1. ATMOSPHERIC REENTRY TRAJECTORY MODELING AND SIMULATION: APPLICATION TO REUSABLE LAUNCH VEHICLE MISSION (Progress Seminar Presentation - 2) K. Sivan (Roll No. 01401703) Department of Aerospace Engineering IIT Bombay August 2003

2. PROBLEM DEFINITION Return Mission of RLV Reentry Trajectory Planning and Trajectory Control Literature survey on RLV mission configuration, reentry models, trajectory planning algorithms Generic RLV Configuration definition Reentry trajectory simulator development Trajectory planning and trajectory control algorithm development, robustness studiy and performance evaluation

3. CONFIGURATION SELECTION AND SIMULATOR DESIGN CRITERIA Generic RLV configuration definition - Complete aerodynamic characterization - Mass properties - Consistent vehicle characteristics and configuration Reentry Trajectory Simulator * Need to Simulate Reentry Dynamics of RLV - 3 DOF translational dynamics (CM motion in 3-D space) - 3 DOF angular dynamics (Angular motion about CM) * Simulator should be - Realistic (Models response close to the actual ones) - Generalized (All the phases of RLV/Any RLV/ Any application – 3DOF or 6 DOF) - Avoid computational difficulties (singularities) - Provision for future expansion - Validation of the simulator

4. GENERIC RLV CONFIGURATION Literature configuration - Configuration available - Complete characteristics not available in single literature - Overall information is available in bits and pieces - Finer details not available (not possible) RLV study configurations of ISRO - Finer details can be used for the studies - Mass properties can be used - But the total aerodynamic characterization is not ready Generic RLV configuration - One of the RLV study configurations of ISRO - Aerodynamic characteristics of different literature combined to form full set - Fine details if required can be used from RLV study configurations

5. GENERIC RLV CONFIGURATION

6. REENTRY TRAJECTORY SIMULATOR 6 DOF reentry dynamics influenced by external forces & moments Emphasis - Realistic models to simulate forces & moments - Simulation of vehicle & trajectory dynamics using these forces & moments

7. DEFINITION & MODEL REQUIREMENTS OF REENTRY TRAJECTORY SIMULATOR Definitions - Represent data * Coordinate System Definition - Represent forces & moments - Represent Dynamics - Attitude definitions w.r.t ref. frames * Vehicle Attitude Definition - Commands for control (for trajectory & attitude) - Simulation measurements on vehicle onboard * Coordinate Transformation - To transfer data between ref. frames

8. DEFINITION & MODEL REQUIREMENTS OF REENTRY TRAJECTORY SIMULATOR - Contd... Models - Earth Geometry * Environment Model - Gravitation model (Vehicle operating environment)- Atmosphere model - Wind model - Mass properties * Vehicle Model - Propulsion systems model (Main & RCS) - Aerodynamics model - Sensors * Vehicle Subsystem Model - Navigation (Systems to command vehicle - Guidance & control algorithm control & trajectory)- Actuators * Vehicle Dynamics Model - Translational dynamics & kinematics - Attitude dynamics & kinematics

9. COORDINATE SYSTEMS & ATTITUDE DEFINITIONS Coordinate Systems

10. Body Coordinate System COORDINATE SYSTEMS & ATTITUDE DEFINITIONS – Contd…

11. Aerodynamic Wind Frame COORDINATE SYSTEMS & ATTITUDE DEFINITIONS – Contd…

12. Definition of Relative Euler Angles COORDINATE SYSTEMS & ATTITUDE DEFINITIONS – Contd…

13. COORDINATE TRANSFORMATIONS

14. EARTH MODEL Oblate Earth with zonal harmonics up to J4 term considered Altitude corresponding to oblate Earth Gravitational potential in ECI frame Gravity acceleration in ECI frame

15. ATMOSPHERE MODEL * General Look up table - p a, r, T, C s as function of altitude - Flexibility of inputting any atmosphere - C s and r as optional * Properties from temperature profile - Assumption : (g/RL z ) constant WIND MODEL * Input data in G-frame - Zonal - Meridional - Vertical * Convert into ECI frame

16. VEHICLE MODEL (1) Aerodynamic Model * Allow to build up to any configuration and flight condition * General model – can be used in all phases of RLV mission C x = Basic coefficient + Increment due to control surface deflection ( elevator, aileron, body flap, rudder, speed brake) + Increment due to dynamic conditions (a-dot, b-dot, p, q, r) + Increment due to vehicle flexibility + Increment due to landing gear extension + Increment due to ground effects * Forces & moments coefficients expressed in body frame

17. VEHICLE MODEL– contd…. (2) Propulsion Model * Rocket motors/engines with atmospheric corrections * General model for n engines * General thrust orientation and location w.r.t body frame * Total forces and moments w.r.t body frame (3) Mass Properties Model * Mass update due to - Engine burning - Continuous reduction of inert mass - Jettisonable mass * CM updated through input data (function of propellant mass) * Moments & products of inertia updated through input data (function of propellant mass) * for general configuration

18. VEHICLE SUBSYSTEM MODEL (1) Sensors * Sensor parameters at sensor location * Sensor response – 2 nd order dynamics * Sensor output errors (2) Navigation * Different navigation output for black out & normal phases (3) Actuators * Actuators response – 2 nd order dynamics * RCS – on-off characteristics (4) Guidance & Control Algorithm * To be included as external block

19. VEHICLE DYNAMICS * Translational Dynamics - Spherical Coordinate System: Singularity at latitude + p/2 - Rotating frame: Inertial forces > actual forces * Rotational Dynamics - All moments in body frame - Inertia constant in body frame * Rotational Kinematics - Angular representation (Euler or a/d angles): Singularity at p/2 for middle rotation Translational dynamics & kinematics in ECI frame Rotational dynamics in body frame Quaternion approach

20. SIMULATION STRUCTURE

21. VALIDATION OF THE SIMULATOR TOOL 1.Module level tests 2.Comparison with analytical solutions 3.Comparison with reference trajectory

22. COMPARISON WITH ANALYTICAL SOLUTION Initial ConditionsLocation of Landing Point Results of the SimulatorAnalytical Solution Case-1 h(km) 130.2608205 v(m/s) 5426.6656766 g(deg) 1.5024290 Az(deg) 104.4896320 Latitude(deg) 12.2604888 Longitude(deg) 85.464222 Case-2 h (km) 247.2606513 v (m/s) 4079.9528041 g (deg) 19.7724067 Az (deg) 169.9938794 Latitude (deg) 10.4675403 Longitude(deg) 81.5471406 Case-3 h (km) 162.3515483 v (m/s) 7757.2258785 g (deg) 0.5346059 Az (deg) 105.4645370 Latitude (deg) 8.8041388 Longitude(deg) 99.4491961 Latitude (deg) : 8.8448351 Longitude(deg): 96.743040 Latitude (deg) : -7.1769368 Longitude(deg): 82.3525617 Latitude (deg) : -9.2499092 Longitude(deg): 266.9832884 8.8449329 96.7427399 -7.1765934 82.3525419 -9.2500764 266.9827025

23. COMPARISON WITH REFERENCE TRAJECTORY OF RLV * Space Shuttle (not in single literature) 3 DOF validation Ideal control mode (Aerodynamic angles – command values) Sufficient for validating guidance performance evaluation

24. SIMULATOR RESULTS Assumption: - Space shuttle aerodynamics - mass properties of space shuttle - Ideal control

25. SIMULATION STUDIES * Trajectory planning & trajectory Control through aerodynamic angle modulations * Study carried out to estimate the effectiveness - Without  command profile - Perturbing  command profile - Perturbing  command profile - Perturbing  command profile

26. APPLICATIONS OF THE SIMULATOR (1)Good test bed for evaluating Navigation, Guidance and Control algorithms of reentry flight (2)Fully nonlinear 6 DOF simulation and analysis of reentry vehicle (3)Robust control and guidance analysis of the vehicle (4)Suitable for model linearization analysis (useful for classical and modern control approaches)

27. Further Developments Development of an adaptive trajectory planning algorithm Algorithm based on Predictor-Corrector method –Target : Altitude, Latitude, Longitude at TAEM interface. – Control variable : ,  and time of Bank reversal –Constraints: Dynamic pressure, Normal load, Heat flux, Equilibrium glide

28. Proposed Method Propagate trajectory to TAEM through numerical integration The target errors are used to correct the control variables The process is repeated until the errors are less than acceptable Advantages Equations of motion are explicitly modeled State vectors available at every instant - constraints are activated directly No separate trajectory control law (both trajectory planning and trajectory control combined)

29. Disadvantages Computational load more –Present day computers can handle –Computational cycle can be increased Risk of convergence

30. PLAN OF ACTION Development of trajectory planningFeb, 04 Implementation of the algorithmMar, 04 Robustness studyMay, 04 MC analysis for performance Evaluation June, 04

31. THANK YOU