INTRODUCTION. One of the more important close loop systems necessary for guiding and controlling the space launch vehicle is the thrust vector control (TVC) ...
2012 12th International Conference on Control, Automation and Systems Oct. 17-21, 2012 in ICC, Jeju Island, Korea
Modeling and Simulation of a Launch Vehicle Thrust Vector Control System Choong-Seok Oh1 , Byung-Chan Sun, Yong-Kyu Park and Woong-Rae Roh 1
Launcher System Design Department, KARI, Daejeon, Korea (Tel : +82-42-860-2046; E-mail: {csoh, bcsun, kyu2002, rwr}@kari.re.kr)
Abstract: The dynamics associated with the thrust vector control system of the launch vehicle is investigated. The objective of the thrust vector control system is to position the thrust vector to some commanded position. The thrust vector control system is the major source of nonlinearity in the flight control system. The modeling and simulation analysis of the TVC system of a sample engine are presented. Using this modeling method, the preliminary design of TVC system for the 75tf thrust engine is conducted. From the simulation analysis of TVC model for the 75tf thrust engine, the nonlinear response, the stability analysis and the bandwidth of the TVC system are presented. Keywords: Launch vehicle, Thrust vector control,
Electrohydraulic actuation, Actuator modeling
1. INTRODUCTION One of the more important close loop systems necessary for guiding and controlling the space launch vehicle is the thrust vector control (TVC) system. The objective of this TVC system is to position the thrust vector to some commanded position. The thrust vector is the amount of force generated by an engine, or a cluster of engines, for the purpose of lifting the launch vehicle and its pay load to its destination. The engines are mounted to the vehicle stage through a gimbal bearing which is designed to have the engine thrust pivot about the center of the bearing. The engines that are used to change the direction of the resultant thrust vector have two actuators per engine mounted at 90 degrees to each other. These actuators are positioned by a command from the control computer which has scaled the individual signals so that the vehicle can be controlled in pitch, yaw, and roll. The electrohydraulic actuation is usually used as the actuator of TVC system. The power system of the electrohydraulic actuation consists of a primary source using a power takeoff device to utilize free energy and a secondary source using alternate technology. The primary source uses a hydraulic pump driven by the LOX pump. The secondary power is provided by a hydraulic pump driven by a turbine powered by high pressure gas from the engine. The actuator consists of redundant servovalves flow summed to a single power spool. In this paper, the modeling and simulation analysis of the TVC system of a sample engine are presented. Using this modeling method, the preliminary design of TVC system for the 75tf thrust engine is conducted. From the simulation analysis of TVC model for the 75tf thrust engine, the nonlinear response, the stability analysis and the bandwidth of the TVC system are presented.
2. TVC MODELING
Fig. 1 TVC model in linear motion The engine gimbal system of Saturn Launch Vehicle is modeled in Fig. 1. The engine gimbal model is more conveniently dealt with if the system is converted to an equivalent one shown in Fig. 1. The parameters of TVC model are defined as following. The mass M in this figure is the equivalent mass of the engine converted to linear motion. The B is the viscous friction coefficient, A is actuating piston area, F is static friction, K L is actuator structure, load spring constant, K is actuator oil spring constant, K T is total equivalent spring constant, H is conversion constant , K V is servovalve gain, β is ideal piston position, β is actual piston position, β is engine position. Figure 2 shows the TVC system nonlinear block diagram of the sample engine [1]. The nonlinear dynamics equations of TVC system are described as following. a.
M e βe b.
Actuator force equation
D βe
Fg
FL t
KT βi
βe
(1)
Servovalve flow (Q)
QS 3 ( PS + ΔP ) ΔP = +1 QS1 PS + ΔP PS
1/ 2
,
QS 2 ( PS − ΔP) ΔP = −1 QS1 PS − ΔP PS
1/ 2
(2)
0.5deg and load condition. The disturbance load condition is rated load, FL = 34263 + 66746 sin(500 t ) N .
If QS 2 > 0 Q = QS 2 , else Q = QS 3
c.
Actuator position feedback ( β p )
β p = βe +
KT ( βi − β e ) KL
(3)
Fig. 2 TVC system nonlinear block diagram for the sample engine
Table 1 Parameter values for the sample engine
gimballed mass about gimbal point R, Engine actuator moment arm
x p , Stroke
±97
mm
δ max , Angular deflection
±7.95
deg
PS , Hydraulic system supply pressure
20.7
MPa
PR , Hydraulic system reservoir pressure
0.37
MPa
A, Piston area
3.23e-3
m2
FS = A( PS − PR ) = AΔP , Stall force
65.7
kN
Value
Unit
2817
kg
D, Viscous friction coefficient
6000
N m / sec
Fg , Static friction
8.010
kN
1.170e7
N/m
90.7
7.662e7
N/m
908
1.015e7
N/m
in linear motion
constant
tf
K act , Actuator oil, piston spring
constant
kg
KT , Total equivalent spring
constant
2
1373 kg ⋅ m 0.699
mass of engine
K L , Actuator structure, load spring
Value Unit
I R , Engine moment of inertia of
Unit
M e ,Equivalent
Using the TVC modeling method, the TVC model of the sample engine is analyzed. The model parameters and the specification of the sample engine and TVC are shown in Table 1, 2 [1-3].
M R , Rocket engine gimballed mass
Value
Parameter
3.1 TVC for the sample engine
Tc , Control engine thrust
Parameter
Table 3 Parameter values for TVC block diagram of the sample engine
3. SIMULATION AND ANALYSIS
Parameter
Table 2 Parameter values for TVC of sample engine
m
The parameter values of the nonlinear TVC block diagram are shown in Table 3. From the linear TVC block diagram, the transfer function of β e / β c is given by 0.053s + 1 βe = × β c ( s / 283 + 1)( s / 40.39 + 1)( s /15.01 + 1) 1
(3)
( s 2 / 258.652 + 2(0.77) / 258.65s + 1)(s 2 / 49.712 + 2(0.19) / 49.71s + 1)
The bandwidth at -3dB is 9.45Hz, and the phase bandwidth at -90deg is 5.43Hz for no load condition. The frequency response for load condition can be obtained from the nonlinear simulation. Figure 3 and Table 4 show the simulation result for the bode diagram. The bandwidth at -3dB is 8.86Hz, and the phase bandwidth at -90deg is 5.0Hz for the actuator input of
Fig. 3 Bode diagram for TVC of the sample engine (Rated load condition) The linear TVC block diagram using the dynamic
pressure feedback (DPF) is expressed as Fig. 4. Using this linear TVC block, the roots locus, the gain and phase margin, the Nyquist diagram can be obtained as shown in Fig. 5. The gain and phase margin are increased using the DPF loop as shown Table 5. For the lower resonance frequency of the actuator structure, the dynamic pressure feedback (DPF) is needed to augment the gain and phase margin. Table 4 Bandwidth for TVC of the sample engine Gain Bandwidth Phase Bandwidth Input (deg) ( at -3dB) ( at -90deg) 0.25
9.24Hz
5.00Hz
0.5
8.86Hz
5.00Hz
1.0
7.20Hz
4.17Hz
3.0
2.53Hz
3.23Hz
Fig. 4 TVC linear block with DPF loop Table 5 Gain and phase margin for TVC of the sample engine Gain margin(dB) Phase margin(deg) without DPF
-0.18
3.66
with DPF
9.23
71.6
Fig. 5 Roots locus, gain and phase margin, Nyquist diagram for TVC of the sample engine 3.2 TVC for the 75tf thrust Using the analysis method in the TVC model of the sample engine, the TVC model of the 75tf thrust engine is analyzed. The model parameters and the specification of the 75tf thrust engine and TVC are shown in Table 6, 7. Table 6 Parameter values for the 75tf thrust engine Parameter
Value Unit
Tc , Control engine thrust
76
tf
M R , Rocket engine gimballed mass
585
kg
I R , Engine moment of inertia of gimballed mass about gimbal point R, Engine actuator moment arm
560 kg ⋅ m2 0.53
m
Table 7 Parameter values for TVC of the 75tf thrust engine Parameter
Value
Unit
x p , Stroke
±55.5
mm
δ max , Angular deflection
±6.0
deg
PS , Hydraulic system supply pressure
11.34
MPa
PR , Hydraulic system reservoir pressure
0.25
MPa
A, Piston area
5.79e-3
m2
FS = A( PS − PR ) = AΔP , Stall force
64.3
kN
TS = FS R , Stall torque
34.1
kNm
The parameter values of the nonlinear TVC block diagram are shown in Table 8. From the linear TVC block diagram, the transfer function of β e / β c is given by 0.053s + 1 βe = × β c 108.11( s / 254.64 + 1)( s / 73.77 + 1)( s /16.73 + 1)
(3)
1 ( s 2 / 247.632 + 2(0.77) / 247.63s + 1)(s 2 / 68.82 2 + 2(0.34) / 68.82 s + 1)
The bandwidth at -3dB is 12.33Hz, and the phase bandwidth at -90deg is 6.68Hz for no load condition. The frequency response for load condition can be obtained from the nonlinear simulation. Figure 6 shows the simulation result for the bode diagram. The bandwidth at -3dB is 9.30Hz, and the phase bandwidth at -90deg is 5.72Hz for the actuator input of 0.5deg and load condition as shown in Table 9. The disturbance load condition is rated load, FL = 38253 + 66746 sin(500 t ) N . Table 8 Parameter values for TVC block diagram of the 75tf thrust engine Parameter
Value
Unit
1994
kg
D, Viscous friction coefficient
6000
N m / sec
Fg , Static friction
4.647
kN
1.996e7
N/m
1.078e8
N/m
1.685e7
N/m
M e ,Equivalent
mass of engine
in linear motion
K L , Actuator structure, load spring
constant K act , Actuator oil, piston spring
constant KT , Total equivalent spring
constant
Fig. 6 Bode diagram for TVC of the 75tf thrust
engine (Rated load condition)
Table 9 Bandwidth for the 75tf thrust engine TVC Gain Bandwidth Phase Bandwidth Input (deg) ( at -3dB) ( at -90deg) 0.3
12.70Hz
6.47Hz
0.5
9.30Hz
5.72Hz
1.0
5.02Hz
4.60Hz
3.0
1.76Hz
2.00Hz
vehicles ", NASA report, 1968.
Fig. 7 Roots locus, gain and phase margin, Nyquist diagram for the 75tf thrust engine TVC Using the TVC linear block diagram with DPF loop in Fig. 4., the roots locus, the gain and phase margin, the Nyquist diagram can be obtained as shown in Fig. 7. The gain and phase margin are increased using the DPF loop as shown Table 10. Form the simulation results, the dynamic requirements of TVC system for the 75tf thrust engine are summarized as following. -3dB bandwidth (0.3deg command) ≥ 8Hz ▷ -90deg bandwidth (0.3deg command) ≥ 4.4Hz Table 10 Gain and phase margin for 75tf thrust engine TVC Gain margin(dB) Phase margin(deg) without DPF
-0.23
2.59
with DPF
11.3
72.4
4. CONCLUSION The equations of motion for the components of the thrust vector control system have been developed. The modeling and simulation analysis of the TVC system of the sample engine have been presented. Using this modeling method, the preliminary design of TVC system for the 75tf thrust engine has been conducted and the simulation results were presented. From the simulation analysis of TVC model for the 75tf thrust engine, the nonlinear response, the stability analysis and the bandwidth of the TVC system has been presented.
REFERENCES [1]
Grunden, C. A., and Sterling, J. T., "Single parameter testing", NASA report, 1967.
[2]
"Skylab Saturn IB flight manual", NASA report, 1972.
[3]
"Astrionics
system
handbook-Saturn
launch
