Skip to main content
SpringerLink
Log in

A Simple Active Controller to Supress Helicopter Air Resonance in Hover and Forward Flight

  • Conference paper
Dynamics of Controlled Mechanical Systems

  • 238 Accesses

Summary

A coupled rotor/fuselage helicopter analysis with the important effects of blade torsional flexibility, unsteady aerodynamics, and forward flight is presented. This model is used to illustrate the effect of unsteady aerodynamics, forward flight, and torsional flexibility on air resonance. Next a nominal configuration, which experiences air resonance in forward flight, is selected. A simple multivariable compensator using conventional swashplate inputs and a single body roll rate measurement is then designed. The controller design is based on a linear estimator in conjunction with optimal feedback gains, and the design is done in the frequency domain using the Loop Transfer Recovery method. The controller is shown to suppress the air resonance instability throughout wide range helicopter loading conditions and forward flight speeds.

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

Access this chapter

Log in via an institution
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.

Abbreviations

a:

Rotor blade lift curve slope

aT :

Horizontal tail lift curve slope

AR:

Horizontal tail aspect ratio

A, B, C:

First order system, control, and output matrices

b:

Blade semi chord

CdO :

Blade drag coefficient

CdOT :

Horizontal tail drag coefficient

e:

Hinge offset

f:

Fuselage drag area = \(\mathop f\limits^-/2\mathop {bR}\limits^ - \)

FFT, GGT :

State and observation noise covariances

G(s), K(s):

System and compensator matrices

Ib :

Blade flap inertia about hinge offset

Icxx, Icyy :

Fuselage roll and pitch inertias

Jx :

Blade pitch inertia

Jy, Jz :

Integral of the blade flap and lead-lag bending inertias

Kc, Kf:

Feedback and filter gains

Kx, Ky, Kz :

Flap, lag, and torsion spring constants

l:

Blade length

lm :

Model error function

L(S):

Unstructured multiplicative error matrix

MF :

Fuselage mass

Nb :

Number of blades

Pc, Pf :

Positive semi-definite solutions to the Riccati equation

qc :

Recovery factor

Q, R:

State weight and control weight matrices

Rc :

Elastic coupling coefficient

RMX, RMY, RMZ :

Translational degrees of freedom of the fuselage

S(S), T(S):

Sensitivity and command response transfer matrices

ST :

Horizontal tail area

V:

Forward flight speed

WS, WO :

State and observation noise processes

xA :

Blade aerodynamic center offset from the blade elastic axis

xb, yb, zb :

Position of the blade center of mass from the hinge offset

XMC, ZMC :

X and Z position of the fuselage center of mass

XMH, ZMH :

X and Z position of the rotor hub center from point M

XMT, ZMT :

X and Z position of the horizontal tail a.c. from point M

x, u, y:

System state, control, and input vectors

\(\mathop x\limits^ \wedge\), ŷ:

Estimator state and output vectors

αR :

Rotor trim pitch angle

βP :

Blade precone angle

γ:

Lock number

θ0, θ1s, θ1c :

Collective, sine, and cosine inputs

θpk :

Pitch of k-th blade

σ:

Solidity ratio = 2Nbb/π

μ:

Advance ratio = \(\mathop V\limits^{\_} \,Cos(\alpha _R )/\mathop {R\Omega }\limits^{\_}\)

ψk :

K-th blade angle =ψ + (k- 1)2π/Nb

ψ:

Azimuth angle of blade measure from straight aft position

ωc :

Cross over frequency

ωL :

Inplane lead-lag frequency

ωF1, ωL1, ωT1 :

Rotating first flap, lag, and torsional blade frequencies

σ[•], \(\mathop \sigma \limits^\_\)[•]:

Mimimum and Maximum singular values

(•):

Derivative wrt to the azimuth angle

MIMO:

Multiple Input/Multiple Output

SISO:

Single input/Single output

LTR:

Loop Transfer Recovery

References

  1. Burkam, J.E., and Miao, W., “Exploration of Aeroelastic Stability Boundaries with a Soft-in-plane Hingeless Rotor Model,” Journal of the American Helicopter Society Vol. 17, No. 4, October 1972, pp. 27–35.

    Article  Google Scholar 

  2. Donham, R.E., Cardinale, S.V., and Sachs, I.B., “Ground and Air Resonance Characteristics of a Soft Inplane Rigid Rotor System,” Journal of the American Helicopter Society Vol. 14, No. 4, October 1969, pp. 33–44.

    Article  Google Scholar 

  3. Shaw, J., and Albion, N., “Active Control of the Helicopter Rotor for Vibration Reduction,” 36th Annual Forum of the American Helicopter Society, Washington D.C., May, 1980.

    Google Scholar 

  4. Wood, E.R., and Powers, R.W., “Practical Design Considerations for a Flightworthy Higher Harmonic Control system,” 36th Annual Forum of the American Helicopter Society, Washington D.C., May, 1980.

    Google Scholar 

  5. Wood, R.E., Powers, R.W., Cline, J.H., and Hammond, C.E., ”On Developing and Flight Testing a Higher Harmonic Control System,” Journal of the American Helicopter Society Vol. 30, No. 1, January, 1985, pp. 3–20.

    Google Scholar 

  6. Straub, F.K., and Warmbrodt, W., “The Use of Active Controls to Augment Rotor/Fuselage Stability,” Journal of the American Helicopter Society Vol. 30, No. 3, July, 1985, pp. 13–22.

    Article  Google Scholar 

  7. Straub, F.K., “Optimal Control of Helicopter Aeromechanical Stability,” Vertica Vol. 11, No. 3, 1987, pp. 12–22.

    Google Scholar 

  8. Young, M.I., Bailey, D.J. and Hirschbein, M.S., “Open and Closed Loop Stability of Hingeless Rotor Helicopter Air and Ground Resonance,” Paper number 20, NASA-SP 352, 1974.

    Google Scholar 

  9. Takahashi, M.D., “Active Control of Helicopter Aeromechanical and Aeroelastic Instabilities,” Ph.D. Dissertation, University of California, Los Angeles, To Be Published, 1988.

    Google Scholar 

  10. Takahashi, M.D., and Friedmann, P.P., “Active Control of Helicopter Air Resonance in Hover and Forward Flight,” AIAA paper 88–2407, Proceedings of 29-th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Fort Magruder, VA, April 18–20, 1988, pp. 1521–1532.

    Google Scholar 

  11. Greenberg, J.M., “Airfoil in Sinsoidal Motion in a Pulsating Stream,” NACA-TN 1326, 1947.

    Google Scholar 

  12. Venkatesan C., and Friedmann, P., “Aeroelasic Effects in Multi-Rotor Vehicles with Applications to a Heavy-Lift System,” NASA-CR 3822, August 1984.

    Google Scholar 

  13. Pitt, D.M., and Peters, D.A., “Theoretical Predictions of Dynamic Inflow Derivatives,” Vertica Vol. 5, 1981, pp.21–34.

    Google Scholar 

  14. Friedmann, P.P., “Formulation and Solution of Rotary-Wing Aeroelastic Stability and Response Problems” Vertica Vol. 7, No. 2, 1983, pp. 101–141.

    Google Scholar 

  15. Hohenemeser, K.H., and Yin, Shcng-Kuang, “Some Applications of the Method of Multi-Blade Coordinates” Journal of the American Helicopter Society Vol. 17, No. 4, 1972, pp.1–12.

    Google Scholar 

  16. Kwakernaak, H., and Sivan, R., Linear Optimal Control Systems John Wiley & Sons inc., New York, 1972, Chapters 3 and 5.

    MATH  Google Scholar 

  17. Horowitz, I.M., and Shaked, U., “Superiority of Transfer Function Over State-Variable Methods in Linear Time-Invariant Feedback System Design,” IEEE Transactions on Automatic Control, Vol. AC-20, No. 1, February, 1975, pp. 84–97.

    Article  Google Scholar 

  18. Doyle, J.C., and Stein, G., “Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis,” IEEE Transactions on Automatic Control, Vol. AC-26, No. 1, February 1981, pp. 4–16.

    Article  Google Scholar 

  19. Safonov, M.G., Laub, A.J., and Hartmann, G.L., “Feedback Properties of Multivariable Systems: The Role and Use of the Return Difference Matrix,” IEEE Transactions on Automatic Control, Vol. AC-26, No. 1, February, 1981, pp. 47–65.

    Article  MathSciNet  Google Scholar 

  20. Stein, G., “The LQG/LTR Procedure for Multivariable Feedback Control Design,” IEEE Transactions on Automatic Control, Vol. AC-32, No. 2, February 1987, pp. 105–114.

    Article  Google Scholar 

  21. Madiwale, A., and Williams, D.E., “Some Extensions of Loop Transfer Recovery,” Proceedings of the American Control Conference, Vol. 2, 1985, pp.790–795.

    Google Scholar 

  22. Johnson, W., Helicopter Theory Princeton University Press, 1980.

    Google Scholar 

  23. Takahashi, M.D., and Friedmann, P.P., “Design of a Simple Active Controller to Suppress Helicopter Air Resonance,” Proceedings of 44-th Annual Forum of the American Helicopter Society, Washington D.C., June 16–18, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical, Aerospace, and Nuclear Engineering Department, University of California, Los Angeles, California, USA

    P. P. Friedmann & M. D. Takahashi

Authors
  1. P. P. Friedmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. D. Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mechanics, ETH-Zentrum, CH-8092, Zurich, Switzerland

    G. Schweitzer

  2. Institute of Automatic Control, ETH-Zentrum, CH-8092, Zurich, Switzerland

    M. Mansour

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Friedmann, P.P., Takahashi, M.D. (1989). A Simple Active Controller to Supress Helicopter Air Resonance in Hover and Forward Flight. In: Schweitzer, G., Mansour, M. (eds) Dynamics of Controlled Mechanical Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83581-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-83581-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83583-4

  • Online ISBN: 978-3-642-83581-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation