Flight Dynamics, Simulation, and Control For Rigid and Flexible Aircraft

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Acronyms
Preface
Author
Chapter 1 Introduction to Flight Vehicles
1.1 Introduction
1.2 Components of an Aeroplane
1.2.1 Fuselage
1.2.2 Wings
1.2.3 Tail Surfaces or Empennage
1.2.4 Landing Gear
1.3 Basic Principles of Flight
1.3.1 Forces Acting on an Aeroplane
1.3.2 Drag and Its Reduction
1.3.3 Aerodynamically Conforming Shapes: Streamlining
1.3.4 Stability and Balance
1.4 Flying Control Surfaces: Elevator, Ailerons and Rudder
1.4.1 Flaps, High-Lift and Flow Control Devices
1.4.2 Introducing Boundary Layers
1.4.3 Spoilers
1.5 Pilot's Controls: The Throttle, the Control Column and Yoke, the Rudder Pedals and the Toe Brakes
1.6 Modes of Flight
1.6.1 Static and In-Flight Stability Margins
1.7 Power Plant
1.7.1 Propeller-Driven Aircraft
1.7.2 Jet Propulsion
1.8 Avionics, Instrumentation and Systems
1.8.1 Autonomous Navigation
1.9 Geometry of Aerofoils and Wings
1.9.1 Aerofoil Geometry
1.9.2 Chord Line
1.9.3 Camber
1.9.4 Leading and Trailing Edges
1.9.5 Specifying Aerofoils
1.9.6 Equations Defining Mean Camber Line
1.9.7 Aerofoil Thickness Distributions
1.9.8 Wing Geometry
Chapter Highlights
Exercises
Answers to Selected Exercises
References
Chapter 2 Basic Principles Governing Aerodynamic Flows
2.1 Introduction
2.2 Continuity Principle
2.2.1 Streamlines and Stream Tubes
2.3 Bernoulli's Principle
2.4 Laminar Flows and Boundary Layers
2.5 Turbulent Flows
2.6 Aerodynamics of Aerofoils and Wings
2.6.1 Flow Around an Aerofoil
2.6.2 Mach Number and Subsonic and Supersonic Flows
2.7 Properties of Air in the Atmosphere
2.7.1 Composition of the Atmosphere: The Troposphere, Stratosphere, Mesosphere, Ionosphere and Exosphere
2.7.2 Air Density
2.7.3 Temperature
2.7.4 Pressure
2.7.5 Effects of Pressure and Temperature
2.7.6 Viscosity
2.7.7 Bulk Modulus of Elasticity
2.7.8 Temperature Variations with Altitude: The Lapse Rate
2.8 International Standard Atmosphere (from ESDU 77021, 1986)
2.9 Generation of Lift and Drag
2.10 Aerodynamic Forces and Moments
2.10.1 Aerodynamic Coefficients
2.10.2 Aerofoil Drag
2.10.3 Aircraft Lift Equation and Lift Curve Slope
2.10.4 Centre of Pressure
2.10.5 Aerodynamic Centre
2.10.6 Pitching Moment Equation
2.10.7 Elevator Hinge Moment Coefficient
Chapter Highlights
Exercises
Answers to Selected Exercises
References
Chapter 3 Mechanics of Equilibrium Flight
3.1 Introduction
3.2 Speeds of Equilibrium Flight
3.3 Basic Aircraft Performance
3.3.1 Optimum Flight Speeds
3.4 Conditions for Minimum Drag
3.5 Stability in the Vicinity of the Minimum Drag Speed
3.6 Range and Endurance Estimation
3.7 Trim
3.8 Stability of Equilibrium Flight
3.9 Longitudinal Static Stability
3.9.1 Neutral Point (Stick-Fixed)
3.9.2 Neutral Point (Stick-Free)
3.10 Manoeuvrability
3.10.1 Pull-Out Manoeuvre
3.10.2 Manoeuvre Margin: Stick-Fixed
3.10.3 Manoeuvre Margin: Stick-Free
3.11 Lateral Stability and Stability Criteria
3.12 Experimental Determination of Aircraft Stability Margins
3.13 Summary of Equilibrium- and Stability-Related Equations
Chapter Highlights
Exercises
Answers to Selected Exercises
References
Chapter 4 Aircraft Non-Linear Dynamics: Equations of Motion
4.1 Introduction
4.2 Aircraft Dynamics
4.3 Aircraft Motion in a 2D Plane
4.4 Moments of Inertia
4.5 Euler's Equations and the Dynamics of Rigid Bodies
4.6 Description of the Attitude or Orientation
4.7 Aircraft Equations of Motion
4.8 Motion-Induced Aerodynamic Forces and Moments
4.9 Non-Linear Dynamics of Aircraft Motion and Stability Axes
4.9.1 Equations of Motion in Wind Axis Coordinates, V[sub(T)], α and β
4.9.2 Reduced-Order Modelling: The Short-Period Approximations
4.10 Trimmed Equations of Motion
4.10.1 Non-Linear Equations of Perturbed Motion
4.10.2 Linear Equations of Motion
Chapter Highlights
Exercises
References
Chapter 5 Small Perturbations and the Linearised, Decoupled Equations of Motion
5.1 Introduction
5.2 Small Perturbations and Linearisations
5.3 Linearising the Aerodynamic Forces and Moments: Stability Derivative Concept
5.4 Direct Formulation in the Stability Axis
5.5 Decoupled Equations of Motion
5.5.1 Case I: Motion in the Longitudinal Plane of Symmetry
5.5.2 Case II: Motion in the Lateral Direction, Perpendicular to the Plane of Symmetry
5.6 Decoupled Equations of Motion in Terms of the Stability Axis Aerodynamic Derivatives
5.7 Addition of Aerodynamic Controls and Throttle
5.8 Non-Dimensional Longitudinal and Lateral Dynamics
5.9 Simplified State-Space Equations of Longitudinal and Lateral Dynamics
5.10 Simplified Concise Equations of Longitudinal and Lateral Dynamics
Chapter Highlights
Exercises
Reference
Chapter 6 Longitudinal and Lateral Linear Stability and Control
6.1 Introduction
6.2 Dynamic and Static Stability
6.2.1 Longitudinal Stability Analysis
6.2.2 Lateral Dynamics and Stability
6.3 Modal Description of Aircraft Dynamics and the Stability of the Modes
6.3.1 Slow–Fast Partitioning of the Longitudinal Dynamics
6.3.2 Slow–Fast Partitioning of the Lateral Dynamics
6.3.3 Summary of Longitudinal and Lateral Modal Equations
6.3.3.1 Phugoid or Long Period
6.3.3.2 Short Period
6.3.3.3 Third Oscillatory Mode
6.3.3.4 Roll Subsidence
6.3.3.5 Dutch Roll
6.3.3.6 Spiral
6.4 Aircraft Lift and Drag Estimation
6.4.1 Fuselage Lift and Moment Coefficients
6.4.2 Wing–Tail Interference Effects
6.4.3 Estimating the Wing's Maximum Lift Coefficient
6.4.4 Drag Estimation
6.5 Estimating the Longitudinal Aerodynamic Derivatives
6.6 Estimating the Lateral Aerodynamic Derivatives
6.7 Perturbation Analysis of Trimmed Flight
6.7.1 Perturbation Analysis of Longitudinal Trimmed Flight
6.7.2 Perturbation Analysis of Lateral Trimmed Flight
6.7.2.1 Control Settings for Steady Sideslip
6.7.2.2 Control Settings for Turn Coordination and Banking
6.7.3 Perturbations of Coupled Trimmed Flight
6.7.4 Simplified Analysis of Complex Manoeuvres: The Sidestep Manoeuvre
Chapter Highlights
Exercises
Answers to Selected Exercises
Note
References
Chapter 7 Aircraft Dynamic Response: Numerical Simulation and Non-Linear Phenomenon
7.1 Introduction
7.2 Longitudinal and Lateral Modal Equations
7.3 Methods of Computing Aircraft Dynamic Response
7.3.1 Laplace Transform Method
7.3.2 Aircraft Response Transfer Functions
7.3.3 Direct Numerical Integration
7.4 System Block Diagram Representation
7.4.1 Numerical Simulation of Flight Using MATLAB[sup(®)]/Simulink[sup(®)]
7.5 Atmospheric Disturbance: Deterministic Disturbances
7.6 Principles of Random Atmospheric Disturbance Modelling
7.6.1 White Noise: Power Spectrum and Autocorrelation
7.6.2 Linear Time-Invariant System with Stochastic Process Input
7.7 Application to Atmospheric Turbulence Modelling
7.8 Aircraft Non-Linear Dynamic Response Phenomenon
7.8.1 Aircraft Dynamic Non-Linearities and Their Analysis
7.8.2 High-Angle-of-Attack Dynamics and Its Consequences
7.8.3 Post-Stall Behaviour
7.8.4 Tumbling and Autorotation
7.8.5 Lateral Dynamic Phenomenon
7.8.6 Flat Spin and Deep Spin
7.8.7 Wing Drop, Wing Rock and Nose Slice
7.8.8 Fully Coupled Motions: The Falling Leaf
7.8.9 Regenerative Phenomenon
Chapter Highlights
Exercises
References
Chapter 8 Aircraft Flight Control
8.1 Automatic Flight Control Systems: An Introduction
8.2 Functions of a Flight Control System
8.3 Integrated Flight Control System
8.3.1 Guidance System: Interfacing to the Automatic Flight Control System
8.3.2 Flight Management System
8.4 Flight Control System Design
8.4.1 Block Diagram Algebra
8.4.2 Return Difference Equation
8.4.3 Laplace Transform
8.4.4 Stability of Uncontrolled and Controlled Systems
8.4.5 Routh's Tabular Method
8.4.6 Frequency Response
8.4.7 Bode Plots
8.4.8 Nyquist Plots
8.4.9 Stability in the Frequency Domain
8.4.10 Stability Margins: Gain and Phase Margins
8.4.11 Mapping Complex Functions and Nyquist Diagrams
8.4.12 Time Domain: State Variable Representation
8.4.13 Solution of the State Equations and the Controllability Condition
8.4.14 State-Space and Transfer Function Equivalence
8.4.15 Transformations of State Variables
8.4.16 Design of a Full-State Variable Feedback Control Law
8.4.17 Root Locus Method
8.4.18 Root Locus Principle
8.4.19 Root Locus Sketching Procedure
8.4.20 Producing a Root Locus Using MATLAB®
8.4.21 Application of the Root Locus Method: Unity Feedback with a PID Control Law
8.5 Optimal Control of Flight Dynamics
8.5.1 Compensating Full-State Feedback: Observers and Compensators
8.5.2 Observers for Controller Implementation
8.5.3 Observer Equations
8.5.4 Special Cases: Full- and First-Order Observers
8.5.5 Solving the Observer Equations
8.5.6 Luenberger Observer
8.5.7 Optimisation Performance Criteria
8.5.8 Good Handling Domains of Modal Response Parameters
8.5.9 Cooper–Harper Rating Scale
8.6 Application to the Design of Stability Augmentation Systems and Autopilots
8.6.1 Design of a Pitch Attitude Autopilot Using PID Feedback and the Root Locus Method
8.6.2 Example of Pitch Attitude Autopilot Design for the Lockheed F104 by the Root Locus Method
8.6.3 Example of Pitch Attitude Autopilot Design, Including a Stability Augmentation Inner Loop, by the Root Locus Method
8.6.4 Design of an Altitude Acquire-and-Hold Autopilot
8.6.5 Design of a Lateral Roll Attitude Autopilot
8.6.6 Design of a Lateral Yaw Damper
8.6.7 Design of a Lateral Heading Autopilot
8.6.8 Turn Coordination with Sideslip Suppression
8.6.9 Application of Optimal Control to Lateral Control Augmentation Design
8.7 Performance Assessment of a Command or Control Augmentation System
8.8 Linear Perturbation Dynamics Flight Control Law Design by Partial Dynamic Inversion
8.8.1 Design Example of a Longitudinal Autopilot Based on Partial Dynamic Inversion
8.9 Design of Controllers for Multi-Input Systems
8.9.1 Design Example of a Lateral Turn Coordination Using the Partial Inverse Dynamics Method
8.9.2 Design Example of the Simultaneously Operating Auto-Throttle and Pitch Attitude Autopilot
8.9.3 Two-Input Lateral Attitude Control Autopilot
8.10 Decoupling Control and Its Application: Longitudinal and Lateral Dynamics Decoupling Control
8.11 Full Aircraft Six-DOF Flight Controller Design by Dynamic Inversion
8.11.1 Control Law Synthesis
8.11.2 Example of Linear Control Law Synthesis by Partial Dynamic Inversion: Fully Propulsion-Controlled MD11 Aircraft
Chapter Highlights
Exercises
Answers to Selected Exercises
References
Chapter 9 Piloted Simulation and Pilot Modelling
9.1 Introduction
9.2 Piloted Flight Simulation
9.2.1 Full Moving-Base Simulation: The Stewart Platform
9.2.2 Kinematics of Motion Systems
9.2.3 Principles of Motion Control
9.2.4 Motion Cueing Concepts
9.3 Principles of Human Pilot Physiological Modelling
9.3.1 Auricular and Ocular Sensors
9.4 Human Physiological Control Mechanisms
9.4.1 Crossover Model
9.4.2 Neal–Smith Criterion
9.4.3 Pilot-Induced Oscillations
9.4.4 PIO Categories
9.4.5 PIOs Classified Under Small Perturbation Modes
9.4.6 Optimal Control Models
9.4.7 Generic Human Pilot Modelling
9.4.8 Pilot–Vehicle Simulation
9.5 Spatial Awareness
9.5.1 Visual Displays
9.5.2 Animation and Visual Cues
9.5.3 Visual Illusions
Chapter Highlights
Exercises
References
Chapter 10 Flight Dynamics of Elastic Aircraft
10.1 Introduction
10.2 Flight Dynamics of Flexible Aircraft
10.3 Newton–Euler Equations of a Rigid Aircraft
10.4 Lagrangian Formulation
10.4.1 Generalised Coordinates and Holonomic Dynamic Systems
10.4.2 Generalised Velocities
10.4.3 Virtual Displacements and Virtual Work
10.4.4 Principle of Virtual Work
10.4.5 Euler–Lagrange Equations
10.4.6 Potential Energy and the Dissipation Function
10.4.7 Euler–Lagrange Equations of Motion in Quasi-Coordinates
10.4.8 Transformation to Centre of Mass Coordinates
10.4.9 Application of the Lagrangian Method to a Rigid Aircraft
10.5 Vibration of Elastic Structures in a Fluid Medium
10.5.1 Effects of Structural Flexibility in Aircraft Aeroelasticity
10.5.2 Wing Divergence
10.5.3 Control Reversal
10.5.4 Wing Flutter
10.5.5 Aerofoil Flutter Analysis
10.6 Unsteady Aerodynamics of an Aerofoil
10.7 Euler–Lagrange Formulation of Flexible Body Dynamics
10.8 Application to an Aircraft with a Flexible Wing Vibrating in Bending and Torsion
10.8.1 Longitudinal Small Perturbation Equations with Flexibility
10.8.2 Lateral Small Perturbation Equations with Flexibility
10.9 Kinetic and Potential Energies of the Whole Elastic Aircraft
10.9.1 Kinetic Energy
10.9.2 Simplifying the General Expression
10.9.3 Mean Axes
10.9.4 Kinetic Energy in Terms of Modal Amplitudes
10.9.5 Tisserand Frame
10.10 Euler–Lagrange Matrix Equations of a Flexible Body in Quasi-Coordinates
10.11 Slender Elastic Aircraft
10.12 Aircraft with a Flexible Flat Body Component
10.12.1 Elastic Large Aspect Ratio Flying Wing Model
10.12.2 Flexible Aircraft in Roll
10.13 Estimating the Aerodynamic Derivatives: Modified Strip Analysis
Chapter Highlights
Exercises
Answers to Selected Exercises
References
Chapter 11 Dynamics and Control of Drones and Unmanned Aerial Vehicles
11.1 Introduction
11.2 Dynamics of a Generic Drone
11.3 Rigid Body Kinematics
11.3.1 Defining the Body Frame
11.3.2 Defining the Body Angular Velocity Components
11.4 Translational Dynamics
11.5 Attitude Dynamics
11.6 Attitude Kinematics
11.6.1 The Quaternion Representation of the Attitude
11.6.2 The Relations Between Quaternion Rates and Angular Velocities
11.7 Aerodynamic Forces
11.8 Propulsion-Based Control
11.9 Stability and Control
11.10 Automatic Flight Control
11.11 Autonomous Flight Control
11.12 The Quadrotor Drone
11.12.1 Dynamics of the Quadrotor Drone
11.12.2 Quadrotor Control Allocation
11.12.3 Quadrotor Control Strategies
11.12.4 PID Control of a Quadrotor
11.13 Optimal Controller Synthesis for Drones
11.14 Unconventional Multi-Rotor Drones
11.14.1 Quadrotors with Bi-Directional Motors
11.14.2 Quadcopters: Dynamics of the Quadcopter
11.14.3 Body Forces and Body Moments Acting on a Quadcopter
11.14.4 The Unsymmetrically Actuated Quadcopter
11.14.5 The Pentacopter
11.14.6 Equations of Motion of a Pentacopter
11.14.7 The Hexa-Rotor and the Hexa-Copter
11.14.8 Dynamics of a Hexa-Rotor Drone
11.14.9 The Basic Hexa-Rotor Configuration: Derivation of the Body Forces and Moments
11.14.10 Alternate Tri-Axial Multi-Rotor Configurations
11.14.11 The Hexa-Rotor Configuration with Two Rotors Tilted: The Hexa-Copter
11.14.12 A Hexa-Copter with Three Tilt-Controlled Rotors
11.14.13 Six DOFs Configuration: Derivation of the Body Forces and Moments
11.14.14 Control of a Fully Actuated Hexa-rotor Drone: Decoupling
11.14.15 The Octocopter and Over-Actuated Multi-Rotor Drones
11.14.16 Dynamics of an Octocopter Drone
11.14.17 Nonlinear and Linear Dynamic Modelling of Multi-Rotor Drones
11.14.18 H[sup(∞)] Optimal Control of an Octocopter Drone
11.14.19 Typical Simulation Example
11.15 Drones and Unmanned Aerial Vehicles with Aerodynamic Lifting Surfaces
Chapter Highlights
Exercises
References
Index