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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

Fig. 2
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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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Authors and Affiliations

  1. Programa de Engenharia Biomédica - Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa em Engenharia (Coppe), Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Luciano Luporini Menegaldo

  2. Instituto de Engenharias e Desenvolvimento Sustentável (IEDS), Universidade da Integração Internacional da Lusofonia Afro-Brasileira, Acarape, CE, Brazil

    Sérgio Servilha de Oliveira

  3. Programa de Engenharia de Defesa, Instituto Militar de Engenharia, Rio de Janeiro, RJ, Brazil

    Sérgio Servilha de Oliveira

  4. Departamento de Projetos da Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil

    Ronaldo Vieira Cruz

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  1. Luciano Luporini Menegaldo
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  2. Sérgio Servilha de Oliveira
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  3. Ronaldo Vieira Cruz
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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, L′u, L′w, L′v, N′u, N′w, N′v [rad/s m]

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

Moment/angular velocity: Mq, Mp, Mr, L′q, L′p, L′r, N′q, N′p, N′r [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). https://doi.org/10.1007/s40430-019-2141-9

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