Flight Mechanics Modeling and Analysis

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgements
Authors
Introduction
I.1 Modeling
I.2 Flight Simulation
I.3 Flight Control
I.4 Artificial Neural Networks (ANNs) in Control
I.5 Fuzzy Logic-Based Control
I.6 Evaluation of Aircraft Control-Pilot Interactions
I.7 Chapter Highlights
References
Chapter 1 Aerodynamic Principles and Fundamentals
1.1 Aerodynamic Concepts and Relationships
1.1.1 Air Pressure
1.1.2 Air Density
1.1.3 Air Temperature
1.1.4 Altitudes
1.1.5 Airspeeds-IAS, CAS, EAS, TAS
1.1.6 Bernoulli's Continuity Equations
1.1.7 Mach Number
1.1.8 Reynold's Number
1.1.9 Viscosity
1.2 Aircraft Force Parameters
1.2.1 Lift
1.2.2 Weight
1.2.3 Thrust
1.2.4 Drag
1.2.5 Load Factor
1.2.6 Drag Polars
1.3 Aerodynamic Derivatives – Preliminary Determination
1.4 Aircraft Propulsion and Its Performance
1.5 Aircraft Sensors-Instrumentation Systems
1.5.1 Air-Data Instruments
1.5.2 Pressure Altimeter
1.5.3 Air Speed Indicator
1.5.4 Mach Meter
1.5.5 Vertical Speed Indicator
1.5.6 Accelerometers
1.6 Energy Awareness, Convergence, and Management
1.7 Angle of Attack Awareness and Management
Appendix 1A Airflow
1A.1 Boundary Layer
Appendix 1B Aircraft Engines
1B.1 Engine Thrust Computations
1B.2 For Turbojet-Type Engine
Epilogue
References
Chapter 2 Engineering Dynamics
2.1 Introduction
2.2 Kinematics
2.2.1 Rectangular Cartesian Coordinates
2.2.2 Curvilinear Coordinates
2.3 Relative Motion
2.3.1 Displacement and Time Derivatives
2.3.2 Angular Velocity and Acceleration
2.3.3 Velocity and Acceleration Using a Moving Reference Frame
2.4 Kinematics of Constraint Rigid Bodies
2.4.1 General Equations
2.4.2 Eulerian Angles
2.5 Inertial Effects
2.5.1 Linear and Angular Momentum
2.5.2 Inertial Properties
2.5.3 Rate of Change of Angular Momentum
2.6 Newton–Euler Equations of Motion
2.6.1 Fundamental Equations and Planar Motion
2.6.2 N-E Equations for a System
2.6.3 Principles of Momentum and Energy
2.7 Analytics Mechanics
2.7.1 Generalized Coordinates and Kinematical Constraints
2.7.2 Virtual Displacements
2.7.3 Generalized Forces
2.7.4 Lagrange's Equations
2.8 Constraint Generalized Coordinates
2.9 Alternative Formulations
2.9.1 Hamilton's Principle
2.9.2 Generalized Momentum Principles
2.10 Gyroscopic Effects
2.10.1 Free Motion of Axisymmetric Body
Epilogue
Exercises
References
Chapter 3 Equations of Motion
3.1 Introduction
3.2 Rigid Body Equations of Motion (EOM)
3.3 Resolution of Inertial Forces and Moments
3.4 Resolution of Aerodynamic, Gravity, and Thrust Forces
3.5 Complete Sets of EOM
3.5.1 Rectangular Form
3.5.2 Polar Form
3.6 Missile Dynamic Equations
3.7 Rotorcraft Dynamics
3.7.1 Momentum Theory
3.7.2 Blade-Element Theory
3.7.3 Rotorcraft Modeling Formulations
3.7.4 Limitations of Rigid Body Model
Appendix 3A Aircraft Geometry and Coordinate Systems
3A.1 Aircraft Axis and Notations
3A.2 Axes-Coordinates Transformations and Quaternions
3A.3 Transformation From Body to Earth Axis
3A.4 Transformation From Stability Axis to Body Axis
3A.5 Transformation From Stability Axis to Wind Axis (w)
3A.6 Transformation From Body Axis to Wind Axis
Appendix 3B Helicopter Aerodynamics
Appendix 3C Types of Helicopters and Controls
3C.1 Rotor Systems
3C.1.1 Fully Articulated Rotor
3C.1.2 Semi-Rigid/Teetering Rotor and Rigid Rotor
3C.2 Helicopter Controls
Epilogue
Exercises
References
Chapter 4 Aerodynamic Derivatives
4.1 Introduction
4.2 Basic Aerodynamic Forces and Moments
4.3 Aerodynamic Parameters
4.3.1 Definition of Aerodynamic Derivatives
4.3.2 Longitudinal Derivatives
4.3.2.1 Effect of Forward/Axial Speed u Along the X-Axis: (X[sub(u)], Z[sub(u)], M[sub(u)])
4.3.2.2 Effect of Change in Vertical Speed w (Equivalently AOA) Along the Vertical Z-Axis (X[sub(w)], Z[sub(w)], M[sub(w)])
4.3.2.3 Effect of Change in Pitch Rate q: (X[sub(q)], Z[sub(q)], M[sub(q)])
4.3.2.4 Effect of Change in Elevator Control Surface Deflection: (X[sub(δe)], Z[sub(δe)], M[sub(δe)])
4.3.3 Lateral-Directional Derivatives
4.3.3.1 Effect of Change in Side Speed v (Equivalently the AOSS): (Y[sub(v)] , L[sub(β)], N[sub(β)])
4.3.3.2 Effect of Change in the Time Rate Change in the Side Velocity (ν): (Y[sub(ν)] , L[sub(ν)], N[sub(ν)])
4.3.3.3 Effect of Change in Roll Rate p: (Y[sub(p)], L[sub(p)], N[sub(p)])
4.3.3.4 Effect of Change in Yaw Rate r: (Y[sub(r)], L[sub(r)], N[sub(r)])
4.3.3.5 Effect of Change in Aileron and Rudder Control Surface Deflection: (Y[sub(δa)] , L[sub(δa)], N[sub(δa)], Y[sub(δr)], L[sub(δr)], N[sub(δr)])
4.3.4 Compound Lateral-Directional Derivatives
4.4 Missile Aerodynamic Derivatives
4.4.1 Longitudinal Derivatives
4.4.2 Lateral-Directional Derivatives
4.4.2.1 Roll Derivatives
4.4.2.2 Yaw Derivatives
4.5 Rotorcraft Aerodynamic Derivatives
4.6 Role of Derivatives in Aircraft Design Cycle and Flight Control Law Development
4.7 Aircraft Aerodynamic Models
Appendix 4A Aircraft's Static and Dynamic Stability
4A.1 Neutral and Maneuver Points
Appendix 4B Transformations of Aerodynamic Derivatives
Appendix 4C Wind Tunnel Experimental Method for Aerodynamic Coefficients
Epilogue
Exercises
References
Chapter 5 Mathematical Modeling and Simplification of Equations of Motion
5.1 Introduction
5.2 Mathematical Model Structures
5.2.1 Transfer Function Models
5.2.1.1 Continuous-Time Model
5.2.1.2 Discrete-Time Model
5.2.1.3 Delta Form TF
5.2.2 State-Space Models
5.2.2.1 Physical Representation
5.2.2.2 Controllable Canonical Form
5.2.2.3 Observable Canonical Form
5.2.2.4 Diagonal Canonical Form
5.2.2.5 A General Model
5.2.3 Time-Series Models
5.3 Models for Noise and Error Processes
5.4 Strategies for Simplification of EOM
5.4.1 Choice of Coordinate Systems
5.4.2 Linearization of Model Equations
5.4.3 Simplification Using Measured Data
5.5 Longitudinal Models and Modes
5.5.1 Short-Period Mode
5.5.2 Phugoid
5.6 Lateral and Lateral-Directional Models and Modes
5.6.1 Dutch Roll Mode
5.6.2 3DOF Spiral and Roll Subsidence Modes
5.6.3 Spiral Mode
5.6.4 Roll Mode
5.7 Missile Aerodynamic Transfer Functions
5.8 Rotorcraft Linear Modeling
5.8.1 Rotor Plus Body Models
5.8.2 Stability-Derivative Models
5.8.3 Rotor-Response Decomposition Models
5.8.4 Evaluation/Validation of Linear Flight Dynamics Models
5.9 UAV Dynamics
5.10 MAV Dynamics
5.11 Lighter-than-Air Vehicle/BLIMP Dynamics
Appendix 5A Equilibrium, Stability, and Damping
Appendix 5B Stalls and Spins
Epilogue
Exercises
References
Chapter 6 Flight Simulation
6.1 Introduction
6.2 Aircraft Subsystem Data and Models
6.2.1 Aero Database
6.2.2 Mass, Inertia, and Center of Gravity Characteristics
6.2.3 Instrumentation System
6.2.4 Inertial Navigation System - INS
6.2.5 Flight Management System
6.2.6 Actuator Models
6.2.7 Engine Model
6.2.8 Landing Gear
6.2.9 Control Loading and Sound Simulation
6.2.10 Motion Cues
6.2.11 Turbulence and Gust Models
6.2.12 Sensor Modeling
6.2.13 Flight Dynamics
6.3 Steady-State Flight and Trim Conditions
6.3.1 The Rate of Climb and Turn Coordination Flights
6.3.2 Computation of Linear Models for Control Law Design
6.4 Six DOF Simulation and Validation
6.4.1 Flight Simulation Model Validation for a Rotorcraft
6.4.2 Flight Simulation Model Validation Using the Concept of Coefficient Matching
6.4.3 Flight Simulation Model Validation Using Direct Update
6.5 PC MATLAB- and SIMULINK-Based Simulation
6.6 Real-Time Desktop Simulator for the Evaluation of Flying Qualities
6.6.1 NALSIM Framework
6.6.2 Flying and Handling Quality Evaluation
6.6.2.1 Variable Damping and Natural Frequency Features
6.6.2.2 Tracking Tasks
6.7 Hardware-in-the-Loop-Simulation (HILS) for a Mini UAV
6.7.1 A 6DOF Model for SLYBIRD
6.7.2 Subsystems of the HILS
6.7.2.1 Real-Time Target Machine and Interference
6.7.2.2 Autopilot Hardware
6.7.2.3 Ground Control Station
6.7.3 Model-Based Design Framework
Epilog
Exercises
References
Chapter 7 Flight Test Maneuvers and Database Management
7.1 Introduction
7.2 Planning of Flight Test Maneuvers
7.2.1 Flight Test Evaluation of a Transport Aircraft
7.2.2 Takeoff and Landing Tasks
7.2.2.1 Approach and Landing Task
7.2.2.2 Take Off Task
7.2.3 Other Maneuvers
7.3 Specific Flight Test Data Generation and Analysis Aspects
7.3.1 Longitudinal Axis Data Generation
7.3.2 Lateral-Directional Data Generation
7.4 Quality of Flight Test Maneuvers
7.5 Input Signals for Exciting Maneuvers
7.5.1 Design Consideration for Input Signals
7.5.2 Specific Input Types
7.6 Specific Maneuvers for Aerodynamic Modeling
7.6.1 Small-Amplitude Maneuvers
7.6.1.1 Longitudinal Short-period Maneuver
7.6.1.2 Phugoid Maneuver
7.6.1.3 Thrust Input Maneuver
7.6.1.4 Flaps Input Maneuver
7.6.1.5 Lateral-Directional Maneuvers
7.6.1.6 Aileron Input Roll Maneuver
7.6.1.7 Rudder Input Maneuver
7.6.1.8 Dutch Roll Maneuver
7.6.1.9 Steady Heading Sideslip Maneuver
7.6.2 Large-Amplitude Maneuvers
7.6.3 A Typical Flight Test Exercise
7.7 Specific Dynamic Maneuvers for Determination of Drag Polars
7.7.1 Roller Coaster (Pull-up Pushover) Maneuver
7.7.2 Slowdown Maneuver
7.7.3 Acceleration and Deceleration Maneuver
7.7.4 Windup Turn Maneuver
7.8 Specific Maneuvers for Rotorcraft
7.9 Flight Test Database Management
7.9.1 Basic Requirements
7.9.2 Selection and Classification of Flight Data
7.9.2.1 Classification Based on Type of Maneuvers
7.9.2.2 Classification Based on Flight Conditions
7.9.2.3 Classification Based on Aircraft Configuration
7.9.3 Data Storage and Organization
7.9.4 Flight Test Database in Oracle
7.9.5 Brief Description of a Typical Program
7.9.5.1 Transactions
7.9.5.2 Graphs/Reports
7.9.5.3 User Maintenance
Epilogue
Appendix 7A Aircraft Certification Process and Weight Analysis
Exercises
References
Chapter 8 Flight Control
8.1 Introduction
8.2 Control System: A Dynamic System Concept
8.2.1 Bode Diagrams and Transfer Functions
8.2.2 Performance: Order, Type of System, and Steady-State Error
8.2.3 Stability Criteria
8.2.3.1 Static Stability
8.2.3.2 Routh–Hurwitz Criterion
8.2.3.3 Nyquist Criterion
8.2.3.4 Gain and Phase Margins
8.3 Digital Control System
8.4 Design Compensation for Linear Control System
8.5 Root Locus
8.6 Aircraft Flight Control
8.6.1 Requirements of Flight Control
8.6.2 Stability and Control Augmentation Strategies
8.6.3 Performance Requirements and Criteria
8.6.4 Procedure for the Design and Evaluation of Control Laws
8.7 Stability Augmentation Systems
8.7.1 Dampers: Acquisition of Dynamic Stability
8.7.1.1 Yaw Damper
8.7.1.2 Pitch Damper
8.7.1.3 Phugoid Damper
8.7.2 Feedback-Acquisition of Static Stability
8.7.2.1 Feedback of AOA
8.7.2.2 Feedback of Load Factor
8.7.2.3 Feedback of Sideslip
8.7.3 Basic Autopilot Systems
8.7.3.1 Longitudinal Autopilots
8.7.3.2 Lateral Autopilots
8.7.4 Navigational Autopilot Systems
8.7.4.1 Longitudinal Autopilot
8.7.4.2 Lateral Autopilot
8.8 Flight Control Design Examples
8.8.1 Designing a High AOA Pitch Mode Control
8.8.2 Tuning of a Two-Loop Autopilot
8.8.2.1 Model of Airframe Autopilot
8.8.2.2 Tuning with Looptune
8.8.2.3 Addition of a Tracking Requirement
8.8.3 DC-8 Aircraft Pitch Attitude Control
8.9 Fuzzy Logic Control
8.10 Fault Management and Reconfiguration Control
8.10.1 Models for Faults
8.10.2 Aircraft FTR Control System
8.10.2.1 Sensor Fault Detection Scheme
8.10.2.2 Actuator Fault Detection Scheme
8.10.2.3 Reconfiguration Concept
8.10.2.4 Non-Model-Based Approach
Appendix 8A Flight Control: The Systems Approach
Appendix 8B Aspects of Fly-by-Wire Flight Control Design
Appendix 8C Missile Control Methods
Epilogue
Exercises
References
Chapter 9 System Identification and Parameter Estimation for Aircraft
9.1 Introduction
9.2 System Identification
9.2.1 Time-Series and Regression Model Identification
9.2.2 Comparison of Several Model Order Criteria
9.2.3 Transfer Function Models From Real Flight Data
9.2.4 Expert Systems for System Identification
9.3 Aircraft Parameter Estimation
9.3.1 Maneuvers, Measurements, and Mathematical Models
9.3.2 Parameter Estimation Methods
9.3.2.1 Equation Error Method
9.3.2.2 Maximum-Likelihood Output Error Method
9.3.2.3 Maximum-likelihood Estimation for Dynamic System
9.3.2.4 Filtering Methods
9.3.3 Parameter Estimation Approaches for Inherently Unstable, Augmented Aircraft
9.3.3.1 Stabilized Output Error Methods
9.4 Determination of Stability and Control Derivatives From Flight Data – Case Studies
9.4.1 Fighter Aircraft FA1
9.4.2 Fighter Aircraft FA2
9.4.3 Basic and Modified Transport Aircraft
9.4.4 Trainer Aircraft
9.4.5 Light Canard Research Aircraft
9.4.6 Helicopter
9.4.7 AGARD Standard Model
9.4.8 Dynamic Wind Tunnel Experiments
9.4.9 Iron Bird Results
9.5 Approaches for Determination of Drag Polars From Flight Data
9.5.1 Model-Based Approach for Determination of Drag Polar
9.5.2 Non-Model-Based Approach for Drag Polar Determination
9.6 Analysis of Large-Amplitude Maneuver Data
9.7 Global Nonlinear Analytical Modeling
9.8 Fuzzy Kalman Filter for State Estimation
9.8.1 Tracking of Maneuvering Target
9.9 Derivative-Free Kalman Filter for State Estimation
Appendix 9A Gaussian Sum Filter for Parameter Estimation
9A.1 Gaussian Sum-Extended Kalman Filter
9A.1.1 Time Propagation Evolution
9A.1.2 Measurement Data Update
9A.2 Gaussian Sum Filter with Pruning
9A.3 Lyapunov Stability Analysis of GSF Via Observer
9A.4 Aircraft Parameter Estimation
Appendix 9B Gaussian Sum Information Filter for Parameter Estimation
9B.1 Gaussian Sum-Extended Information Filter
9B.1.1 Time Propagation Evolution
9B.1.2 Measurement Data Update
9B.2 Aircraft Parameter Estimation
Appendix 9C APE Using ANNs
9C.1 APE with Feed-forward Neural Networks
9C.2 APE with Recurrent Neural Networks
Epilogue
Exercises
References
Chapter 10 Aircraft Handling Qualities Analysis
10.1 Introduction
10.2 Pilot Opinion Rating
10.3 Human Operator Modeling
10.3.1 Motion Plus Visual and Only Visual Cue Experiments
10.4 Handling Qualities Criteria
10.4.1 Longitudinal HQ Criteria
10.4.1.1 LOTF (Lower-Order Equivalent TF)
10.4.1.2 CAP-Control Anticipation Parameter
10.4.1.3 Bandwidth Criterion
10.4.1.4 Neal-Smith Criterion
10.4.1.5 Closed-Loop Criterion
10.4.1.6 Pitch Rate Response
10.4.1.7 C* (C-star) Criterion
10.4.1.8 Gibson's Criterion
10.4.2 Lateral-Directional HQ Criteria
10.4.2.1 LOTF (Lower-Order Equivalent TF)
10.4.2.2 Role Angle/Side Slip Mode Ratio
10.4.2.3 Lateral/Directional Modes
10.4.2.4 Roll Rate and Bank Angle Oscillations
10.4.2.5 Roll Performance
10.4.2.6 Sideslip Excursions
10.5 Evaluation of HQ Criteria
10.5.1 HQ for Large Transport Aircraft (LTA)
10.5.2 Rotorcraft Handling Qualities
10.5.3 Handling Qualities Analysis Tool (HAT)
10.5.3.1 HLSR-Pitch Axis Response (PAR) Criteria
10.5.3.2 HLSR-Roll Axis Response (RAR) Criteria
10.5.3.3 HLSR-Yaw Axis Response (YAR) Criteria
10.5.3.4 HLSR-Heave Axis Response (HAR) Criteria
10.6 HQ Aspects for UAVs
10.7 Pilot-Aircraft Interactions
10.7.1 Longitudinal PIO Criteria
10.7.1.1 Ralph Smith Criterion
10.7.1.2 Smith-Geddes Criterion
10.7.1.3 Phase Rate Criterion
10.7.1.4 Loop Separation Parameter
10.7.1.5 N-S Time Domain Criterion
10.7.1.6 Bandwidth PIO Criterion
10.7.1.7 Lateral PIO Criteria
10.7.1.8 Ralph-Smith
10.7.1.9 Phase Rate
10.8 Model Order Reduction for Evaluations of HQ
Epilogue
Exercises
References
Chapter 11 Aeroservoelastic Concepts
11.1 Introduction
11.1.1 Modeling Procedures
11.1.1.1 Minimum State for Approximating Unsteady Aerodynamics
11.1.1.2 Unsteady Aerodynamic Corrections Factor Methodology
11.1.2 Analysis Methods
11.1.2.1 Matched Filter Theory (MFT)
11.1.3 Synthesis Methodology
11.1.3.1 Integrated Structure Control Law Design Methodology
11.1.3.2 Design Using Constrained Optimization with Singular Value Constraints
11.1.4 Validation of Methods Through Experimentation
11.2 Flight Dynamics of a Flexible Aircraft
11.2.1 ASE Formulation
11.2.1.1 Kinetic Energy
11.2.1.2 Potential Energy
11.2.1.3 Generalized Forces and Moments
11.2.1.4 Equations for Elastic Airplane
11.3 Parameter Estimation for Flexible Aircraft
11.3.1 Flexible Aircraft Model
11.3.1.1 Structural Deformation Model
11.3.1.2 Extended Aerodynamic Model
11.3.2 Estimation of Modeling Variables
11.3.2.1 Estimating Modal Displacements
11.3.2.2 Estimating Modal Rates
11.3.2.3 Estimating Airflow Angles
11.3.2.4 Estimating Modal Accelerations
11.3.2.5 Kalman Filtering to Improve the Modal State Estimation
11.3.2.6 Practical Aspects
11.4 X-56A Aircraft and Flight Tests
11.4.1 Aircraft
11.4.2 Instrumentation
11.4.3 Flight Testing
11.4.4 Flight Test Results
Epilogue
Exercises
References
Appendix A: Atmospheric Disturbance Models
Appendix B: Artificial Neural Network-Based Modeling
Appendix C: Fuzzy Logic-Based Modeling
Appendix D: Statistics and Probability
Appendix E: Signal and Systems Concepts
Bibliography
Index