Advanced Techniques for Clearance of Flight Control Laws

Lecture Notesin Control and Information Sciences......Page 2
Advanced Techniquesfor Clearanceof Flight Control Laws......Page 4
Table of Contents......Page 7
1.1.1 Project Background......Page 10
1.1.2 Flight Control Systems......Page 11
1.1.3 The Clearance Process and Potential Improvements......Page 12
1.2.1 Project Organisation......Page 14
1.2.2 The HIRM+ Analysis Challenge......Page 15
1.2.3 Other Project Activities......Page 16
1.3 Objectives and Structure of This Book......Page 17
2.2 Steps of the Analysis Process......Page 19
2.3.2 Linear Model......Page 21
2.3.4 Inclusion of Uncertainties in the Model......Page 22
2.3.5 Type and E!ect of Uncertainties......Page 24
2.4.1 Stability Analysis......Page 31
2.4.2 Handling Analysis......Page 32
2.4.3 Nonlinear Analysis......Page 33
2.5.1 Methods......Page 36
2.5.2 Software Tools and Visualisation......Page 37
2.6 Conclusions......Page 39
3.1 Introduction......Page 40
3.2 Computation of µ......Page 44
3.2.2 Computation of Real µ......Page 45
3.3 µ-Tools for Clearance of Stability Margin Criterion......Page 47
3.4 µ-Tools for the Worst Case Eigenvalue Criterion......Page 51
3.6 Conclusions......Page 55
4.2 The e-Margin, a Generalised Stability Margin......Page 59
4.3.1 The Effect of Weighting the ²-Margin
......Page 61
4.3.2 Selecting Weights for Gain/Phase Stability Analysis......Page 62
4.4.1 Definitions......Page 66
4.4.3 Frequency-Wise Computation of the v-Gap......Page 67
4.4.4 Visualising the v-Gap Metric......Page 68
4.4.5 The Weighted v-Gap Metric......Page 69
4.5 An Approximation of the v-Gap......Page 70
4.6 Linearising the Approximation of the v-Gap for Parametric Uncertainty......Page 71
4.7 Illustration of the Parametric Uncertainty Approximation......Page 73
4.8.1 Approximate Lower Bound on the Worst-Case Stability Margin......Page 74
4.8.3 A Polynomial-Time Approach Using º-Gap Information......Page 76
5.1 An Overview of Polynomial-Based Methods......Page 78
5.2 D-Stability Problem Statement......Page 80
5.3 The Proposed Algorithm......Page 82
5.4 An Example......Page 85
5.5 Conclusions......Page 87
6.1 Background to Bifurcation Methods......Page 90
6.2 Application of Bifurcation Analysis......Page 92
6.2.1 Visualisation of Results......Page 93
6.2.2 Types of Elementary Bifurcation......Page 94
6.3 Conventional Bifurcation Analysis Implementation......Page 96
6.4 Application to Control Law Clearance......Page 97
6.5 Description of the Analysis Cycle......Page 99
6.6 Assumptions Implicit in the Analysis Cycle......Page 103
6.7 Conclusions and Recommendations......Page 105
6.8 Acknowledgements......Page 106
7.1 Classical versus Optimisation-Based Approach......Page 108
7.2 Description of the Analysis Cycle......Page 111
7.3 Optimisation Algorithms Suitable for Clearance......Page 113
7.3.1 Gradient-Based Local Search Methods......Page 114
7.3.2 Gradient-Free Local Search Methods......Page 115
7.3.3 Global Search Methods......Page 116
7.4 Conclusions......Page 117
8.1 Introduction......Page 119
8.2 The HIRM+ Object Model......Page 121
8.2.1 Mass Characteristics and Geometric Data......Page 123
8.2.2 Aerodynamics......Page 125
8.2.3 Engine Dynamics......Page 127
8.2.4 Actuator Dynamics......Page 128
8.2.5 Sensor Dynamics......Page 129
8.3 Automated Model Generation for Parametric Time Simulations and Trim Computations......Page 130
8.4 Flight Conditions and Envelope Limits......Page 132
8.4.1 Load Factor Limits......Page 133
8.4.2 Control Surface Deflection Limits......Page 134
9.1 Introduction......Page 138
9.3 Trimming the RIDE Control Laws......Page 139
9.4 Dynamic Pressure Scheduler Implementation......Page 141
9.5 Linearisation of the HIRM+RIDE......Page 145
9.6 Verification of the Linearised Model......Page 146
10.1 Introduction......Page 148
10.2 Flight Envelope and Model Uncertainties......Page 149
10.3 Stability Margin Criterion (Class I)......Page 152
10.4 Unstable Eigenvalues Criterion (Class I)......Page 155
10.5 Average Phase Rate and Absolute Amplitude Criteria (Class II)......Page 157
10.6 AoA/nz-Limit Exceedance Criteria (Class IV)......Page 160
11.1 Introduction......Page 163
11.2.1 Definition of LFTs......Page 164
11.2.3 Special Cases......Page 166
11.2.4 Star Product and Feedback......Page 168
11.2.5 Normalization......Page 169
11.3.1 From State-Space Realization to Input/Output Realization......Page 170
11.3.2 Object-Oriented Realization......Page 171
11.3.3 Morton’s Approach......Page 173
11.3.4 Tree Decomposition......Page 175
11.4.1 Minimality and Similarity Transformation......Page 177
11.4.2 The 1–D Approach......Page 180
11.4.3 The n–D Approach......Page 181
11.4.4 Interpolation and Other Approximations......Page 182
11.4.5 Analytical Approaches to LFT Modelling......Page 184
11.5.1 Min-Max Method......Page 185
11.6 Simulink Model Based LFT Generation......Page 186
11.7 Conclusion......Page 187
12.1 Introduction......Page 190
12.2 Construction of the Symbolic Nonlinear Flight Dynamics Model......Page 194
12.2.1 Derivation of Nonlinear Equations......Page 195
12.2.2 Fitting of Aerodynamic Tables and Tuning of the Model......Page 196
12.3 From PUM to LFT......Page 199
12.4 Robustness Analysis......Page 200
12.5 Conclusions......Page 202
13.1 Introduction......Page 204
13.2.1 Uncertainty Modelling......Page 205
13.2.2 Trends and Bands Based Uncertainty Modelling......Page 207
13.2.3 Nonlinearity Compensation......Page 208
13.2.4 Number of Data Points Required......Page 211
13.3 Conclusions......Page 212
Introduction......Page 214
The Simplified Aerodynamic Model......Page 215
Definition: Flat Outputs [5]......Page 219
Nominal Dynamic Feedback......Page 220
Flatness of Simplified HIRM+ Longitudinal Model......Page 221
Flatness of the RIDE Controller......Page 222
Flatness of HIRM+RIDE......Page 224
Path Planning......Page 225
Definitions......Page 226
HIRM+ Perturbed Flat Model......Page 228
Introduction......Page 229
Transformation of a State-Space Model to a LFT......Page 230
Academic Example......Page 231
LFT Model of Perturbed HIRM+ Longitudinal Model......Page 233
Conclusions......Page 235
15.1 Introduction......Page 237
15.3 Initial Considerations......Page 238
15.5 Linear Stability Analysis......Page 239
15.6 Pilot In-the-Loop Oscillation (PIO) Analysis......Page 244
15.7 Nonlinear Response Analysis......Page 247
15.8 Conclusions......Page 250
16.1 Introduction......Page 254
16.2.1 Unaccelerated g-Trim......Page 255
16.2.2 Pullup-Pushover-a-Trim......Page 260
16.2.3 Pullup-Pushover-nz-Trim......Page 263
16.3.2 Pullup-Pushover-g-Trim......Page 265
16.4 A Note on LFT Modelling......Page 269
16.5 Comparison with the Baseline Analysis......Page 271
16.6 Conclusions......Page 272
17.1 Introduction......Page 274
17.2 Model Definition and Flight Conditions......Page 275
17.3.1 Lateral HIRM+ Dynamics......Page 276
17.3.2 Longitudinal HIRM+ Dynamics......Page 277
17.4 Approximations of Nichols Plot Exclusion Zones......Page 278
17.5 Robust Stability Analysis......Page 280
17.5.1 Trends versus No Trends......Page 281
17.5.2 Validation of LFTs......Page 282
17.5.3 Robust Stability with Reduced AoA-Intervals......Page 283
17.5.4 Investigation of Parametric Interdependency......Page 284
17.5.5 Mach Number and Altitude as Variabilities......Page 286
17.5.6 Optimisation Based Skew µ......Page 287
17.6.1 Differential Tailplanes
......Page 289
17.6.4 Symmetrical Tailplanes......Page 290
17.6.5 Comparison of Single-loop and Multi-loop Analysis......Page 295
17.7.2 Continuous Coverage of AoA Intervals......Page 296
17.7.3 Unstable Real Eigenvalues......Page 297
17.8 Summary of Analysis Cycle......Page 298
17.9 Conclusions......Page 299
18.1 Introduction......Page 301
18.2.1 Single-loop Stability Margin......Page 302
18.2.2 Multi-loop Stability Margin......Page 303
18.3 Limitations of the HIRM+RIDE Model......Page 304
18.4 Analysis Cycle......Page 305
18.5.1 Lateral Analysis......Page 308
18.6 Results for all Trim Points......Page 313
18.6.1 Realating the e-scaled-Margin and Standard Nichols Exclusion Regions......Page 316
18.6.3 Validating the v-Gap Approximation......Page 317
18.6.4  Effect of Weights
......Page 318
18.7 Conclusions......Page 319
19.1 Description of the Analysis Cycle......Page 321
19.1.1 Trimming and Linearisation Routine Development......Page 323
19.1.3 Algorithm Parameter Setting......Page 324
19.1.4 Procedure Running and Result Visualization......Page 326
19.2 Analysis Results for Nominal HIRM+RIDE Flight Envelope......Page 327
19.3 Analysis Results for Single Uncertain Parameter and AOA......Page 331
19.4 Analysis Results for the Complete Set of Parameters......Page 334
19.5 Conclusions......Page 340
20.2 HIRM+RIDE Model Implementation......Page 342
20.2.1 Quasi-Trim Solutions......Page 343
20.2.2 Linearisation......Page 344
20.3 Clearance Criteria Analysed......Page 345
20.4 Presentation of Results......Page 346
20.5.1 Nominal Results......Page 347
20.5.2 Results with Worst-Case Uncertainties......Page 352
20.7 Man-Hour and Computation Time Estimates......Page 363
20.8 Conclusion and Recommendations......Page 368
21.1 Optimisation-Based Clearance of Linear Criteria......Page 371
21.2 Results for the Stability Margin Criterion......Page 375
21.3 Results for the Unstable Eigenvalues Criterion......Page 383
21.4 Results for the Average Phase Rate and Absolute Amplitude Criteria......Page 388
21.5 Evaluation of Results and Conclusions......Page 396
22.1 Introduction......Page 400
22.2 Optimisation-Based Clearance of the AoA/nz-Limit Exceedance Criteria......Page 401
22.3.1 Description of the Criterion......Page 406
22.3.2 Analysis Results for Slow Ramp......Page 407
22.3.3 Analysis Results for Quick Ramp......Page 409
22.3.4 Comparison......Page 411
22.4 Extended Analysis......Page 412
22.5 Conclusions......Page 414
23.1 Introduction......Page 416
23.2.1 Evaluation Procedure......Page 417
23.2.2 Industrial Evaluation Guidelines and Questionnaire......Page 418
23.3.1 Comparison of Analysis Results......Page 419
23.3.2 Baseline Solution......Page 420
23.3.4 µ-Analysis Techniques......Page 422
23.3.5 Bifurcation and Continuation Method......Page 423
23.3.6 Polynomial Based Method......Page 424
23.3.7 Optimisation-Based Worst-Case Search......Page 425
23.4 Conclusions......Page 426
24.1 Introduction......Page 429
24.2 Customer and Certification Requirements......Page 430
24.4 Uncertainties in Aircraft Dynamics......Page 431
24.5.1 Flight Envelope and Flight Conditions......Page 432
24.5.2 Stability Requirements......Page 433
24.6 Applicability of the Presented FCL Clearance Techniques for Civil Aircraft......Page 434
24.7 Recommendations for Future Research......Page 437
25.1 Summary of Achievements......Page 439
25.2 Future Research......Page 440