Modelling and

Open Loop Simulation of

Reentry Trajectory for RLV Missions

Ashok Joshi and K. Sivan

Department of Aerospace Engineering

Indian Institute of Technology Bombay

4TH International Symposium on

ATMOSPHERIC REENTRY VEHICLES & SYSTEMS

ARCACHON, FRANCE, 21-23 March 2005

Motivation, Aim and Scope• Atmospheric reentry phase is expected to

dissipate large orbital energy, efficiently

• Reentry phase is also an uncertain domain with respect to aerodynamics, propulsion and control

• Present study proposes mathematical models that reflect the complexity and at the same time retain the ease of their simulation

• A generic RLV is taken up for development of model and verification through simulations

RLV Configuration

• Wing-Body Configuration with both Aerodynamic and Reaction Control System

• Both FADS and SIGI Sensors• Total of seven aerodynamic control surfaces

i.e. 4 Elevons, one each of Body Flap, Rudder and Speed Brake

Generic RLV Dynamic Model

Coordinate Systems Definition Vehicle Attitude Definition Coordinate Transformation

Environmental Model

- Earth shape- Gravity- Atmosphere- Wind

Vehicle Model- Aerodynamics- Propulsion- Mass Properties

Subsystem Model

- Sensors- Navigation- Actuators

Dynamics- Translational- Rotational- Kinematics

Guidance & Control

YBR XBR

BRZ

BX

OB

BZ

YB

Inertial Coordinate System

Body Coordinate System

Inertial / Body Coordinates

Wind Axis System

Vehicle Attitude Coordinates

Euler Angles

Aerodynamic Model Coefficient Based

Propulsion Model Atmospheric corrections

Vehicle Models

dynrefref

n

m

l

A qSb

C

C

C

M

dynref

N

Y

A

A qS

C

C

C

F

ieaieivi AppTT )(

ii

ii

i

iiT

SS

CS

C

TF

Sensors 2nd order dynamics

Navigation 2 Error ModelsLarger errors for pure inertial NavigationSmaller errors for combined Navigation

Actuators 2nd order dynamics

Subsystem Models

22

2

0 2 nn

ni

ssp

p

22

2

2 ncncc

nc

c

s

ss

Other Models

Earth• Oblate Earth with zonal harmonics up to 4th Jeffrey term considered

Atmosphere• pa , r , T, Cs as functions of altitude• Flexibility of defining any atmosphere

Wind• Zonal and Meridional components

Simulation Algorithm Schematic

Atmospheric Model

Earth Model

Gravity Model

Aero Parameters Model

Flight Dynamics

Kinematics

Mass Properties

Aerodynamic Model

INS Sensor

Simulator

GPS Simulator

Propulsion Model

Air DataSimulator Actuator

Dynamics RCS

Simulator Navigation Package

Flight Control Guidance

Open Loop Simulation Method Reentry trajectory modulation by aerodynamic angles

Simulation by perturbing angles , &

Assumption: Ideal control

Parameters monitored:Input : , & Output : h, VR, ground trace (lat – / long –

)

Test casesCase-1 : Bank angle = 0Case-2 : 10o change in Case-3 : 10o change in Case-4 : 10o change in

Open Loop Simulation: = 0

-10

-5

0

5

10

0 500 1000 1500 2000

Time (s)

(d

eg)

-50

0

50

100

0 500 1000 1500 2000

Bank = 0Nominal Bank

(deg

)

0

10

20

30

40

50

0 500 1000 1500 2000

(d

eg)

Control Inputs

Open Loop Simulation: = 0

0

50

100

150

200

0 1000 2000 3000

Bank = 0Nominal

h (km

)

0

2000

4000

6000

8000

0 1000 2000 3000

Bank = 0Nominal

Time (s)

VR (m

/s)

Time Histories

Open Loop Simulation: = 0

-20

-15

-10

-5

0

0 50 100 150

Bank = 0Nominal

(deg)

(deg)

Ground Trace

Open Loop Simulation: = 10

0

10

20

30

40

50

0 500 1000 1500 2000

Alpha PerturbedNominal

(d

eg)

-50

0

50

100

0 500 1000 1500 2000

(d

eg)

-10

-5

0

5

10

0 500 1000 1500 2000

Time (s)

(d

eg)

Control Inputs

Open Loop Simulation: = 10

0

30

60

90

120

150

0 500 1000 1500 2000 2500

Alpha PerturbedNominal

h (km

)

0

2000

4000

6000

8000

0 500 1000 1500 2000 2500

Alpha PerturbedNominal

Time (s)

VR (m

/s)

Time Histories

Open Loop Simulation: = 10

-30

-20

-10

0

0 20 40 60 80

Alpha PerturbedNominal

(deg)

(deg)

Ground Trace

Open Loop Simulation: = 10

0

10

20

30

40

50

0 500 1000 1500 2000

(d

eg)

-10

-5

0

5

10

0 500 1000 1500 2000

Time (s)

(d

eg)

-50

0

50

100

0 500 1000 1500 2000

Bank PerturbedNominal

(deg

)

Control Inputs

Open Loop Simulation: = 10

0

30

60

90

120

150

0 500 1000 1500 2000

Bank PerturbedNominal

Time (sec)

h (km

)

0

2000

4000

6000

8000

0 500 1000 1500 2000

Bank PerturbedNominal

Time (s)

VR (m

/s)

Time Histories

Open Loop Simulation: = 10

-20

-15

-10

-5

0

0 10 20 30 40

Bank PerturbedNominal

(deg)

(deg)

Ground Trace

Open Loop Simulation: = 10

-50

0

50

100

0 500 1000 1500 2000

(d

eg)

-10

0

10

20

0 500 1000 1500 2000

With BetaNominal

Time (s)

(d

eg)

0

10

20

30

40

50

0 500 1000 1500 2000

(d

eg)

Control Inputs

Open Loop Simulation: = 10

0

30

60

90

120

150

0 500 1000 1500 2000

With BetaNominal

h (km

)

0

2000

4000

6000

8000

0 500 1000 1500 2000

With BetaNominal

Time (sec)

VR (m

/sec

)

Time Histories

Open Loop Simulation: = 10

-20

-15

-10

-5

0

0 10 20 30 40

With BetaNominal

(deg)

(deg)

Ground Trace

Conclusions

• Generalized 6-DOF Reentry Flight Dynamic Model of a Generic RLV is evolved

• Multiple coordinate systems are used for ease of representation

• Both RCS and Aerodynamic control surfaces are included, along with Flush Air Data Sensor and GPS

• 3-DOF Comparison with literature data validates the model & solution methodology

• Open loop simulations provide adequacy and sensitivity of the model presented