Performance Evaluation and Design of Flight Vehicle Control Systems

Eric T. Falangas was a Lead Engineer/ Specialist and Project Manager at Boeing, Rockwell International and Aerospace Corporation in the fields of flight control design, spacecraft attitude control, vibration control and active vibration isolation, and other control and dynamics related projects. He received a BS in Electrical Engineering from the University of London and a MS in Control Systems from the University of Manchester Institute of Science and Technology. Eric has published several papers in magazines and conferences and was awarded 4 patents for developing active vibration control systems using piezo-electric actuator devices, and Flixan, which is a flight vehicle modelling and performance evaluation methodology, implemented in a Windows based program.

• Preface xi Acknowledgments xiiiIntroduction 11 Description of the Dynamic Models 71.1 Aerodynamic Models, 81.2 Structural Flexibility, 91.3 Propellant Sloshing, 101.4 Dynamic Coupling between Vehicle, Actuators, and Control Effectors, 121.5 Control Issues, 131.6 Coordinate Axes, 15Nomenclature, 162 Nonlinear Rigid-Body Equations Used in 6-DOF Simulations 192.1 Force and Acceleration Equations, 192.2 Moment and Angular Acceleration Equations, 212.3 Gravitational Forces, 222.4 Engine TVC Forces, 222.5 Aerodynamic Forces and Moments, 242.6 Propellant Sloshing Using the Pendulum Model, 282.7 Euler Angles, 292.8 Vehicle Altitude and Cross-Range Velocity Calculation, 302.9 Rates with Respect to the Stability Axes, 302.10 Turn Coordination, 312.11 Acceleration Sensed by an Accelerometer, 312.12 Vehicle Controlled with a System of Momentum Exchange Devices, 322.13 Spacecraft Controlled with Reaction Wheels Array, 332.14 Spacecraft Controlled with an Array of Single-Gimbal CMGs, 372.14.1 Math Model of a SGCMG Array, 382.14.2 Steering Logic for a Spacecraft with SGCMGs, 423 Linear Perturbation Equations Used in Control Analysis 473.1 Force and Acceleration Equations, 473.2 Linear Accelerations, 483.3 Moment and Angular Acceleration Equations, 503.4 Gravitational Forces, 513.5 Forces and Moments due to an Engine Pivoting and Throttling, 523.6 Aerodynamic Forces and Moments, 583.7 Modeling a Wind-Gust Disturbance, 703.8 Propellant Sloshing (Spring–Mass Analogy), 733.9 Structural Flexibility, 803.9.1 The Bending Equation, 853.10 Load Torques, 903.10.1 Load Torques at the Nozzle Gimbal, 913.10.2 Hinge Moments at the Control Surfaces, 933.11 Output Sensors, 973.11.1 Vehicle Attitude, Euler Angles, 973.11.2 Altitude and Cross-Range Velocity Variations, 983.11.3 Gyros or Rate Gyros, 983.11.4 Acceleration Sensed by an Accelerometer, 1003.11.5 Angle of Attack and Sideslip Sensors, 1013.12 Angle of Attack and Sideslip Estimators, 1023.13 Linearized Equations of a Spacecraft with CMGs in LVLH Orbit, 1043.14 Linearized Equations of an Orbiting Spacecraft with RWA and Momentum Bias, 1063.15 Linearized Equations of Spacecraft with SGCMG, 1074 Actuators for Engine Nozzles and Aerosurfaces Control 1094.1 Actuator Models, 1114.1.1 Simple Actuator Model, 1124.1.2 Electrohydraulic Actuator, 1144.1.3 Electromechanical Actuator, 1184.2 Combining a Flexible Vehicle Model with Actuators, 1234.3 Electromechanical Actuator Example, 1265 Effector Combination Logic 1375.1 Derivation of an Effector Combination Matrix, 1385.1.1 Forces and Moments Generated by a Single Engine, 1395.1.2 Moments and Forces Generated by a Single Engine Gimbaling in Pitch and Yaw, 1415.1.3 Moments and Forces of an Engine Gimbaling in a Single Skewed Direction, 1425.1.4 Moments and Forces Generated by a Throttling Engine or an RCS Jet, 1435.1.5 Moment and Force Variations Generated by a Control Surface Deflection from Trim, 1445.1.6 Vehicle Accelerations due to the Combined Effect from all Actuators, 1455.2 Mixing-Logic Example, 1475.3 Space Shuttle Ascent Analysis Example, 1525.3.1 Pitch Axis Analysis, 1535.3.2 Lateral Axes Flight Control System, 1635.3.3 Closed-Loop Simulation Analysis, 1686 Trimming the Vehicle Effectors 1716.1 Classical Aircraft Trimming, 1716.2 Trimming along a Trajectory, 1726.2.1 Aerodynamic Moments and Forces, 1766.2.2 Moments and Forces from an Engine Gimbaling in Pitch and Yaw, 1786.2.3 Numerical Solution for Calculating the Effector Trim Deflections and Throttles, 1806.2.4 Adjusting the Trim Profile along the Trajectory, 1837 Static Performance Analysis along a Flight Trajectory 1877.1 Transforming the Aeromoment Coefficients, 1887.2 Control Demands Partial Matrix (CT), 1887.2.1 Vehicle Moments and Forces Generated from a Double-Gimbaling Engine, 1907.2.2 Vehicle Moments and Forces Generated by an Engine Gimbaling in Single Direction, 1917.2.3 Moment and Force Variations Generated by a Throttling Engine, 1917.2.4 Vehicle Moments and Forces Generated by Control Surfaces, 1927.2.5 Total Vehicle Moments and Forces due to All Effectors Combined, 1927.3 Performance Parameters, 1947.3.1 Aerodynamic Center, 1947.3.2 Static Margin, 1957.3.3 Center of Pressure, 1957.3.4 Pitch Static Stability/Time to Double Amplitude Parameter (T2), 1957.3.5 Derivation of Time to Double Amplitude, 1967.3.6 Directional Stability (Cn𝛽-dynamic), 1977.3.7 Lateral Static Stability/Time to Double Amplitude Parameter (T2), 1987.3.8 Authority of the Control Effectors, 1987.3.9 Biased Effectors, 2007.3.10 Control to Disturbance Moments Ratio (M𝛼/M𝛿), 2017.3.11 Pitch Control Authority Against an Angle of Attack 𝛼max Dispersion, 2017.3.12 Lateral Control Authority Against an Angle of Sideslip 𝛽max Disturbance, 2037.3.13 Normal and Lateral Loads, 2047.3.14 Bank Angle and Side Force During a Steady Sideslip, 2047.3.15 Engine-Out or Ycg Offset Situations, 2057.3.16 Lateral Control Departure Parameter, 2067.3.17 Examples Showing the Effects of LCDP Sign Reversal on Stability, 2097.3.18 Effector Capability to Provide Rotational Accelerations, 2117.3.19 Effector Capability to Provide Translational Accelerations, 2127.3.20 Steady Pull-Up Maneuverability, 2127.3.21 Pitch Inertial Coupling Due to Stability Roll, 2147.3.22 Yaw Inertial Coupling Due to Loaded Roll, 2157.3.23 Moments at the Hinges of the Control Surfaces, 2167.4 Notes on Spin Departure (By Aditya A. Paranjape), 2177.4.1 Stability-Based Criteria, 2177.4.2 Solution-Based Criteria, 2207.5 Appendix, 224References, 2248 Graphical Performance Analysis 2258.1 Contour Plots of Performance Parameters versus (Mach and Alpha), 2258.2 Vector Diagram Analysis, 2288.2.1 Maximum Moment and Force Vector Diagrams, 2298.2.2 Maximum Acceleration Vector Diagrams, 2338.2.3 Moment and Force Partials Vector Diagrams, 2348.2.4 Vector Diagram Partials of Acceleration per Acceleration Demand, 2388.3 Converting the Aero Uncertainties from Individual Surfaces to Vehicle Axes, 2398.3.1 Uncertainties in the Control Partials, 2418.3.2 Uncertainties due to Peak Control Demands, 2418.3.3 Acceleration Uncertainties, 2439 Flight Control Design 2459.1 LQR State-Feedback Control, 2469.2 H-Infinity State-Feedback Control, 2489.3 H-Infinity Control Using Full-Order Output Feedback, 2499.4 Control Design Examples, 2519.5 Control Design for a Reentry Vehicle, 2519.5.1 Early Reentry Phase, 2539.5.2 Midphase, 2619.5.3 Approach and Landing Phase, 2689.6 Rocket Plane with a Throttling Engine, 2759.6.1 Design Model, 2769.6.2 LQR Control Design, 2779.6.3 Simulation of the Longitudinal Control System, 2789.6.4 Stability Analysis, 2819.7 Shuttle Ascent Control System Redesign Using H-Infinity, 2829.7.1 Pitch Axis H-Infinity Design, 2839.7.2 Lateral Axes H-Infinity Design, 2899.7.3 Sensitivity Comparison Using Simulations, 2949.8 Creating Uncertainty Models, 2989.8.1 The Internal Feedback Loop Structure, 2999.8.2 Implementation of the IFL Model, 30310 Vehicle Design Examples 30510.1 Lifting-Body Space-Plane Reentry Design Example, 30510.1.1 Control Modes and Trajectory Description, 30710.1.2 Early Hypersonic Phase Using Alpha Control, 30710.1.3 Normal Acceleration Control Mode, 31710.1.4 Flight-Path Angle Control Mode, 32910.1.5 Approach and Landing Phase, 34110.1.6 Six-DOF Nonlinear Simulation, 36110.2 Launch Vehicle with Wings, 38110.2.1 Trajectory Analysis, 38210.2.2 Trimming along the Trajectory, 38210.2.3 Trimming with an Engine Thrust Failure, 38510.2.4 Analysis of Static Performance along the Trajectory, 38710.2.5 Controllability Analysis Using Vector Diagrams, 39010.2.6 Creating an Ascent Dynamic Model and an Effector Mixing Logic, 39310.2.7 Ascent Control System Design, Analysis and Simulation, 39310.3 Space Station Design Example, 40010.3.1 Control Design, 40110.3.2 Simulation and Analysis, 405Bibliography 409Index 413