Skip to main content

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

Abstract

The current state-of-the-art in the fields of control-oriented LPV modelling and LPV system identification is surveyed and the potential synergies between the two research areas are highlighted and discussed. Indeed, a number of methods and tools for the development of LPV models from nonlinear systems and for the identification of black-box LPV models from input/output data have been derived, in a rather independent way, in different research communities. The relative merits of analytical and experimental methods for the derivation of LPV models, as well as possible combinations of the two approaches, are analysed and eventually evaluated on a case study based on the modelling of a thermo-fluid system.

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., Noll, D.: Nonsmooth H  ∞  synthesis. IEEE Transactions on Automatic Control 51(1), 71–86 (1996)

    Article  MathSciNet  Google Scholar 

  2. Bamieh, B., Giarré, L.: Identification of linear parameter varying models. In: Proceedings of the IEEE Conference on Decision and Control, Phoenix, USA (1999)

    Google Scholar 

  3. Bamieh, B., Giarré, L.: Identification of linear parameter varying models. International Journal of Robust and Nonlinear Control 12(9), 841–853 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bergamasco, M., Lovera, M.: Subspace identification of continuous-time state-space LPV models. In: Linear Parameter-Varying System Identification: New Developments and Trends. Advanced Series in Electrical and Computer Engineering. World Scientific (2012)

    Google Scholar 

  5. Bergamasco, M., Lovera, M.: State space model identification: from unstructured to structured models with an h  ∞  approach. In: IFAC Symposium on System Structure and Control, Grenoble, France (Submitted, 2013)

    Google Scholar 

  6. Boonto, S., Werner, H.: Closed-loop system identification of LPV input-output models: application to an arm-driven inverted pendulum. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico (2008)

    Google Scholar 

  7. Boonto, S., Werner, H.: Closed-loop identification of LPV models using cubic splines with application to an arm-driven inverted pendulum. In: Proceedings of the American Control Conference, Baltimore, MD, USA (2010)

    Google Scholar 

  8. Bruls, J., Chou, C., Haverkamp, B., Verhaegen, M.: Linear and non-linear system identification using separable least-squares. European Journal of Control 5(1), 116–128 (1999)

    MATH  Google Scholar 

  9. Casella, F., Leva, A.: Modelling of thermo-hydraulic power generation processes using Modelica. Mathematical and Computer Modelling of Dynamical Systems 10(1), 19–33 (2006)

    Article  Google Scholar 

  10. Casella, F., Lovera, M.: LPV/LFT modelling and identification: Overview, synergies and a case study. In: 2008 IEEE Multi-conference on Systems and Control, San Antonio, USA (2008)

    Google Scholar 

  11. Chabaan, R.: H-infinity control and gain scheduling method for electric power assist steering system. US Patent 6651771 (2003)

    Google Scholar 

  12. De Caigny, J., Camino, J., Swevers, J.: Interpolating model identification for SISO linear parameter-varying systems. Mechanical Systems and Signal Processing 23, 2395–2417 (2009)

    Article  Google Scholar 

  13. De Caigny, J., Camino, J., Swevers, J.: Interpolation-based modeling of MIMO LPV systems. IEEE Transactions on Control Systems Technology 19, 46–63 (2011)

    Article  Google Scholar 

  14. Doll, C., Chiappa, C., Biannic, J.M.: LFT modelling of the 2-dof longitudinal nonlinear aircraft behaviour. In: 2008 IEEE Multi-conference on Systems and Control, San Antonio, USA (2008)

    Google Scholar 

  15. Felici, F., van Wingerden, J.W., Verhaegen, M.: Subspace identification of MIMO LPV systems using a periodic scheduling sequence. Automatica 43(10), 1684–1697 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fialho, I.J., Balas, G.: Design of nonlinear controllers for active vehicle suspensions using parameter-varying control synthesis. Vehicle Systems Dynamics 33(5), 351–370 (2000)

    Article  Google Scholar 

  17. Gahinet, P., Apkarian, P.: Decentralized and fixed-structure H  ∞  control in MATLAB. In: 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, USA (2011)

    Google Scholar 

  18. Ghersin, A., Sanchez Pena, R.: LPV control of a 6-DOF vehicle. IEEE Transactions on Control Systems Technology 10(6), 883–887 (2002)

    Article  Google Scholar 

  19. Giarré, L., Bauso, D., Falugi, P., Bamieh, B.: LPV model identification for gain scheduling control: An application to rotating stall and surge control problem. Control Engineering Practice 14(4), 351–361 (2006)

    Article  Google Scholar 

  20. Groot Wassink, W., van de Wal, M., Scherer, C., Bosgra, O.: LPV control for a wafer stage: beyond the theoretical solution. Control Engineering Practice 13, 231–245 (2005)

    Article  Google Scholar 

  21. Hara, S.: Workshop on ”glocal control”. In: IEEE Multi-Conference on Systems and Control, Yokohama, Japan (2010)

    Google Scholar 

  22. Hashemi, S., Abbas, H., Werner, H.: LPV modelling and control of a 2-DOF robotic manipulator using PCA-based parameter set mapping. In: Proceedings of the 48th IEEE Conference on Decision and Control (with the 28th Chinese Control Conference), Shangai, P.R. China (2009)

    Google Scholar 

  23. van Helvoort, J., Steinbuch, M., Lambrechts, P., van de Molengraft, R.: Analytical and experimental modelling for gain-scheduling of a double scara robot. In: Proceedings of the 3rd IFAC Symposium on Mechatronic Systems, Sydney, Australia (2004)

    Google Scholar 

  24. Henry, R., Applebee, M.: Vehicle suspension system with gain scheduling. US Patent 5497324 (1996)

    Google Scholar 

  25. Hingwe, P., Tan, H., Packard, A., Tomizuka, M.: Linear parameter varying controller for automated lane guidance: experimental study on tractor-trailers. IEEE Transactions on Control Systems Technology 10(6), 793–806 (2002)

    Article  Google Scholar 

  26. Hong, K., Sohn, H., Hedrick, J.: Modified skyhook control of semi-active suspensions: A new model, gain scheduling, and hardware-in-the-loop tuning. Journal of Dynamic Systems, Measurement, and Control 124(1), 158–167 (2002)

    Article  Google Scholar 

  27. Hunt, K., Johansen, T., Kalkkuhl, J., Fritz, H., Gottsche, T.: Speed control design for an experimental vehicle using a generalized gain scheduling approach. IEEE Transactions on Control System Technology 8(3), 381–395 (2000)

    Article  Google Scholar 

  28. Kron, A., de Lafontaine, J., Peuvédic, C.L.: Mars entry and aerocapture robust control using static output feedback and LPV techniques. In: 6th International ESA Conference on Guidance, Navigation and Control Systems, Loutraki, Greec (2005)

    Google Scholar 

  29. Laub, A., Heath, M., Paige, C., Ward, R.: Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Transactions on Automatic Control 32, 115–122 (1987)

    Article  MATH  Google Scholar 

  30. Lee, C., Shin, M., Chung, M.: A design of gain-scheduled control for a linear parameter varying system: an application to flight control. Control Engineering Practice 9(1), 11–21 (2001)

    Article  Google Scholar 

  31. Lee, L., Poolla, K.: Identification of linear parameter-varying systems using nonlinear programming. ASME Journal of Dynamic Systems, Measurement and Control 121(1), 71–78 (1999)

    Article  Google Scholar 

  32. Leith, D.J., Leithead, W.E.: Survey of gain-scheduling analysis and design. International Journal of Control 73(11), 1001–1025 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  33. Lopes Dos Santos, P., Azevedo Perdicoulis, T.P., Novara, C., Ramos, J.A., Rivera, D. (eds.): Linear Parameter-Varying System Identification: New Developments and Trends. Advanced Series in Electrical and Computer Engineering. World Scientific (2012)

    Google Scholar 

  34. Lovera, M., Mercere, G.: Identification for gain-scheduling: a balanced subspace approach. In: 2007 American Control Conference, New York, USA (2007)

    Google Scholar 

  35. Lovera, M., Novara, C., Lopes Dos Santos, P., Rivera, D.: Guest editorial, special issue on applied LPV modeling and identification. IEEE Transactions on Control Systems Technology 19(1), 1–4 (2011)

    Article  Google Scholar 

  36. Lovera, M., Verhaegen, M., Chou, C.T.: State space identification of MIMO linear parameter varying models. In: Proc. of the International Conference on Mathematical Theory of Networks and Systems, Padova, Italy (1996)

    Google Scholar 

  37. Lu, B., Wu, F.: Probabilistic robust linear parameter-varying control of an F-16 aircraft. Journal of Guidance, Control and Dynamics 29(6), 1454–1460 (2006)

    Article  MathSciNet  Google Scholar 

  38. Lu, B., Wu, F., Kim, S.: Switching LPV control of an F-16 aircraft via controller state reset. IEEE Transactions on Control System Technology 14(2), 267–277 (2006)

    Article  Google Scholar 

  39. Marcos, A., Balas, G.: Development of linear-parameter-varying models for aircraft. Journal of Guidance, Control and Dynamics 27(2), 218–228 (2004)

    Article  Google Scholar 

  40. Marcos, A., Penin, L., Sotto, E.D.: LFT modelling for the analysis of relative motion controllers in eccentric orbits. In: 2008 IEEE Multi-conference on Systems and Control, San Antonio, USA (2008)

    Google Scholar 

  41. Matsumura, F., Namerikawa, T., Hagiwara, K., Fujita, M.: Application of gain scheduled h8 robust controllers to a magnetic bearing. IEEE Transactions on Control System Technology 4(5), 484–493 (1996)

    Article  Google Scholar 

  42. Mercère, G., Laroche, E., Lovera, M.: Identification of a flexible robot manipulator using a linear parameter-varying descriptor state-space structure. In: IEEE Conference on Decision and Control and European Control Conference, Orlando, USA (2011)

    Google Scholar 

  43. Mohammadpour, J., Scherer, C.W. (eds.): Control of Linear Parameter Varying Systems with Applications. Springer (2012)

    Google Scholar 

  44. Moore, B.: Principal component analysis in linear systems: controllability, observability and model reduction. IEEE Transactions on Automatic Control 26, 17–32 (1981)

    Article  MATH  Google Scholar 

  45. Ohara, A., Yamaguchi, Y., Morito, T.: LPV modeling and gain scheduled control of re-entry vehicle in approach and landing phase. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, Montreal, Canada (2001)

    Google Scholar 

  46. Onat, C., Kucukdemiral, I., Sivrioglu, S., Yuksek, I.: LPV model based gain-scheduling controller for a full vehicle active suspension system. Journal of Vibration and Control 13(11), 1629–1666 (2007)

    Article  MATH  Google Scholar 

  47. Paijmans, B., Symens, W., Brussel, H.V., Swevers, J.: A gain-scheduling-control technique for mechatronic systems with position-dependent dynamics. In: Proceedings of the 2006 American Control Conference, Minneapolis, USA (2006)

    Google Scholar 

  48. Pfifer, H., Hecker, S.: Generation of optimal linear parametric models for LFT-based robust stability analysis and control design. IEEE Transactions on Control Systems Technology 19(1), 118–131 (2011)

    Article  Google Scholar 

  49. Previdi, F., Carpanzano, E.: Design of a gain scheduling controller for knee-joint angle control by using functional electrical stimulation. IEEE Transactions on Control System Technology 11(3), 310–324 (2000)

    Article  Google Scholar 

  50. Prot, O., Mercere, G., Ramos, J.: Null-space-based technique for the estimation of linear-time invariant structured state-space representations. In: 16th IFAC Symposium on System Identification, Brussels, Belgium (2012)

    Google Scholar 

  51. Qin, W., Wang, Q.: An LPV approximation for admission control of an internet web server: identification and control. Control Engineering Practice 15(12), 1457–1467 (2007)

    Article  Google Scholar 

  52. Qin, W., Wang, Q.: Modeling and control design for performance management of web servers via an LPV approach. IEEE Transactions on Control Systems Technology 15(2), 259–275 (2007)

    Article  Google Scholar 

  53. Rugh, W., Shamma, J.: Research on gain scheduling. Automatica 36(10), 1401–1425 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  54. Lopes dos Santos, P., Ramos, J.A., Martins de Carvalho, J.L.: Identification of bilinear systems using an iterative deterministic-stochastic approach. In: 44th IEEE Conference on Decision and Control and European Control Conference (2005)

    Google Scholar 

  55. Lopes dos Santos, P., Ramos, J.A., Martins de Carvalho, J.L.: Identification of linear parameter varying systems using an iterative deterministic-stochastic subspace approach. In: European Control Conference (2007)

    Google Scholar 

  56. Lopes dos Santos, P., Ramos, J.A., Martins de Carvalho, J.L.: Identification of LPV systems using successive approximations. In: 44th IEEE Conference on Decision and Control (2008)

    Google Scholar 

  57. Lopes dos Santos, P., Ramos, J.A., Martins de Carvalho, J.L.: Identification of bilinear systems with white noise inputs: An iterative deterministic-stochastic subspace approach. IEEE Transactions on Control Systems Technology 17(3), 1145–1153 (2009)

    Article  Google Scholar 

  58. Steinbuch, M., van de Molengraft, R., van der Voort, A.: Experimental modelling and LPV control of a motion system. In: Proceedings of the 2003 American Control Conference, Denver, USA (2003)

    Google Scholar 

  59. Tan, H.: Estimating vehicle velocities using linear-parameter-varying and gain varying scheduling theories. US Patent 6618651 (2003)

    Google Scholar 

  60. Tanelli, M., Ardagna, D., Lovera, M.: LPV model identification for power management of web service systems. In: IEEE International Symposium on CACSD, San Antonio, USA (2008)

    Google Scholar 

  61. Tóth, R.: Modeling and Identification of Linear Parameter-Varying Systems. LNCIS, vol. 403. Springer, Heidelberg (2010)

    Book  MATH  Google Scholar 

  62. van Wingerden, J., Verhaegen, M.: Subspace identification of bilinear and LPV systems for open- and closed-loop data. Automatica 45, 372–381 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  63. Verdult, V.: Nonlinear system identification: a state space approach. Ph.D. thesis, University of Twente (2002)

    Google Scholar 

  64. Verdult, V., Lovera, M., Verhaegen, M.: Identification of linear parameter varying state space models with application to helicopter rotor dynamics. International Journal of Control 77, 1149–1159 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  65. Verdult, V., Verhaegen, M.: Subspace identification of multivariable linear parameter varying systems. Automatica 38, 805–814 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  66. Verdult, V., Verhaegen, M.: Kernel methods for subspace identification of multivariable LPV and bilinear systems. Automatica 41, 1557–1565 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  67. Verdult, V., Verhaegen, M., Chou, C., Lovera, M.: Efficient and systematic identification of mimo bilinear state-space models. In: IEEE Conference on Decision and Control, Tampa, USA (1998)

    Google Scholar 

  68. Wassink, M.G., van de Wal, M., Scherer, C., Bosgra, O.: LPV control for a wafer stage: beyond the theoretical solution. Control Engineering Practice 13(2), 231–245 (2005)

    Article  Google Scholar 

  69. Wei, X., del Re, L.: Gain scheduled h  ∞  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 

  70. Xin, T., Tanaka, H., Ohta, Y.: Grey-box modeling of rotary type pendulum system with position-variable load. In: 16th IFAC Symposium on System Identification, Brussels, Belgium (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Lovera .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lovera, M., Bergamasco, M., Casella, F. (2013). LPV Modelling and Identification: An Overview. 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_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36110-4_1

  • 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