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Robust control synthesis using coefficient diagram method and µ-analysis: an aerospace example

  • Seid Farhad Abtahi
  • Ehsan Azadi YazdiEmail author
Article
  • 27 Downloads

Abstract

This paper develops a structured controller synthesis method which satisfies robust stability and robust performance. In the proposed method (µ-CDM), coefficient diagram method (CDM) is employed to synthesize a structured controller and µ-analysis is used to evaluate the robustness of the controller. A supervisory particle swarm optimization utilizes the CDM and µ-analysis in an iterative manner in order to reach an optimal robustness bound. To evaluate the performance of the proposed method, it has been used to synthesize a robust autopilot for an aerospace system. Numerical simulations confirm the feasibility of µ-CDM and show the acceptable closed-loop performance in presence of various model uncertainties. The performance of the proposed controller is compared with that of a conventional CDM controller and a D–K iterations controller.

Keywords

Robust control µ-Analysis Uncertain systems Coefficient diagram method Autopilot 

References

  1. 1.
    Skogestad S, Postlethwaite I (2007) Multivariable feedback control: analysis and design. Wiley, New YorkzbMATHGoogle Scholar
  2. 2.
    Athans M (1971) The role and use of the stochastic linear-quadratic-Gaussian problem in control system design. IEEE Trans Autom Control 16(6):529–552MathSciNetCrossRefGoogle Scholar
  3. 3.
    Perruquetti W, Barbot JP (2002) Sliding mode control in engineering. CRC Press, New YorkCrossRefGoogle Scholar
  4. 4.
    Ogata K (2002) Modern control engineering. Prentice Hall, New DelhizbMATHGoogle Scholar
  5. 5.
    Zames G (1981) Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans Autom Control 26(2):301–320MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Glover K, Doyle JC (1988) State-space formulae for all stabilizing controllers that satisfy an H-norm bound and relations to relations to risk sensitivity. Syst Control Lett 11(3):167–172CrossRefzbMATHGoogle Scholar
  7. 7.
    Doyle JC, Glover K, Khargonekar PP, Francis BA (1989) State-space solutions to standard H2 and H control problems. IEEE Trans Autom Control 34(8):831–847CrossRefzbMATHGoogle Scholar
  8. 8.
    Reichert RT (1990) Robust autopilot design using μ-synthesis. In: American control conference, pp 2368–2373Google Scholar
  9. 9.
    Doyle JC (1985) Structured uncertainty in control system design. In: 24th IEEE conference on decision and control, vol 24, pp 260–265Google Scholar
  10. 10.
    Shi K, Tang Y, Liu X, Zhong S (2017) Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation. ISA Trans 1(66):185–199CrossRefGoogle Scholar
  11. 11.
    Shi K, Tang Y, Zhong S, Yin C, Huang X, Wang W (2018) Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process. Int J Robust Nonlinear Control 28(5):1693–1714MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Manabe S (1998) Coefficient diagram method. In: The 14th IFAC symposium on automatic control in aerospaceGoogle Scholar
  13. 13.
    Manabe S (2002) Application of coefficient diagram method to MIMO design in aerospace. In: The 15th triennial world congress, Barcelona, Spain, IFAC proceedings volumes, vol 35(1), pp 43–48Google Scholar
  14. 14.
    Cahyadi AI, Isarakorn D, Benjanarasuth T, Ngamwiwit J, Komine N (2004) Application of coefficient diagram method for rotational inverted pendulum control. In: Control, automation, robotics and vision conference, vol 3, pp 1769–1773Google Scholar
  15. 15.
    Hamamci SE (2004) Simple polynomial controller design by the coefficient diagram method. WSEAS Trans Circuits Syst 3(4):951–956Google Scholar
  16. 16.
    Ocal O, Bir A, Tibken B (2009) Digital design of coefficient diagram method. In: American control conference. ACC’09, pp 2849–2854Google Scholar
  17. 17.
    Manabe S (2016) The design of PID control by coefficient diagram method. In: The 26th workshop on JAXA astrodynamics and flight mechanicsGoogle Scholar
  18. 18.
    Kennedy J (2011) Particle swarm optimization. Encyclopedia of machine learning. Springer, New York, pp 760–766Google Scholar
  19. 19.
    Das S, Abraham A, Konar A (2008) Particle swarm optimization and differential evolution algorithms: technical analysis, applications and hybridization perspectives. In: Liu Y, Sun A, Loh HT, Lu WF, Lim EP (eds) Advances of computational intelligence in industrial systems. Springer, Berlin, pp 1–38Google Scholar
  20. 20.
    Jackson PB (2010) Overview of missile flight control systems. Johns Hopkins APL Tech Dig 29(1):9–24Google Scholar
  21. 21.
    Chowdhury A, Das S (2013) Analysis and design of missile two loop autopilot. Adv Electron Electr Eng 3:959–964Google Scholar
  22. 22.
    Bhowmick P, Das G (2012) Modified design of three loop lateral missile autopilot based on LQR and reduced order observer (DGO). Int J Eng Res Dev 6(2):01–07Google Scholar
  23. 23.
    Budiyono A, Rachman H (2011) Proportional guidance and CDM control synthesis for a short-range homing surface-to-air missile. J Aerosp Eng 25(2):168–177CrossRefGoogle Scholar
  24. 24.
    Xin M, Balakrishnan SN, Stansbery DT, Ohlmeyer EJ (2004) Nonlinear missile autopilot design with theta-D technique. J Guid Control Dyn 27(3):406–417CrossRefGoogle Scholar
  25. 25.
    Zheng D, Lin D, Xu X, Tian S (2017) Dynamic stability of rolling missile with proportional navigation and PI autopilot considering parasitic radome loop. Aerosp Sci Technol 67:41–48CrossRefGoogle Scholar
  26. 26.
    Lhachemi H, Saussié D, Zhu G (2016) Handling hidden coupling terms in gain-scheduling control design: application to a pitch-axis missile autopilot. In AIAA guidance, navigation, and control conference, p 365Google Scholar
  27. 27.
    Urban TJ (1991) Synthesis of missile autopilots robust to the presence of parametric variations. Doctoral dissertation, Massachusetts Institute of TechnologyGoogle Scholar
  28. 28.
    Shamma JS, Cloutier JR (1993) Gain-scheduled missile autopilot design using linear parameter varying transformations. J Guid Control Dyn 16(2):256–263CrossRefGoogle Scholar
  29. 29.
    Reichert RT (1992) Dynamic scheduling of modern-robust-control autopilot designs for missiles. IEEE Control Syst 12(5):35–42CrossRefGoogle Scholar
  30. 30.
    Shao-ming H, De-fu L (2014) Missile two-loop acceleration autopilot design based on L1 adaptive output feedback control. Int J Aeronaut Space Sci 15(1):74–81CrossRefGoogle Scholar
  31. 31.
    Ebli HG, Khani A, Azizi A (2013) Gain scheduling controller for missile flight control problem by applying LQR. J World’s Electr Eng Technol 2:17–21Google Scholar
  32. 32.
    Nichols RA, Reichert RT, Rugh WJ (1993) Gain scheduling for H-infinity controllers: a flight control example. IEEE Trans Control Syst Technol 1(2):69–79CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShiraz UniversityShirazIran

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