Skip to main content
Log in

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

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

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.

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

Similar content being viewed by others

References

  1. Skogestad S, Postlethwaite I (2007) Multivariable feedback control: analysis and design. Wiley, New York

    MATH  Google Scholar 

  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):529–552

    Article  MathSciNet  Google Scholar 

  3. Perruquetti W, Barbot JP (2002) Sliding mode control in engineering. CRC Press, New York

    Book  Google Scholar 

  4. Ogata K (2002) Modern control engineering. Prentice Hall, New Delhi

    MATH  Google Scholar 

  5. Zames G (1981) Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans Autom Control 26(2):301–320

    Article  MathSciNet  MATH  Google Scholar 

  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):167–172

    Article  MATH  Google Scholar 

  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):831–847

    Article  MATH  Google Scholar 

  8. Reichert RT (1990) Robust autopilot design using μ-synthesis. In: American control conference, pp 2368–2373

  9. Doyle JC (1985) Structured uncertainty in control system design. In: 24th IEEE conference on decision and control, vol 24, pp 260–265

  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):185–199

    Article  Google Scholar 

  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):1693–1714

    Article  MathSciNet  MATH  Google Scholar 

  12. Manabe S (1998) Coefficient diagram method. In: The 14th IFAC symposium on automatic control in aerospace

  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 43–48

  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 1769–1773

  15. Hamamci SE (2004) Simple polynomial controller design by the coefficient diagram method. WSEAS Trans Circuits Syst 3(4):951–956

    Google Scholar 

  16. Ocal O, Bir A, Tibken B (2009) Digital design of coefficient diagram method. In: American control conference. ACC’09, pp 2849–2854

  17. Manabe S (2016) The design of PID control by coefficient diagram method. In: The 26th workshop on JAXA astrodynamics and flight mechanics

  18. Kennedy J (2011) Particle swarm optimization. Encyclopedia of machine learning. Springer, New York, pp 760–766

    Google Scholar 

  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 1–38

    Google Scholar 

  20. Jackson PB (2010) Overview of missile flight control systems. Johns Hopkins APL Tech Dig 29(1):9–24

    Google Scholar 

  21. Chowdhury A, Das S (2013) Analysis and design of missile two loop autopilot. Adv Electron Electr Eng 3:959–964

    Google Scholar 

  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):01–07

    Google Scholar 

  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):168–177

    Article  Google Scholar 

  24. Xin M, Balakrishnan SN, Stansbery DT, Ohlmeyer EJ (2004) Nonlinear missile autopilot design with theta-D technique. J Guid Control Dyn 27(3):406–417

    Article  Google Scholar 

  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 67:41–48

    Article  Google Scholar 

  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 365

  27. Urban TJ (1991) Synthesis of missile autopilots robust to the presence of parametric variations. Doctoral dissertation, Massachusetts Institute of Technology

  28. Shamma JS, Cloutier JR (1993) Gain-scheduled missile autopilot design using linear parameter varying transformations. J Guid Control Dyn 16(2):256–263

    Article  Google Scholar 

  29. Reichert RT (1992) Dynamic scheduling of modern-robust-control autopilot designs for missiles. IEEE Control Syst 12(5):35–42

    Article  Google Scholar 

  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):74–81

    Article  Google Scholar 

  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 2:17–21

    Google Scholar 

  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):69–79

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ehsan Azadi Yazdi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abtahi, S.F., Azadi Yazdi, E. Robust control synthesis using coefficient diagram method and µ-analysis: an aerospace example. Int. J. Dynam. Control 7, 595–606 (2019). https://doi.org/10.1007/s40435-018-0462-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-018-0462-7

Keywords

Navigation