Spacecraft System for Orbit Raising, and Flight Dynamics

Figure 3-1 illustrates the spacecraft in deployed configuration and its major components.

The major subsystem elements of the spacecraft system are Payload Subsystem, Structure and Mechanisms Subsystem (SMS), Thermal Control Subsystem (TCS), Electrical Power Subsystem (EPS), Command and Data Handling Subsystem (C&DH), Radio Frequency Subsystem (RFS), Reaction Control Subsystem (RCS), Attitude Control Subsystem (ACS) and Flight Software Subsystem (FSW). The spacecraft bus provides structure, RF power, electrical power, thermal control, attitude control, orbit raising, and data support to the instrument [32], [61]. Table 3-1 shows the F3 constellation spacecraft bus key design features.

3.2.2 Spacecraft Propulsion for Thrust Burn

The spacecraft propulsion subsystem (also named the RCS) is a blowdown monopropellant Hydrazine (N2H4) Propulsion Subsystem with gas-helium (GHe) as the pressurant. And the designed blowdown ratio is 5:1 with the MEOP (Maximum Expected Operating Pressure) of 400 psia at 50ºC. The initial tank pressure is pressurized to about 330 psia at 20^oC. We utilize the RCS to provide impulses for attitude control during orbit-raising and to transfer the satellite from the injection orbit to an intermediate orbit if required, and finally to the mission orbit of the constellation. Figure 3-2 shows the block diagram of the RCS. For F3 spacecraft system the RCS consists of a propellant tank, gaseous helium and Hydrazine service valves, a latching valve, a filter, an orifice, four thrusters, pressure transducer, and a set of pipelines. The spacecraft RCS characteristics are summarized as follows [57]-[58]:

–Thrust Force: 1.1 [Beginning of Life (BOL)]－0.2 N [End of Life (EOL)];

–Specific Impulse: 217－194 s;

–Propellant Mass: ~6.65 kg;

–Thrust Type: OFF pulsing (Duty Cycle ≦ 50%).

Figure 3-3 shows the locations of the four thrusters (R1, R2, R3, and R4) which are located in

the four quadrants of the x-z plane of the satellites. These four thrusters are canted by 10° to enable three-axis control capability. By modulating the off-pulsing duration of the four thrusters, control torque is generated for the attitude control around X, Y, and Z axis of the satellite. The estimated thrust and specific impulse over the entire blowdown pressure range are shown in Figure 3-4.

3.2.3 Spacecraft Attitude Control for Orbit Raising

The function of the spacecraft ACS is to control the attitude of the satellite in the Safe Mode, the Stabilization Mode, the Nadir Mode, the Nadir-Yaw Mode, and the Thrust Mode.

And the ACS sensors for attitude estimation include Earth horizon sensors, coarse sun sensors, and a magnetometer. The ACS actuators for attitude control include magnetic torquers, a reaction wheel and thrusters [57], [61].

Figure 3-5 shows the functional block diagram of the spacecraft ACS where FC stands for Flight Computer and ACE means the Attitude Control Electronics. In Figure 3-5 the Attitude Reference System (ARS) includes attitude and rate estimators using a Kalman filter algorithm with measurements from the sensors. The ACS Controller processes the attitude and rate estimation from ARS through the control gains/algorithm, and distributes the torque commands to the actuators. The ACS also receives the satellite position and velocity data from the bus GPS receiver (GPSR). Based on this information it then propagates and computes necessary information for the navigation purpose, the ARS and the commanded angles for the Solar Array Drive (SAD).

The Thrust Mode is dedicated to the orbit-raising operation. When the orbit-raising operation is performed, the satellite first maneuvers itself to a yaw angle of 90° to align the thrust direction with the velocity direction. Then, as soon as the ACS enters Thrust Mode the thruster ignition starts up, the attitude is controlled by thrusters while orbit-raising proceeds. When the operation is terminated or finished, the ACS enters the Nadir-Yaw

Mode and maneuvers itself to a pre-set yaw angle.

A proportional-integral-derivative (PID) controller is designed for the Thrust Mode to compute the desired 3-axis control torque. Four thrusters are commanded off-pulsing in each control cycle to provide both the impulse for orbit raising and the 3-axis control torque to diminish the attitude errors. Figure 3-6 shows the concept of the “off-pulsing” in each control cycle. In orbit-raising operations, the thrust turn-on time in each control cycle is either kept constant as the “InitialThurstPower” value, or increased by “AddThrustIncrement”

seconds in every “AddThrustInterval” control cycles. The Thrust Mode control gains are adjusted in order to compensate for changes in thrust level during the RCS blowdown process.

The PID controller will minimize the attitude control error and improve the orbit-raising performance, but it suffers from the relative instability issue. This is because the control system may diverge with a large thruster turn on time when the PID integral terms are not yet converged to their steady-state values. Therefore, during orbit-raising operations, the PID controller requires a series of “calibration burns” in order to converge the attitude integral terms and to ramp up the thruster turn-on time to a larger value. Calibration burn is usually a smaller burn than the full-thrust burn. During the calibration process, the final values of the thrust turn on time and the integral terms of a previous burn are used as the initial values for the next burn. In this way, it takes about 6~8 calibration burns to reach the so-called full-thrust burn.

3.2.4 Flight Dynamics and Orbit Dynamics

The main function of ground-based Flight Dynamics Facility (FDF) is to conduct various orbit dynamics analyses including orbit determination, orbit-ephemeris propagation, orbit-maneuver planning, orbit-parameter trending, and orbit-event prediction. In the F3 mission, we use the commercial off-the-shelf software package called “Orbit Analysis System

(OASYS)” in FDF for orbit analysis. The OASYS database includes the thrusting model of the onboard RCS and ACS, such as the thruster number, location and direction; propellant mass and pressure; pressurant mass; blowdown curves for thrust and specific impulse; and thrust type, thruster duty cycle and efficiency [57], [61].

The blowdown curves for thrust force (F) and specific impulse (Isp) as shown in Figure 3-4 are modeled as the equations:

F = (0.001141+0.0006*P)* 4.448221 (in newtons). (1)

I_sp = 222.84 - 2268.4/P_m(in seconds). (2) where

F the thrust force;

Isp the specific impulse;

P_m the Propellant Mass.

and used in the OASYS database for F3 orbit raising. Both equations are functions of the propellant tank pressure in the unit of psia.

The thrust power in each ACS control cycle is modeled as the duty cycle of the thruster and listed as Duty Cycle = Thrust Power/Control Cycle. In full-thrust orbit-raising burns, the thrust power in each control cycle is kept constant, as the duty cycle is in the OASYS model. However, in calibration burns, the thrust power in each control cycle is linearly ramped up to the end of the burn. In other words, the duty cycle in each control cycle also increases in the same way as the thrust power does. Unfortunately, there is no way in OASYS to correctly model the calibration burns with increasing thrust powers. Instead, an averaged thrust power (duty cycle) using the initial and final thrust powers of the burn is used in the OASYS database to model the thrusting of a calibration burn.

The OASYS is also used to conduct an orbit determination to compare the actual post-burn orbit and the OASYS-planned post-burn orbit after a thrust-burn is completed.

Based on the actual and OASYS-planned orbit altitude, a thrusting efficiency is recalculated,

which in turn provides another input for the next orbit-raising planning.