Mode shape matching for LPV modeling to handle mode veering phenomena

  • Ali Khudhair Al-JibooryEmail author
  • Guoming Zhu


New approach is developed in this paper for mode matching of LTI models at different grid points such that a Linear Parameter Varying model can be obtained through interpolation. The approach is based on matching eigenvector associated with each eigenvalue such that state consistency can be guaranteed for local LTI models. The novelty of the developed approach is the ability to handle mode veering phenomena, where two distinct real poles converge into two repeated ones then separate into complex conjugate poles and vise versa. Linear interpolation procedure based on Least-Squares errors is also presented to interpolate local LTI models. The proposed approach is demonstrated through numerical example.


LPV modeling Mode matching Mode veering Aerospace applications 


  1. 1.
    Hoffmann C, Werner H (2015) A survey of linear parameter-varying control applications validated by experiments or high-fidelity simulations. IEEE Trans Control Syst Technol 23(2):416–433CrossRefGoogle Scholar
  2. 2.
    Apkarian P, Adams RJ (1998) Advanced gain-scheduling techniques for uncertain systems. IEEE Trans Control Syst Technol 6(1):21–32. CrossRefzbMATHGoogle Scholar
  3. 3.
    Shamma JS, Athans M (1991) Guaranteed properties of gain scheduled control for linear parameter-varying plants. Automatica 27(3):559–564MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Al-Jiboory AK, Zhu GG, Choi J (2016) Guaranteed performance state-feedback gain-scheduling control with uncertain scheduling parameters. J Dyn Syst Meas Control 138(1):014,502. CrossRefGoogle Scholar
  5. 5.
    Al-Jiboory AK, White A, Zhang S, Zhu G, Choi J (2015) Linear matrix inequalities approach to input covariance constraint control with application to electronic throttle. Trans ASME J Dyn Syst Meas Control 139(9)Google Scholar
  6. 6.
    Al-Jiboory AK, Zhu G, Sultan C (2014) LMI control design with input covariance constraint for a tensegrity simplex structure. In: ASME dynamic systems and control conference, DSCC 2014, vol 3Google Scholar
  7. 7.
    Lovera M, Novara C, dos Santos PL, Rivera D (2011) Guest editorial special issue on applied lpv modeling and identification. IEEE Trans Control Syst Technol 19(1):1–4. CrossRefGoogle Scholar
  8. 8.
    De Caigny J, Pintelon R, Camino JF, Swevers J (2014) Interpolated modeling of LPV systems. IEEE Trans Control Syst Technol 22(6):2232–2246. CrossRefGoogle Scholar
  9. 9.
    De Caigny J, Camino JF, Swevers J (2009) Interpolating model identification for SISO linear parameter-varying systems. Mech Syst Signal Process 23(8):2395–2417.
  10. 10.
    Varga A, Hansson A, Puyou G (2012) Optimization based clearance of flight control laws. Lecture notes in control and information science. Springer, Berlin, pp 11–36CrossRefGoogle Scholar
  11. 11.
    Puyou G, Losser Y (2012) Clearance benchmark for a civil aircraft. In: Optimization based clearance of flight control laws, p. 121. SpringerGoogle Scholar
  12. 12.
    Theis J, Takarics B, Pfifer H, Balas G, Werner H (2015) Modal matching for LPV model reduction of aeroservoelastic vehicles. In: AIAA science and technology forumGoogle Scholar
  13. 13.
    Zhu J, Wang Y, Pant K, Suh PM, Brenner MJ (2017) Genetic algorithm-based model order reduction of aeroservoelastic systems with consistent states. J Aircr. 10(2514/1):C034129. Google Scholar
  14. 14.
    Zhu J, Wang Y, Pant K, Suh PM, Brenner MJ (2017) Genetic algorithm-guided, adaptive model order reduction of flexible aircrafts. In: 58th AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, p 1598 (2017).
  15. 15.
    Al-Jiboory AK, Zhu G, Swei SSM, Su W, Nguyen NT (2017) LPV modeling of a flexible wing aircraft using modal alignment and adaptive gridding methods. Aerosp Sci Technol 66:92–102CrossRefGoogle Scholar
  16. 16.
    Al-jiboory A, Zhu GG, Swei SSM, Su W, Nguyen NT (2017) LPV model development for a flexible wing aircraft. Am Inst Aeronaut Astronaut. Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical EngineeringUniversity of DiyalaBaqubahIraq
  2. 2.Mechanical EngineeringMichigan State UniversityEast LansingUSA

Personalised recommendations