Design of Attitude Determination and Control Subsystem

Transcription

1 Design of Attitude Determination and Control Subsystem 1) Control Modes and Requirements Control Modes: Control Modes Explanation 1 ) Spin-Up Mode - Acquisition of Stability through spin-up maneuver - Orbit determination phase (tracking from ground station) ) Normal Mode - Waiting for command uplink or data downlink 3 ) Thrusting Mode - Orbit insertion + De-orbiting (3 Experiments) 4 ) Safe Mode - Stand-by mode in case of a major malfunction Performance Requirements: 1.1 ) Spin-Up Mode : This mode is the phase just after leaving the launch vehicle in orbit. Initially, the spacecraft will be unstable prior to spinning. Two pairs of 4-array small solid side thrusters shall achieve spin-up with the aimed rate of 5 rpm. This angular rate is not very strict for our mission, as long as it stays somewhere between 0 ~ 30 rpm. In case of a malfunction in some of the side thruster units, they will still be enough to spin the s/c within the desired range since we have 8 separate side thruster units. At the end of burnout of the side thrusters, the spacecraft shall be spinning with a possible nutation about the maximum moment of inertia axis (resulting from uncertainties with initial motion and possible side thruster misalignments etc.). The excessive nutation shall be damped out using a nutation damper. Attitude Determination Requirements: - All attitudes (meaning that any random attitude shall be sensed) - Spin rate between 10 ~ 60 rpm - Accuracy: Spin rate must be sensed within 0.01 rad/s accuracy Attitude Control Requirements: - Accuracy: Not important - Range: Spin rate between 0 ~ 30 rpm - Any nutation bigger than 0.1 shall be damped using a nutation damper prior to thrusting. - Settling time for nutation shall be less than 3 hours 1. ) Normal Mode : This is the phase in between thrusting maneuvers. Spacecraft shall be spinning without nutation. Attitude of the spacecraft will be monitored at this phase. Ground station will provide the orbit tracking. The spacecraft shall be waiting for any command uplink and data downlink. Thus, antennas should provide enough coverage for communication at this phase. Attitude is random and inertially fixed due to spinning. 1

2 Random attitude means that we are not too concerned about the orientation of the satellite since any orientation will allow us to perform our mission. Attitude Determination Requirements: - Inertially fixed due to spin - All attitudes (orientation + spin rate) - Attitude will be monitored within 0.5 accuracy - Orbit will be tracked from the ground station Attitude Control Requirements: - None 1.3 ) Thrusting Mode : This is the attitude mode during thrusting experiments. The initial and final orientations of the spacecraft shall be determined precisely. Velocity changes shall be monitored during experiments. Each experiment shall be approximately 3 minutes long (thrusting experiments are not very sensitive to small variations in burn time). Attitude Determination Requirements: - Spin rate must be sensed within ~0.01 rad/s precision. - Attitude must be sensed within ~0.5 deg accuracy (Before and after thrusting maneuver) - Accelerations must be sensed with 0.01 m/s accuracy during thrusting Attitude Control Requirements: - None. - The effect of the nutation damper must be insignificant during thrusting (for 3 min). This is a reasonable assumption although the nutation damper will be operational during the experiments. Since the nutation is expected to be eliminated in less than 3 hours, we can overlook the effect of the nutation damper for a three minute period. 1.4 ) Safe (Stand-by) Mode: Safe mode is the operating condition when there is a major malfunction like a thruster problem, spin-up booster malfunction etc. The spacecraft should cut down the energy consumption to minimum and wait for commands from the ground station. Telemetry system should function and must be kept at full power in order to receive commands. Attitude information shall be sensed and stored for down-link if possible. Attitude Determination Requirements: - If spinning, spin rate must be measured and stored - Attitude shall be sensed and stored if possible - Orbit shall be tracked from the ground station

3 Attitude Control Requirements: - None. ) Spacecraft Attitude Control Selection As the experimental approach requires (this is an external requirement), the only spacecraft control shall be passive spin stabilization. This is realistic since, any spinningthrusting vehicle has an inherent gyroscopic stiffness and therefore attitude control systems are not activated without slowing down (or stopping) the spin of the spacecraft. Thus, the spacecraft is going to be a single spinner (pure spin) with inertially fixed attitude in the LEO (Low Earth Orbit) with no attitude control. During the trade studies, several options ranging from a 3-axis stabilized platform to a variable spin control enabling platform and several combinations of other possible options were considered. However due to the nature of the mission, having any control on the spinning platform requires a high degree of sophistication that is beyond the reach of the mission mass, size limitations and the desired low cost requirement. The decision of using no attitude control was chosen because of great simplicity and cost effectiveness. The inertially fixed attitude due to spinning can also be used to determine the thrusting direction, albeit in a limited sense, by specifying the time of thrusting for a specific location in orbit. Although this will not give complete flexibility, it will be sufficient to achieve our mission goals. The de-orbiting requirement will be achieved by the same control idea, again setting the time of initiation of the burn for the solid rocket booster with the aim of decreasing the relative spacecraft velocity and possibly pushing it towards the atmosphere for orbit decay and eventual reentry. 3) Mission Profile and Orbit In order to maximize the possibilities of launching as a secondary payload in any launch vehicle (which is the main driver for determining the envelope of the satellite), the LEO was selected as the mission orbit. Most of the Earth orbiting satellites are placed and lunched in the LEO, so that choosing this orbit regime will maximize the possibilities of getting a ride into the orbit. The orbit selected has a mean altitude of 350 km with a nominal inclination of 40 o. The altitude is somewhat smaller than usual LEO orbits due to the de-orbiting requirement. This altitude will be used in the next section for disturbance environment calculations. Typical values for solar and magnetic exposures, aerodynamic and gravitational disturbances for this altitude will be assumed. 4) Quantifying Disturbance Environment 4.1) Gravity Gradient: Type of disturbance: Cyclic (since spacecraft is inertially fixed) Influenced by: - spacecraft orientation - orbital altitude Formula: 3

4 3µ Tg = I sin( ) 3 z Iy θ (4.1.1) R where, T g = maximum gravity torque, R = orbit radius, I z, I y = spacecraft moment of inertias, µ = gravitational constant for Earth, θ = maximum deviation of the Z axis from local vertical Parameters are: Altitude = 350 km R = 350 km + R Earth = 350 km km = 678 km R = 678 km (4.1.) Spacecraft moments of inertia were first calculated using a cuboid model given below for initial iterations. Later on the design process, using the actual size and the masses of selected hardware, the moment of inertias were calculated using solid modeling in the Unigraphics CAD Package. The moments of inertias were generated by the software based on the location and masses of the each component. The resulting moments of inertias were found to be (in the principal directions shown above) I x = kg m I = kg m y I z = kg m Since the spacecraft is a single spinner, as dynamics of the motion points out, spinning about the maximum moment of inertia will be the only stable spinning motion. What s more, having the maximum moment of inertia as big as possible compared to inertias about the other axes provides better stability. Our mass budget (most of the mass values were calculated using the actual component masses) indicates that we have approximately % 6 margin in our aimed mass budget. Thus in order to enhance the stability properties of the spacecraft we are going to add additional masses to increase I z moment of inertia. Since we have a big margin, we can have as much as 0.4 kg.m increase in our I z moment of inertia but to stay on the safe side we are going to assume a 4

5 smaller increase in I z moment with added masses at the corners. This will account for some uncertainties during actual manufacturing of the spacecraft. With the modifications, the principal moment of inertia values used in calculation are as follows I = 0.3 x I = 0.36 y I = 0.50 z kg m kg m kg m (4.1.3) The other parameters in equation (4.1.1) are given next: θ = 45 (worst case) (4.1.4) µ = m 3 /s (4.1.5) Thus having defined all the parameters in equation (4.1.1) we can compute T g as follows: T g ( m / s ) kg m sin(90 ) = ( m) 7 Tg = N m (4.1.6) 4.) Solar Radiation: Type of disturbance: Cyclic (since spacecraft is inertially fixed) Influenced by: - spacecraft geometry - spacecraft surface reflectivity - center of gravity location Formula: Tsp = F( Cps Cg) (4..1) Fs where, F = As (1 + q) cos i (4..) C The parameters are defined below: T sp = solar radiation pressure (torque), F s = solar constant, (= 1367 W/m ) C = speed of light, (= m/s) A s = surface area, C sp = location of the center of solar pressure, C g = center of gravity location, q = surface reflectance (ranges between 0~1), i = angle of incidence to the sun 5

6 We set these parameters as follows for the worst-case conditions: A s 0.14 m ( m - the worst possible case) q = 0.6 (semi reflective) cos i = 1 (i = 0 worst case) C sp - C g m (this is an approximation based in the fact that the spacecraft is highly symmetric and the color pattern and surface properties do not vary significantly) Thus from equation (4..1) and (4..) we calculate as follows: 1367W m F = ( 0.14 m ) ( ) cos(0 ) m s (4..3) F = N Thus, T sp = 6 ( ) (0.075 m) 8 Tsp = N m (4..4) 4.3) Magnetic Field: Type of disturbance: Cyclic (since spacecraft is inertially fixed) Influenced by: - orbit altitude - residual spacecraft magnetic dipole - orbit inclination Formula: Tm = D B (4.3.1) where, D is the residual dipole of the vehicle in amp turn m ( Am ) and, M B = (for polar orbit with i = 90 o ) 3 R M B = (for equatorial orbit with i = 0 o ) R 3 Since our inclination is i = 40 o, by linear interpolation we find the corresponding number for our orbit: 13M B = (4.3.) (Exact using linear interpolation) 3 9R In the above equation M is the magnetic moment of the Earth and measured as; M = [tesla m ] and, R is the radius from dipole (Earth) center to spacecraft in [m]. Thus we calculate for R = 678 km, and for D = 1 A m (this is a common value for small-sized, uncompensated vehicle); 6

7 T ( tesla m ) M = (1 A m ) ( m) 5 TM = N m (4.3.3) 4.4) Aerodynamic Disturbance: Type of disturbance: Variable (since spacecraft is inertially fixed) Influenced by: - orbit altitude - spacecraft geometry - center of gravity location Formula: Ta = F ( Cpa Cg) = F L (4.4.1) where, F = 0.5 ρ Cd A V (4.4.) The parameters are defined below: T a = aerodynamic torque, F = aerodynamic force, ρ = atmospheric density C d = drag coefficient (usually between ~.5), A = exposed surface area, V = spacecraft velocity, C pa = center of aerodynamic pressure, C g = center of gravity We assign the following numbers to these parameters; ρ kg/m 3 (mean density at 350 km altitude), C d.5 (usually between and.5 we take it to be constant at.5) A 0.14 m (worst possible case) V max 8000 m/s (this is calculated from the circular velocity at 700km altitude in 14 3 µ m / s orbit where Vcirc = = 7697 m/ s 3 R m Since the spacecraft may not be in the circular orbit during the experiments, we can take V 8000 m/s to compensate higher speeds of an elliptic orbit at perigee. ) C pa -C g 0.1 m (this is an approximation based in the fact that the spacecraft is geometrically symmetric) Thus from equations (4.4.1) and (4.4.) we calculate as follows; 1 3 F = 0.5 ( kg / m ) (.5) (0.14 m ) (8000 m / s) F = N 7

8 5 Thus T a =( N ) (0.1m) 6 Ta = N m (4.4.3) This concludes the calculation of major disturbances in the LEO orbit. Next we will try to give the idea of how significant are the disturbance torques on the motion and the attitude of the spacecraft in orbit. We are going to assume that spacecraft is spinning with 5 rpm about the maximum moment of inertia axis, and all the disturbance torques are acting on the same direction! (This is a much exaggerated assumption but this will give a fairly good idea how effective these torques are). Thus we sum all the disturbing torques; T = T + T + T + T T disturbance g sp M a disturbance = Tdisturbance N m Thus we conclude that even if the torques were exaggerated greatly and assumed to be all in the same direction, the net effect is not very significant. Therefore, for the length of the mission and the possible disturbance environment we do not need to have an active attitude control & compensation system since our experiments do not require an active control other than the initial spin-up. As the last step in our calculations we are going to calculate the nutation frequency of the spacecraft. The relation between the inertial nutation frequency (w ni ) and the spacecraft rotation frequency is: ω I s ni = ωs (4.4.4) IT where w s is the spin frequency and I s and I T are moments of inertia about the spin axis and transverse axis, respectively. Thus setting I s =I z nutation frequencies for the transverse axes x and y are; Thus, Iz 0.5kg m ωni = ω x z = rpm = rpm I 0.3kg m x Iz 0.5kg m ωni = ω y z = rpm = rpm I 0.36kg m ni ni x y y ω = rpm ω = 34.7rpm (4.4.5) We must make sure that the nutation damper to be selected is capable of eliminating nutation within the range of above numbers. 8

9 5) Selection & Sizing of ADCS Hardware In light of above decisions, the attitude determination equipment was selected so that all the selected components are compatible with the accuracy requirements set in Control Modes and Requirements section above. The specific hardware selected for the mission consists of sun sensors, a 3-axial accelerometer and a rate gyro. Currently no extensive sizing information could be found for the nutation damper and, therefore, it is not included in mass budget analysis. But the available mass margin allows for the inclusion of this equipment. The specific information about each selected component is as follows: 5.1) Sun Sensors ( ) : Vendor: TNO TPD Space Instrumentation Part : Sun Acquisition Sensor (SAS) Field of view Hemispherical, typically +/- 97 degrees about boresight. Accuracy Better than +/- 0.5 degrees on boresight for GEO missions under all environmental conditions and for the whole mission lifetime. Albedo will degrade the accuracy in LEO. Power consumption No input power required. Electrical output In current mode 0-30 ma. In voltage mode 0-00 mv. Output can be of individual detectors or of combinations of detectors (balance, sum). Operating temperature Typically -100 C to +100 C. Mass/dimensions Mass: kg Dimensions: 110 x 110 x 8 mm without connector, alignment cube, grounding stud or specific baffling. Reliability Depend strongly on output arrangement (single cell or combination output) and philosophy with regard to redundancy; in SAS for GEO application outputs are redundant; in SAS for LEO application only single-cell type of output is redundant; failure probability for single cell voltage output.4 x 10-4 worst case (+100 degrees C) per year mission duration. Qualification status Fully qualified and flight proven sensor. A technical drawing of the part is given on the next page. 9

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11 5.) Gyroscope ( 1) : Vendor: B E I -T E C H., I N C. SYSTRON DONNER INERTIAL DIVISION Part : Model QRS11Micromachined Angular Rate Sensor 11

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14 5.3) Accelerometer ( 1) : Vendor: PCB PIEZOTRONICS Part : 356B07 Low-Noise Triaxial ICP Accelerometer 14

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16 6) ADCS Cost Estimation: The following table represent the actual and estimated component costs Component Unit Price ($) Number of parts Sun Sensor 0000 (estimated) Gyroscope 450 (actual) 1 Accelerometer 1100 (actual) 1 Nutation Damper 1000 (estimated) 1 Total = $ 7) Two Burn Thrusting Scheme A very good way of providing directional stability for spacecraft and rockets is to spin them about their maximum or minimum principal axes. We know from dynamic analysis of rigid bodies that the angular momentum of a spinning rigid body will remain constant unless acted upon an external torque. Due to production tolerances, small errors in the thruster location and direction are inevitable. Therefore an axially thrusting-spinning spacecraft or rocket will experience unwanted transverse torques during the thrusting maneuver 1, as shown in figure 1. In the FIG. 1 Thrusting Problem example configuration thruster offset causes a body fixed torque in to the page. We know that such a torque will distort the angular momentum vector in inertial coordinates and cause it to trace a circular path as it is shown in figure. The average angular momentum bias angle ρ is measured from the vertical and in the YZ plane, as shown in the 1 Longuski J.M., T. Kia, W.G. Breckenridge, Annihilation of Angular Momentum Bias During Thrusting and Spinning-up Maneuvers, The Journal of the Astronautical Sciences, Vol. 37, No.4, October-December 1989, pp

17 reference 1 and it is shown that the V pointing errors occur along the axis set by ρ in axially thrusting spin-stabilized spacecraft and rockets. In the figure, H o shows the initial position of the angular momentum vector and the H vector is the angular momentum during the thrusting maneuver. FIG. The Angular Momentum and Velocity Pointing Bias During Thrusting A remedy for the problem lies in using a two-burn scheme as proposed 1.And indeed, this method is the simplest and probably most effective way of achieving a solution, provided that we have an on-off type pulse thruster. With the conclusion that that the velocity pointing error will occur along the direction set by the angular momentum bias, then the basic idea lies behind eliminating the angular momentum bias. We know that for the case of spinning and axially thrusting spacecraft with the presence of thruster offset, there is no way of eliminating the angular momentum bias except highly sophisticated controllers. However, with the two-burn scheme proposed by Longuski et al. 1 it is possible to eliminate the time average of the angular momentum bias. The idea is to shift the center of the circle that is traced by the angular momentum vector to the origin of the inertial axis system as shown in figure 3 below. FIG. 3 Initial and Final Paths of the Angular Momentum Vector in Two Burn Scheme Uncompensated angular momentum vector moves on the depicted initial angular momentum path. When the angular momentum vector comes to the point A in the figure 3, along the solid line, the thruster is turned off (coasting) and consequently the angular Longuski J.M., T. Kia, W.G. Breckenridge, Annihilation of Angular Momentum Bias During Thrusting and Spinning-up Maneuvers, The Journal of the Astronautical Sciences, Vol. 37, No.4, October-December 1989, pp

18 momentum vector stops moving since there is no external torques acting on the spacecraft. The A point corresponds to a 60 o rotation of the spacecraft and the time required to arrive this point can be found simply from the relation t b = π / 3Ω, where, t b denotes 1 st burn time and Ω is the spin rate. We note that if we define θ as the spacecraft rotation angle, the time relation of it is simply θ = Ω t After the first ignition, the thruster is kept off for a period of coast time t c = π / 3Ω and after that it is ignited again for the rest of the maneuver. In the end this causes the angular momentum vector to fall in the track of the final path shown in dashed lines, which has an average angular momentum bias of 0 degrees. The resulting behavior of the velocity pointing error and angular momentum path can be obtained numerically using the designed spacecraft parameters (MOI, thrust and an intentional offset value of 5 cm). The promise of the two burn-scheme is evident from the plots given for numerical simulations. Simulations were performed for 180 seconds (3 minutes). FIG. 4 Simulation of Angular Momentum Path and Velocity Path without the Two-Burn Scheme 18

19 FIG. 5 Simulation of Angular Momentum Path and Velocity Path with the Two-Burn Scheme According to the numerical results, the spacecraft departed about 1. m laterally during 3 minute thrusting using the two-burn scheme as compared to the approximately 1 m lateral departure of the single-burn case. 19