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Helicopter stability and control derivatives identification in different flight conditions

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Abstract

Helicopter flight simulators require high-fidelity dynamic models based on a set of stability and control derivatives (SCDs). For different flight conditions, specific sets of SCDs must be identified and utilized in the flight simulator software. In this study, nine sets of SCDs of the AS 355 F2 helicopter have been estimated from experimental flight-testing data, considering different combinations of velocity, mass, and altitude. Linear dynamic models with eight states and four controls were determined for the different flight conditions, using the output-error method. The associated optimization problem was solved with the Gauss–Newton algorithm, and identification reliability was evaluated by the Cramer–Rao (CR) and relative correlation coefficient (RCC) indices. An instrumented AS 355 F2 Helicopter belonging to the Instituto de Pesquisas e Ensaios em Voo, Departamento de Ciência e Tecnologia Aeroespacial, São José dos Campos, Brazil, was utilized for data collection in different flight conditions, totaling 16 test hours. The following natural dynamic modes have been excited: phugoid, short period, spiral and Dutch roll, by command inputs of the type: frequency sweep (sinusoidal), doublet pulse and 3-2-1-1. Considering CR and RCC criteria, the most appropriate maneuver for exciting each dynamic mode is suggested, and the sets of the nine flight conditions are SCDs reported.

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Fig. 1

Adapted from http://www.wikihow.com/Draw-a-Helicopter

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References

  1. 1.

    Lee C, Kang S, Kang SG, Kim KH, Kim KI (2016) Development of key functions for flight simulator. Int J Control Autom 9(1):347–358

  2. 2.

    Code of Federal Regulations—Part 14 Aeronautic and Space, E. U. A., “Federal Administration Regulations, Chapter 60. (FAR 60)—Qualification Performance Standards for Helicopter Full Flight Simulators”, National Archives and Records Administration, Washington DC, E. U. A., 2009

  3. 3.

    Code of Federal Regulations—Part 14 Aeronautic and Space, E. U. A., “Federal Administration Regulations, Chapter 27. (FAR 27)—Airworthiness Standards: Normal Category Rotorcraft”, National Archives and Records Administration, Washington DC, E. U. A., 2009

  4. 4.

    Code of Federal Regulations—Part 14 Aeronautic and Space, E. U. A., “Federal Administration Regulations, Chapter 29. (FAR 29)—Airworthiness Standards: Transport Category Rotorcraft”, National Archives and Records Administration, Washington DC, E. U. A., 2009

  5. 5.

    Bauchau OA, Bottasso CL, Nikishkov YG (2001) Modeling rotorcraft dynamics with finite element multibody procedures. Math Comput Model 33(10):1113–1137

  6. 6.

    Brown Richard E (2000) Rotor wake modeling for flight dynamic simulation of helicopters. AIAA J 38(1):57–63

  7. 7.

    Tishler M, e Remple R (2006) Aircraft and rotorcraft system identification: engineering methods—with flight test examples. American Institute of Aeronautics and Astronautics Inc., pp 330-340. Reston VA, E.U.A

  8. 8.

    Cooke AK, e Fitzpatrick EWH (2002) Helicopter test and evaluation. American Institute of Aeronautics and Astronautics Inc., pp 330-340. Reston VA, E.U.A

  9. 9.

    Padfield GD (2007) Helicopter flight dynamics: the theory and application of flying qualities and simulation modelling, 2nd edn. Blackwell Science, Oxford, pp 185–281

  10. 10.

    Fletcher Jay W (1995) Identification of UH-60 stability derivative models in hover from flight test data. J Am Helicopter Soc 40(1):32–46

  11. 11.

    Hamel PG, Jategaonkar RV (1996) Evolution of flight vehicle system identification. J Aircr 33(1):9–28

  12. 12.

    Jategaonkar RV (2006) Flight vehicle system identification: a time domain methodology. American Institute of Aeronautics and Astronautics Inc., Progress in Astronautics and Aeronautics, Reston VA, USA, pp 59–129

  13. 13.

    Cruz RV, Góes LCS (2010) Results of short-period helicopter system identification using output-error and hybrid search-gradient optimization algorithm. Math Probl Eng 2010:17. https://doi.org/10.1155/2010/231594

  14. 14.

    Cruz RV, Góes LCS, de Andrade D (2009) Results of lateral-directional helicopter system identification using output-error and both genetic and Levenberg-Marquardt optimization algorithms. Brazilian Symposium on Aerospace Eng. & Applications, by Agência Aeroespacial Brasileira –AAB, São José dos Campos, Brasil

  15. 15.

    Cruz RV (2009) Desenvolvimento de um Modelo Dinâmico para Simuladores de Helicópteros. Ph.D. dissertation, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brasil

  16. 16.

    Sumida IY, de Campos Velho HF, Luz EF, Cruz RV, Góes LCS (2017) MPCA for flight dynamics parameters determination. Comput Assist Methods Eng Sci 21(3/4):257–265

  17. 17.

    Oliveira SS (2012) Validação e Ampliação de Resultados da Metodologia Quad-M/CTA na Determinação das Derivadas de Estabilidade e Controle em Voo de Helicópteros, Ph.D. Dissertation in Defense Engineering, Instituto Militar de Engenharia, Rio de Janeiro, RJ, Brasil

  18. 18.

    Maine RE, Iliff KW (1981) Theory and practice of estimating the accuracy of dynamic flight-determined coefficients. NASA RP 1077

  19. 19.

    Hefley RK et al. (1979) A Compilation and analysis of helicopter handling qualities data volume one. National Aeronautics and Space Administration, NASA Contractor Report 3144, Houston, TX, E.U.A

Download references

Acknowledgments

We acknowledge the “Instituto De Pesquisas E Ensaios Em Voo” (IPEV) from the “Departamento de Ciência e Tecnologia Aeroespacial” (DCTA), São José dos Campos, Brazil, for flight data collection, and Brazilian Army for logistic and financial support. The author L.L. Menegaldo holds a Productivity Scholarship from CNPq (Proc. 302181/2018-0).

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Correspondence to Luciano Luporini Menegaldo.

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Appendix: stability and control derivatives for several flight conditions: velocity, mass, altitude, according to Table 2 Cases. Aircraft: AS 355-F2 helicopter. Level and straight flight

Appendix: stability and control derivatives for several flight conditions: velocity, mass, altitude, according to Table 2 Cases. Aircraft: AS 355-F2 helicopter. Level and straight flight

Physical unities for all tables (similar to [ 9 ]):

Force/translational velocity: Xu, Xw, Xv, Zu, Zw, Zv, Yu, Yw, Yv [1/s]

Moment/translational velocity: Mu, Mw, Mv, Lu, Lw, Lv, Nu, Nw, Nv [rad/s m]

Force/angular velocity: Xq, Xp, Xr, Zq, Zp, Zr, Yq, Yp, Yr [m/s rad]

Moment/angular velocity: Mq, Mp, Mr, Lq, Lp, Lr, Nq, Np, Nr [1/s]

Force/control: Xδc, Xδb, Xδa, Zδp, Zδc, Zδb, Zδa, Xδp, Xδc, Xδb, Xδa, Xδp (m/s2 rad)

Moment/control: Mδc, Mδb, Mδa, Mδp, L′δc, L′δb, L′a, L′δp, N′δc, N′δb, N′δa, N′δp (1/s2)

Case 1. 60 kt; 4.000 ft; 2200 kg

  u w q v p r
X − 0.02494 0.02056 0.33652 0.00278 0.06924 − 0.01219
Z − 0.06034 − 0.77379 21.25270 0.00356 − 0.02024 0.15582
M 0.02463 0.01364 − 2.05335 − 0.00092 − 0.26629 0.00635
Y − 0.00039 − 0.00626 0.07037 − 0.10843 − 0.45026 − 21.3275
L − 0.02991 0.03218 0.78405 − 0.15219 − 6.49507 0.18923
N − 0.01004 0.00051 0.05867 0.06544 − 0.66007 − 0.78195
  δc δb δa δp
X 0.48910 − 6.13237 1.05309 − 0.00315
Z − 71.58945 − 14.93226 0.08410 0.00076
M 3.71686 14.10604 − 4.21761 0.00454
Y − 0.72276 − 0.82412 1.44827 3.38374
L 4.48838 − 15.18504 − 38.99614 3.06690
N 1.74749 − 2.65286 − 8.55004 − 7.62205

Case 2. 80 kt; 4.000 ft; 2200 kg

  u W q v p r
X − 0.03118 0.01893 0.75314 0.00237 0.06987 − 0.01405
Z − 0.02634 − 0.84942 28.31778 0.00540 − 0.05870 0.15454
M 0.02280 0.00745 − 2.11812 − 0.00103 − 0.26629 0.00684
Y 0.00029 − 0.00825 0.05466 − 0.13163 − 0.76420 − 28.64937
L − 0.02814 0.01804 0.79890 − 0.15609 − 6.42133 0.18598
N − 0.00830 0.00063 0.09898 0.07277 − 0.65911 − 0.84480
  δc δb δa δp
X − 0.13259 − 6.08823 1.05328 − 0.00344
Z − 78.56980 − 22.11513 0.08411 − 0.00008
M 5.69789 14.27670 − 4.25491 0.00472
Y − 0.98364 − 0.90009 1.30901 3.80328
L 2.77426 − 15.10829 − 39.09486 3.37946
N 1.77364 − 2.42892 − 8.37135 − 8.53255

Case 3. 100 kt; 4.000 ft; 2200 kg

  u w Q v p r
X − 0.03771 0.01722 1.45377 0.00269 0.06277 − 0.01573
Z − 0.00812 − 0.90715 35.43191 0.00453 − 0.06150 0.16902
M 0.02501 0.01250 − 2.18671 − 0.00100 − 0.27743 0.00965
Y 0.00157 − 0.01041 0.06188 − 0.15513 − 1.52085 − 36.0125
L − 0.02401 0.00498 0.81909 − 0.15993 − 6.35180 0.22345
N − 0.00910 0.00485 0.06016 0.07551 − 0.64914 − 0.95196
  δc δb δa δp
X − 0.81433 − 6.12640 1.06615 − 0.00393
Z − 84.71469 − 28.38774 0.01043 0.00122
M 7.35920 14.62176 − 4.32446 0.00677
Y − 1.22871 − 1.00480 1.28747 4.14470
L 1.17878 − 15.42161 − 39.3769 3.71142
N 2.02035 − 2.18805 − 8.27515 − 9.24600

Case 4. 60 kt; 10.000 ft; 2200 kg

  u w q v p r
X − 0.02351 0.01181 0.43597 − 0.00025 0.06688 − 0.01098
Z 0.04170 − 0.54095 24.34855 0.00295 − 0.0131 0.15771
M 0.02556 0.00434 − 2.07377 − 0.00129 − 0.2654 0.00267
Y − 0.00004 − 0.00268 0.06622 − 0.08497 − 0.5398 − 14.96937
L − 0.05650 0.01931 0.71046 − 0.14580 − 8.1179 0.10640
N − 0.01123 0.00041 − 0.24156 0.04900 − 1.2017 − 0.62302
  δc δb δa δp
X 0.27206 − 6.87217 1.05309 − 0.00329
Z − 50.93934 − 10.75547 − 0.08410 0.00068
M 9.48179 14.55842 − 642.2810 0.00462
Y − 0.41408 − 0.76918 3.06741 2.50090
L − 3.43642 − 13.74342 − 5.66990 2.26168
N 2.16426 − 2.31245 − 0.96222 5.63151

Case 5. 100 kt; 10.000 ft; 2200 kg

  u w q v p r
X − 0.03119 0.00862 1.99917 0.00184 − 0.0702 − 0.01491
Z − 0.00500 − 0.61305 40.96593 0.00319 − 0.0370 0.16254
M 0.02230 0.00430 − 2.12684 − 0.00180 − 0.2781 0.00987
Y 0.00124 − 0.00689 0.05803 − 0.11949 − 1.8034 − 25.85601
L − 0.01384 0.00344 0.74116 − 0.15255 − 7.8911 0.13888
N − 0.00029 0.00393 0.01255 0.05420 − 1.2109 − 0.75500
  δc δb δa δp
X − 0.35478 − 8.83193 1.06615 − 0.00481
Z − 57.39188 − 19.62293 0.00092 0.00042
M − 9.53351 15.97643 − 5.04520 − 0.12322
Y − 0.89434 − 0.80384 1.29460 3.09740
L 0.73108 − 12.54973 − 39.5514 2.79122
N 2.32535 − 2.01817 − 8.27515 − 6.89510

Case 6. 60 kt; 4.000 ft; 1.900 kg

  u w q v p r
X − 0.02964 0.02922 0.33942 0.00519 0.0778 − 0.01284
Z − 0.18740 − 0.95979 28.35418 0.00411 − 0.0244 0.15342
M 0.02161 0.01938 − 1.89670 − 0.00067 − 0.2466 0.00650
Y − 0.00081 − 0.01029 0.08214 − 0.13058 − 0.4540 − 26.68132
L − 0.00665 0.04070 0.81426 − 0.10804 − 5.6014 0.16995
N − 0.00670 0.00045 0.34824 0.07371 − 0.5688 − 0.82492
  δc δb δa δp
X 0.72652 − 5.41703 0.46073 − 0.00367
Z − 88.39322 − 18.39379 − 0.22426 0.00025
M − 2.19978 11.16557 − 1.20503 0.00412
Y − 1.09167 − 1.05762 1.45654 4.18119
L 8.48584 − 16.72277 − 34.1260 2.80825
N 1.47034 − 2.40636 − 8.22014 − 8.14509

Case 7. 100 kt; 4.000 ft; 1.900 kg

  u w q v p r
X − 0.0471 0.02538 1.41825 0.00385 0.06548 − 0.01717
Z − 0.0116 − 1.12440 44.44071 0.00594 − 0.0758 0.17511
M 0.02395 0.01720 − 2.05854 − 0.00050 − 0.2434 0.00881
Y 0.00248 − 0.01511 0.07376 − 0.18846 − 1.4751 − 45.0521
L − 0.0358 0.00590 0.89722 − 0.10307 − 5.2586 0.19904
N − 0.0120 0.00342 0.11917 0.08218 − 0.6516 − 1.00884
  δc δb δa δp
X − 1.26138 − 3.43005 1.11461 − 0.00455
Z − 104.70699 − 34.98466 0.01626 0.00137
M 20.73957 10.90181 − 3.60372 0.01354
Y − 1.83702 − 1.37126 1.28984 5.10994
L 1.52408 − 17.58536 − 34.2651 3.39496
N 2.11063 − 1.52212 − 7.67475 − 9.86473

Case 8. 60 kt; 4.000 ft; 2.500 kg

  u w q v p r
X − 0.02341 0.01824 0.33726 0.00139 0.06231 − 0.01301
Z − 0.02894 − 0.63798 16.67792 0.00329 − 0.0174 0.15470
M 0.02788 0.00744 − 2.18762 − 0.00123 − 0.2889 0.00616
Y − 0.00019 − 0.00391 0.06165 − 0.09348 − 0.4471 − 17.56793
L − 0.04542 0.02526 0.77412 -0.19605 − 7.3154 0.20403
N − 0.01285 0.00055 0.12694 0.06167 − 0.7326 − 0.73745
  δc δb δa δp
X 0.44019 − 6.34636 1.11891 − 0.00315
Z − 59.47065 − 12.54363 − 0.04205 0.00040
M 8.79910 17.10820 − 4.82012 0.00462
Y − 0.45925 − 0.81038 1.45929 2.83956
L 0.98183 − 15.95390 − 44.1683 3.26243
N 2.06271 − 2.89937 − 9.64973 − 7.12882

Case 9. 100 kt; 4.000 ft; 2.500 kg

  u w q v p r
X − 0.03361 0.01372 1.49574 0.00222 0.05728 − 0.01607
Z − 0.00673 − 0.74053 30.95279 0.00372 − 0.0502 0.16298
M 0.02576 0.00711 − 2.27746 − 0.00140 − 0.3061 0.01021
Y 0.00124 − 0.00795 0.05399 − 0.13256 − 1.5422 − 29.73850
L − 0.01872 0.00438 0.79280 − 0.21543 − 7.3312 0.24305
N − 0.00440 0.00567 0.04609 0.06810 − 0.6867 − 0.89557
  δc δb δa δp
X − 0.62801 − 7.17193 0.77538 − 0.00370
Z − 69.32814 − 23.52980 − 0.00982 0.00049
M − 5.93754 18.47073 − 5.76595 − 0.00271
Y − 1.11591 − 0.85704 1.24701 3.48683
L 0.98589 − 14.87084 − 44.4540 3.96079
N 2.13747 − 2.60935 − 9.34544 − 8.66732

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Menegaldo, L.L., de Oliveira, S.S. & Cruz, R.V. Helicopter stability and control derivatives identification in different flight conditions. J Braz. Soc. Mech. Sci. Eng. 42, 56 (2020) doi:10.1007/s40430-019-2141-9

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Keywords

  • Helicopters
  • Flight-test
  • System identification
  • Flight dynamics
  • Stability and control derivatives