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