.: Contribution à l’interconnection commande / ordonnancement. PhD thesis, Institut National Polytechnique de Grenoble (2007)

    Google Scholar 

  19. Robert, D., Sename, O., Simon, D.: An h  ∞  LPV design for sampling varying controllers: experimentation with at inverted pendulum. IEEE Transactions on Control Systems Technology 18(3), 741–749 (2010)

    Article  Google Scholar 

  20. Roche, E., Sename, O., Simon, D.: LPV / \(\mathcal{H}_{\infty}\) varying sampling control for autonomous underwater vehicles. In: Proceedings of the IFAC SSSC, Ancona, Italy (2010)

    Google Scholar 

  21. Roche, E., Sename, O., Simon, D.: A hierarchical varying sampling \(\mathcal{H}_{\infty}\) control of an AUV. In: Proceedings of the IFAC World Congress, Milano, Italy (2011)

    Google Scholar 

  22. Santos, A.S.: Contribution à la conception des sous-marins autonomes: architecture des capteurs d’altitude, et commande référencées capteurs. PhD thesis, Ecole nationale supérieure des Mines de Paris (1995) (in French)

    Google Scholar 

  23. Scherer, C.W.: LPV control and full block multipliers. Automatica 37(3), 361–375 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Shirazi, F.A., Mohammadpour Velni, J., Grigoriadis, K.M.: An LPV design approach for voltage control of an electrostatic MEMS actuator. Journal of Microelectromechanical Systems 20(1), 302–311 (2011)

    Article  Google Scholar 

  25. Silvestre, C., Pascoal, A.: Control of the INFANTE AUV using gain scheduled static output feedback. Control Engineering Practice 12(12), 1501–1509 (2004)

    Article  Google Scholar 

  26. Silvestre, C., Pascoal, A.: Depth control of the INFANTE AUV using gain-scheduled reduced order output feedback. Control Engineering Practice 15(7), 883–895 (2007)

    Article  Google Scholar 

  27. Simon, D., Robert, D., Sename, O.: Robust control/scheduling co-design: application to robot control. In: 11th IEEE Real Time and Embedded Technology and Applications Symposium, RTAS 2005, pp. 118–127 (March 2005)

    Google Scholar 

  28. Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11/12(1-4), 625–653 (1999), Interior point methods

    Article  MathSciNet  Google Scholar 

  29. Tóth, R., Heuberger, P.S.C., Van den Hof, P.M.J.: Discretisation of linear parameter-varying state-space representations. IET Control Theory and Applications 4(10), 2082–2096 (2010)

    Article  MathSciNet  Google Scholar 

  30. Wei, X., del Re, L.: Gain scheduled \(\mathcal{H}_{\infty}\) control for air path systems of diesel engines using LPV techniques. IEEE Transactions on Control Systems Technology 15(3), 406–415 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Emilie Roche .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Roche, E., Sename, O., Simon, D. (2013). LPV Approaches for Varying Sampling Control Design: Application to Autonomous Underwater Vehicles. In: Sename, O., Gaspar, P., Bokor, J. (eds) Robust Control and Linear Parameter Varying Approaches. Lecture Notes in Control and Information Sciences, vol 437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36110-4_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36110-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36109-8

  • Online ISBN: 978-3-642-36110-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics