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Flight Dynamics, Simulation, and Control, 2nd Edition

Name: Flight Dynamics, Simulation, and Control, 2nd Edition
Author: Ranjan Vepa
ISBN: 9781000848021

by Ranjan Vepa

April 2023

Intermediate to advanced

642 pages

14h 27m

English

CRC Press

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Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
List of Acronyms
Preface
Author
Chapter 1 Introduction to Flight Vehicles
1.1 Introduction1.2 Components of an Aeroplane1.2.1 Fuselage1.2.2 Wings1.2.3 Tail Surfaces or Empennage1.2.4 Landing Gear1.3 Basic Principles of Flight1.3.1 Forces Acting on an Aeroplane1.3.2 Drag and Its Reduction1.3.3 Aerodynamically Conforming Shapes: Streamlining1.3.4 Stability and Balance1.4 Flying Control Surfaces: Elevator, Ailerons and Rudder1.4.1 Flaps, High-Lift and Flow Control Devices1.4.2 Introducing Boundary Layers1.4.3 Spoilers1.5 Pilot’s Controls: The Throttle, the Control Column and Yoke, the Rudder Pedals and the Toe Brakes1.6 Modes of Flight1.6.1 Static and In-Flight Stability Margins1.7 Power Plant1.7.1 Propeller-Driven Aircraft1.7.2 Jet Propulsion1.8 Avionics, Instrumentation and Systems1.8.1 Autonomous Navigation1.9 Geometry of Aerofoils and Wings1.9.1 Aerofoil Geometry1.9.2 Chord Line1.9.3 Camber1.9.4 Leading and Trailing Edges1.9.5 Specifying Aerofoils1.9.6 Equations Defining Mean Camber Line1.9.7 Aerofoil Thickness Distributions1.9.8 Wing GeometryChapter HighlightsExercisesAnswers to Selected ExercisesReferences
Chapter 2 Basic Principles Governing Aerodynamic Flows
2.1 Introduction2.2 Continuity Principle2.2.1 Streamlines and Stream Tubes2.3 Bernoulli’s Principle2.4 Laminar Flows and Boundary Layers2.5 Turbulent Flows2.6 Aerodynamics of Aerofoils and Wings2.6.1 Flow around an Aerofoil2.6.2 Mach Number and Subsonic and Supersonic Flows2.7 Properties of Air in the Atmosphere2.7.1 Composition of the Atmosphere: The Troposphere, Stratosphere, Mesosphere, Ionosphere and Exosphere2.7.2 Air Density2.7.3 Temperature2.7.4 Pressure2.7.5 Effects of Pressure and Temperature2.7.6 Viscosity2.7.7 Bulk Modulus of Elasticity2.7.8 Temperature Variations with Altitude: The Lapse Rate2.8 International Standard Atmosphere (from ESDU 77021, 1986)2.9 Generation of Lift and Drag2.10 Aerodynamic Forces and Moments2.10.1 Aerodynamic Coefficients2.10.2 Aerofoil Drag2.10.3 Aircraft Lift Equation and Lift Curve Slope2.10.4 Centre of Pressure2.10.5 Aerodynamic Centre2.10.6 Pitching Moment Equation2.10.7 Elevator Hinge Moment CoefficientChapter HighlightsExercisesAnswers to Selected ExercisesReferences

Chapter 3 Mechanics of Equilibrium Flight
3.1 Introduction3.2 Speeds of Equilibrium Flight3.3 Basic Aircraft Performance3.3.1 Optimum Flight Speeds3.4 Conditions for Minimum Drag3.5 Stability in the Vicinity of the Minimum Drag Speed3.6 Range and Endurance Estimation3.7 Trim3.8 Stability of Equilibrium Flight3.9 Longitudinal Static Stability3.9.1 Neutral Point (Stick-Fixed)3.9.2 Neutral Point (Stick-Free)3.10 Manoeuvrability3.10.1 Pull-Out Manoeuvre3.10.2 Manoeuvre Margin: Stick-Fixed3.10.3 Manoeuvre Margin: Stick-Free3.11 Lateral Stability and Stability Criteria3.12 Experimental Determination of Aircraft Stability Margins3.13 Summary of Equilibrium- and Stability-Related EquationsChapter HighlightsExercisesAnswers to Selected ExercisesReferences
Chapter 4 Aircraft Non-Linear Dynamics: Equations of Motion
4.1 Introduction4.2 Aircraft Dynamics4.3 Aircraft Motion in a 2D Plane4.4 Moments of Inertia4.5 Euler’s Equations and the Dynamics of Rigid Bodies4.6 Description of the Attitude or Orientation4.7 Aircraft Equations of Motion4.8 Motion-Induced Aerodynamic Forces and Moments4.9 Non-Linear Dynamics of Aircraft Motion and Stability Axes4.9.1 Equations of Motion in Wind Axis Coordinates, VT, α and β4.9.2 Reduced-Order Modelling: The Short-Period Approximations4.10 Trimmed Equations of Motion4.10.1 Non-Linear Equations of Perturbed Motion4.10.2 Linear Equations of MotionChapter HighlightsExercisesReferences
Chapter 5 Small Perturbations and the Linearised, Decoupled Equations of Motion
5.1 Introduction5.2 Small Perturbations and Linearisations5.3 Linearising the Aerodynamic Forces and Moments: Stability Derivative Concept5.4 Direct Formulation in the Stability Axis5.5 Decoupled Equations of Motion5.5.1 Case I: Motion in the Longitudinal Plane of Symmetry5.5.2 Case II: Motion in the Lateral Direction, Perpendicular to the Plane of Symmetry5.6 Decoupled Equations of Motion in terms of the Stability Axis Aerodynamic Derivatives5.7 Addition of Aerodynamic Controls and Throttle5.8 Non-Dimensional Longitudinal and Lateral Dynamics5.9 Simplified State-Space Equations of Longitudinal and Lateral Dynamics5.10 Simplified Concise Equations of Longitudinal and Lateral DynamicsChapter HighlightsExercisesReference
Chapter 6 Longitudinal and Lateral Linear Stability and Control
6.1 Introduction6.2 Dynamic and Static Stability6.2.1 Longitudinal Stability Analysis6.2.2 Lateral Dynamics and Stability6.3 Modal Description of Aircraft Dynamics and the Stability of the Modes6.3.1 Slow–Fast Partitioning of the Longitudinal Dynamics6.3.2 Slow–Fast Partitioning of the Lateral Dynamics6.3.3 Summary of Longitudinal and Lateral Modal Equations6.3.3.1 Phugoid or Long Period6.3.3.2 Short Period6.3.3.3 Third Oscillatory Mode6.3.3.4 Roll Subsidence6.3.3.5 Dutch Roll6.3.3.6 Spiral6.4 Aircraft Lift and Drag Estimation6.4.1 Fuselage Lift and Moment Coefficients6.4.2 Wing–Tail Interference Effects6.4.3 Estimating the Wing’s Maximum Lift Coefficient6.4.4 Drag Estimation6.5 Estimating the Longitudinal Aerodynamic Derivatives6.6 Estimating the Lateral Aerodynamic Derivatives6.7 Perturbation Analysis of Trimmed Flight6.7.1 Perturbation Analysis of Longitudinal Trimmed Flight6.7.2 Perturbation Analysis of Lateral Trimmed Flight6.7.2.1 Control Settings for Steady Sideslip6.7.2.2 Control Settings for Turn Coordination and Banking6.7.3 Perturbations of Coupled Trimmed Flight6.7.4 Simplified Analysis of Complex Manoeuvres: The Sidestep ManoeuvreChapter HighlightsExercisesAnswers to Selected ExercisesNoteReferences
Chapter 7 Aircraft Dynamic Response: Numerical Simulation and Non-Linear Phenomenon
7.1 Introduction7.2 Longitudinal and Lateral Modal Equations7.3 Methods of Computing Aircraft Dynamic Response7.3.1 Laplace Transform Method7.3.2 Aircraft Response Transfer Functions7.3.3 Direct Numerical Integration7.4 System Block Diagram Representation7.4.1 Numerical Simulation of Flight Using MATLAB®/Simulink®7.5 Atmospheric Disturbance: Deterministic Disturbances7.6 Principles of Random Atmospheric Disturbance Modelling7.6.1 White Noise: Power Spectrum and Autocorrelation7.6.2 Linear Time-Invariant System with Stochastic Process Input7.7 Application to Atmospheric Turbulence Modelling7.8 Aircraft Non-Linear Dynamic Response Phenomenon7.8.1 Aircraft Dynamic Non-Linearities and Their Analysis7.8.2 High-Angle-of-Attack Dynamics and Its Consequences7.8.3 Post-Stall Behaviour7.8.4 Tumbling and Autorotation7.8.5 Lateral Dynamic Phenomenon7.8.6 Flat Spin and Deep Spin7.8.7 Wing Drop, Wing Rock and Nose Slice7.8.8 Fully Coupled Motions: The Falling Leaf7.8.9 Regenerative PhenomenonChapter HighlightsExercisesReferences
Chapter 8 Aircraft Flight Control
8.1 Automatic Flight Control Systems: An Introduction8.2 Functions of a Flight Control System8.3 Integrated Flight Control System8.3.1 Guidance System: Interfacing to the Automatic Flight Control System8.3.2 Flight Management System8.4 Flight Control System Design8.4.1 Block Diagram Algebra8.4.2 Return Difference Equation8.4.3 Laplace Transform8.4.4 Stability of Uncontrolled and Controlled Systems8.4.5 Routh’s Tabular Method8.4.6 Frequency Response8.4.7 Bode Plots8.4.8 Nyquist Plots8.4.9 Stability in the Frequency Domain8.4.10 Stability Margins: Gain and Phase Margins8.4.11 Mapping Complex Functions and Nyquist Diagrams8.4.12 Time Domain: State Variable Representation8.4.13 Solution of the State Equations and the Controllability Condition8.4.14 State-Space and Transfer Function Equivalence8.4.15 Transformations of State Variables8.4.16 Design of a Full-State Variable Feedback Control Law8.4.17 Root Locus Method8.4.18 Root Locus Principle8.4.19 Root Locus Sketching Procedure8.4.20 Producing a Root Locus Using MATLAB®8.4.21 Application of the Root Locus Method: Unity Feedback with a PID Control Law8.5 Optimal Control of Flight Dynamics8.5.1 Compensating Full-State Feedback: Observers and Compensators8.5.2 Observers for Controller Implementation8.5.3 Observer Equations8.5.4 Special Cases: Full- and First-Order Observers8.5.5 Solving the Observer Equations8.5.6 Luenberger Observer8.5.7 Optimisation Performance Criteria8.5.8 Good Handling Domains of Modal Response Parameters8.5.9 Cooper–Harper Rating Scale8.6 Application to the Design of Stability Augmentation Systems and Autopilots8.6.1 Design of a Pitch Attitude Autopilot Using PID Feedback and the Root Locus Method8.6.2 Example of Pitch Attitude Autopilot Design for the Lockheed F104 by the Root Locus Method8.6.3 Example of Pitch Attitude Autopilot Design, Including a Stability Augmentation Inner Loop, by the Root Locus Method8.6.4 Design of an Altitude Acquire-and-Hold Autopilot8.6.5 Design of a Lateral Roll Attitude Autopilot8.6.6 Design of a Lateral Yaw Damper8.6.7 Design of a Lateral Heading Autopilot8.6.8 Turn Coordination with Sideslip Suppression8.6.9 Application of Optimal Control to Lateral Control Augmentation Design8.7 Performance Assessment of a Command or Control Augmentation System8.8 Linear Perturbation Dynamics Flight Control Law Design by Partial Dynamic Inversion8.8.1 Design Example of a Longitudinal Autopilot Based on Partial Dynamic Inversion8.9 Design of Controllers for Multi-Input Systems8.9.1 Design Example of a Lateral Turn Coordination Using the Partial Inverse Dynamics Method8.9.2 Design Example of the Simultaneously Operating Auto-Throttle and Pitch Attitude Autopilot8.9.3 Two-Input Lateral Attitude Control Autopilot8.10 Decoupling Control and Its Application: Longitudinal and Lateral Dynamics Decoupling Control8.11 Full Aircraft Six-DOF Flight Controller Design by Dynamic Inversion8.11.1 Control Law Synthesis8.11.2 Example of Linear Control Law Synthesis by Partial Dynamic Inversion: Fully Propulsion-Controlled MD11 AircraftChapter HighlightsExercisesAnswers to Selected ExercisesReferences
Chapter 9 Piloted Simulation and Pilot Modelling
9.1 Introduction9.2 Piloted Flight Simulation9.2.1 Full Moving-Base Simulation: The Stewart Platform9.2.2 Kinematics of Motion Systems9.2.3 Principles of Motion Control9.2.4 Motion Cueing Concepts9.3 Principles of Human Pilot Physiological Modelling9.3.1 Auricular and Ocular Sensors9.4 Human Physiological Control Mechanisms9.4.1 Crossover Model9.4.2 Neal–Smith Criterion9.4.3 Pilot-Induced Oscillations9.4.4 PIO Categories9.4.5 PIOs Classified under Small Perturbation Modes9.4.6 Optimal Control Models9.4.7 Generic Human Pilot Modelling9.4.8 Pilot–Vehicle Simulation9.5 Spatial Awareness9.5.1 Visual Displays9.5.2 Animation and Visual Cues9.5.3 Visual IllusionsChapter HighlightsExercisesReferences
Chapter 10 Flight Dynamics of Elastic Aircraft
10.1 Introduction10.2 Flight Dynamics of Flexible Aircraft10.3 Newton–Euler Equations of a Rigid Aircraft10.4 Lagrangian Formulation10.4.1 Generalised Coordinates and Holonomic Dynamic Systems10.4.2 Generalised Velocities10.4.3 Virtual Displacements and Virtual Work10.4.4 Principle of Virtual Work10.4.5 Euler–Lagrange Equations10.4.6 Potential Energy and the Dissipation Function10.4.7 Euler–Lagrange Equations of Motion in Quasi-Coordinates10.4.8 Transformation to Centre of Mass Coordinates10.4.9 Application of the Lagrangian Method to a Rigid Aircraft10.5 Vibration of Elastic Structures in a Fluid Medium10.5.1 Effects of Structural Flexibility in Aircraft Aeroelasticity10.5.2 Wing Divergence10.5.3 Control Reversal10.5.4 Wing Flutter10.5.5 Aerofoil Flutter Analysis10.6 Unsteady Aerodynamics of an Aerofoil10.7 Euler–Lagrange Formulation of Flexible Body Dynamics10.8 Application to an Aircraft with a Flexible Wing Vibrating in Bending and Torsion10.8.1 Longitudinal Small Perturbation Equations with Flexibility10.8.2 Lateral Small Perturbation Equations with Flexibility10.9 Kinetic and Potential Energies of the Whole Elastic Aircraft10.9.1 Kinetic Energy10.9.2 Simplifying the General Expression10.9.3 Mean Axes10.9.4 Kinetic Energy in terms of Modal Amplitudes10.9.5 Tisserand Frame10.10 Euler–Lagrange Matrix Equations of a Flexible Body in Quasi-Coordinates10.11 Slender Elastic Aircraft10.12 Aircraft with a Flexible Flat Body Component10.12.1 Elastic Large Aspect Ratio Flying Wing Model10.12.2 Flexible Aircraft in Roll10.13 Estimating the Aerodynamic Derivatives: Modified Strip AnalysisChapter HighlightsExercisesAnswers to Selected ExercisesReferences
Chapter 11 Dynamics and Control of Drones and Unmanned Aerial Vehicles
11.1 Introduction11.2 Dynamics of a Generic Drone11.3 Rigid Body Kinematics11.3.1 Defining the Body Frame11.3.2 Defining the Body Angular Velocity Components11.4 Translational Dynamics11.5 Attitude Dynamics11.6 Attitude Kinematics11.6.1 The Quaternion Representation of the Attitude11.6.2 The Relations between Quaternion Rates and Angular Velocities11.7 Aerodynamic Forces11.8 Propulsion-Based Control11.9 Stability and Control11.10 Automatic Flight Control11.11 Autonomous Flight Control11.12 The Quadrotor Drone11.12.1 Dynamics of the Quadrotor Drone11.12.2 Quadrotor Control Allocation11.12.3 Quadrotor Control Strategies11.12.4 PID Control of a Quadrotor11.13 Optimal Controller Synthesis for Drones11.14 Unconventional Multi-Rotor Drones11.14.1 Quadrotors with Bi-Directional Motors11.14.2 Quadcopters: Dynamics of the Quadcopter11.14.3 Body Forces and Body Moments Acting on a Quadcopter11.14.4 The Unsymmetrically Actuated Quadcopter11.14.5 The Pentacopter11.14.6 Equations of Motion of a Pentacopter11.14.7 The Hexa-Rotor and the Hexa-copter11.14.8 Dynamics of a Hexa-Rotor Drone11.14.9 The Basic Hexa-Rotor Configuration: Derivation of the Body Forces and Moments11.14.10 Alternate Tri-Axial Multi-Rotor Configurations11.14.11 The Hexa-Rotor Configuration with Two Rotors Tilted: The Hexa-copter11.14.12 A Hexa-copter with Three Tilt-Controlled Rotors11.14.13 Six DOFs Configuration: Derivation of the Body Forces and Moments11.14.14 Control of a Fully Actuated Hexa-rotor Drone: Decoupling11.14.15 The Octocopter and Over-Actuated Multi-Rotor Drones11.14.16 Dynamics of an Octocopter Drone11.14.17 Nonlinear and Linear Dynamic Modelling of Multi-Rotor Drones11.14.18 H∞ Optimal Control of an Octocopter drone11.14.19 Typical Simulation Example11.15 Drones and Unmanned Aerial Vehicles with Aerodynamic Lifting SurfacesChapter HighlightsExercisesReferences
Index

Content preview from Flight Dynamics, Simulation, and Control, 2nd Edition

5 Small Perturbations and the Linearised, Decoupled Equations of Motion

DOI: 10.1201/9781003266310-5

5.1 Introduction

Although we have already derived linear dynamic equations of motion about a steady equilibrium flight, as discussed in Chapter 4, we shall examine the derivation process in some detail in this chapter. This is essential particularly as it is important to understand the limitations of such approximations and the context in which they may be applied.

5.2 Small Perturbations and Linearisations

The small perturbation approximations, compatible with conditions of trim, are now introduced. The aircraft’s velocities and angular velocities are perturbed by a steady-operating condition. Thus, the perturbations satisfy

$[\begin{matrix} u \\ v \\ w \end{matrix}] = [\begin{matrix} U_{e} \end{matrix}$

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