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Figure 8. Deg/s-PWM Relation for (a) Gimbal 1, (b) Gimbal 2, (c) Gimbal 3, (d) Gimbal 4. where 6,;, is a preset threshold. It is preferred to saturate the gimbal angle rates using Equation (4) over applying a boundary value to every gimbal angle rate that exceeds the required threshold because the characteristics of the motion are conserved. The saturation threshold is selected to be the minimum value of the maximum gimbal velocity of the four gimbals. The motor driver takes as input a pulse width modulation (PWM) signal for speed control. Thus, it is required to map each angular velocity of the gimbal toa PWM value, in order to control the CMG cluster. As expected, only an approximation of this is feasible in practice. After achieving the steady-state velocity for the four flywheels, each gimba is spun up gradually by increasing the PWM value, while measuring its angular velocity. Figure 8a—d shows the relation between the PWM values and the gimbal rates for each CMG. The equations of the linear approximations that are used to map the commanded gimbal rates to PWM values are also shown in the figure. It is observed that the maximum gimbal velocities are lower than the no-load velocities referred to in the datasheet because of the load they support and the fact that they operate at 5 V instead of their nomina value of 6 V. A cascade control design is implemented and an inner PD controller is used to guarantee that given the commanded gimbal rates, the gimbals follow the desired angle profiles. 3. Flywheel Sizing

Figure 8 Deg/s-PWM Relation for (a) Gimbal 1, (b) Gimbal 2, (c) Gimbal 3, (d) Gimbal 4. where 6,;, is a preset threshold. It is preferred to saturate the gimbal angle rates using Equation (4) over applying a boundary value to every gimbal angle rate that exceeds the required threshold because the characteristics of the motion are conserved. The saturation threshold is selected to be the minimum value of the maximum gimbal velocity of the four gimbals. The motor driver takes as input a pulse width modulation (PWM) signal for speed control. Thus, it is required to map each angular velocity of the gimbal toa PWM value, in order to control the CMG cluster. As expected, only an approximation of this is feasible in practice. After achieving the steady-state velocity for the four flywheels, each gimba is spun up gradually by increasing the PWM value, while measuring its angular velocity. Figure 8a—d shows the relation between the PWM values and the gimbal rates for each CMG. The equations of the linear approximations that are used to map the commanded gimbal rates to PWM values are also shown in the figure. It is observed that the maximum gimbal velocities are lower than the no-load velocities referred to in the datasheet because of the load they support and the fact that they operate at 5 V instead of their nomina value of 6 V. A cascade control design is implemented and an inner PD controller is used to guarantee that given the commanded gimbal rates, the gimbals follow the desired angle profiles. 3. Flywheel Sizing

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Table 1. Component mass. A 4-CMG cluster in pyramid configuration is used for the attitude control of the platform. The main parts of the cluster are the eight micro DC motors. Four Pololu 3058 motors are used to implement the gimbals while four Pololu 3082 motors are used as flywheels. The gear ratio of the gimbal and flywheel motors, g,, equals to 1006:1 and 5:1, respectively. A magnetic encoder is placed on the shaft of every motor. Each encoder is a dual-channel Hall Effect sensor board in combination with a 6-pole magnetic disc. The resolution they provide is 12 counts per revolution of the motor shaft and it can be converted in counts per revolution of the gearbox output shaft, cpr,, through the following equation: The parts that comprise the ACS hardware are the main perfboard along with the microcontroller and the Inertial Measurement Unit (IMU), the battery and the four CMGs. The location of the equipment on the platform has been as symmetric as possible. The mass of each component and the total mass are described in Table 1.
Table 1. Component mass. A 4-CMG cluster in pyramid configuration is used for the attitude control of the platform. The main parts of the cluster are the eight micro DC motors. Four Pololu 3058 motors are used to implement the gimbals while four Pololu 3082 motors are used as flywheels. The gear ratio of the gimbal and flywheel motors, g,, equals to 1006:1 and 5:1, respectively. A magnetic encoder is placed on the shaft of every motor. Each encoder is a dual-channel Hall Effect sensor board in combination with a 6-pole magnetic disc. The resolution they provide is 12 counts per revolution of the motor shaft and it can be converted in counts per revolution of the gearbox output shaft, cpr,, through the following equation: The parts that comprise the ACS hardware are the main perfboard along with the microcontroller and the Inertial Measurement Unit (IMU), the battery and the four CMGs. The location of the equipment on the platform has been as symmetric as possible. The mass of each component and the total mass are described in Table 1.
Figure 1. ACS on hemispherical 3D-printed platform. (a) CAD model and (b) actual CMG-Air bearing setup.
Figure 1. ACS on hemispherical 3D-printed platform. (a) CAD model and (b) actual CMG-Air bearing setup.
To enable a full 360 deg rotation about the gimbal axis for each CMG, the 6-Wire SRC022 sli p ring by Adafruit is used. The motors’ nominal voltage is 6 V. The flywheel of each CMG is made of aluminum and has a radius of 17 mm and a mass of 14.1 g. The flywheel is locked on the motor axis using two headless hexagon M1.6 socket screws placed in an anti-diametrical configuration. The motor drivers, the voltage regulators along with the IMU and the microcontroller are all mounted on a perfboard equipped also with LED units and a photo-resistor for start-stop control. The dimensions of the perfboard are 95 mm (lengt structure as low as possible, only two Pololu 5 V, 1A,57V7F5 step down regulators are used to power the motors’ drivers and the microcontroller. Four Texas Instruments DRV8835 motor drivers are used to control the eight DC motors. The microcontroller used is the Teensy 3.6 256K RAM. It is selected because it provides enough interrupt pins to read both channels of each encoder and there is a prior knowledge of using this board. The experimental data are saved in an SD card placed in the microcontroller’s built-in slot. SparkFun LSM9DS is selected utilized in h) x 77.5 mm (width) x 26 mm (height). In order to keep the weight of the board which embeds an ARM Cortex-M4 processor at 180 MHz, 1M Flash and as the IMU of the system. It is a 9-degrees-of-freedom (DoF) sensor and it is PC mode with gyro resolution of 0.00875 deg/s. A LiPo 25 7.4 V 800 mAh battery that powers the system is placed next to the perfboard. Figure 2 illustrates the electrical connection of the components. Figure 2. Avionics system/board block diagram with all connections.
To enable a full 360 deg rotation about the gimbal axis for each CMG, the 6-Wire SRC022 sli p ring by Adafruit is used. The motors’ nominal voltage is 6 V. The flywheel of each CMG is made of aluminum and has a radius of 17 mm and a mass of 14.1 g. The flywheel is locked on the motor axis using two headless hexagon M1.6 socket screws placed in an anti-diametrical configuration. The motor drivers, the voltage regulators along with the IMU and the microcontroller are all mounted on a perfboard equipped also with LED units and a photo-resistor for start-stop control. The dimensions of the perfboard are 95 mm (lengt structure as low as possible, only two Pololu 5 V, 1A,57V7F5 step down regulators are used to power the motors’ drivers and the microcontroller. Four Texas Instruments DRV8835 motor drivers are used to control the eight DC motors. The microcontroller used is the Teensy 3.6 256K RAM. It is selected because it provides enough interrupt pins to read both channels of each encoder and there is a prior knowledge of using this board. The experimental data are saved in an SD card placed in the microcontroller’s built-in slot. SparkFun LSM9DS is selected utilized in h) x 77.5 mm (width) x 26 mm (height). In order to keep the weight of the board which embeds an ARM Cortex-M4 processor at 180 MHz, 1M Flash and as the IMU of the system. It is a 9-degrees-of-freedom (DoF) sensor and it is PC mode with gyro resolution of 0.00875 deg/s. A LiPo 25 7.4 V 800 mAh battery that powers the system is placed next to the perfboard. Figure 2 illustrates the electrical connection of the components. Figure 2. Avionics system/board block diagram with all connections.
Table 2. DC motor details. 2.1.2. Perfboard
Table 2. DC motor details. 2.1.2. Perfboard
CoM of each CMG changes as the gimbal rotates even though each one was designed to be as symmetric as possible. This is mainly due to the cables coming out of the flywheel connected to the slip ring and small manufacturing and assembling imperfections. Thus, an 1 DoF experimental setup is selected to validate the ACS that allows the rotation only about the yaw axis. The height of the air bearing bottom part is 58.9 mm with a external diameter of just 60 mm. However, due to the 3D printing process a flat side is required to lie the air bearing, increasing the size in one of the axes by 6.2 mm, as depicted in Figure 3. A configuration of three rows of holes was found to work efficiently for the developed uir bearing even though no further analysis and optimization were conducted. The first ‘ow only contains the center hole whilst the second and the third rows contain 9 and 19 1oles, respectively. Each hole has a diameter of 1 mm. The angle of the holes with respect to he horizontal plane are 90 deg, 105 (or 15) deg and 120 (or 30) deg for the first, the second ind the third row. The number of holes for each row is selected so that the air bearing is yperational while not presenting imbalances. However, the configuration of the air bearing will be further studied and optimized in future designs. Table 3 summarizes the main characteristics of the bottom part of the air bearing platform.
CoM of each CMG changes as the gimbal rotates even though each one was designed to be as symmetric as possible. This is mainly due to the cables coming out of the flywheel connected to the slip ring and small manufacturing and assembling imperfections. Thus, an 1 DoF experimental setup is selected to validate the ACS that allows the rotation only about the yaw axis. The height of the air bearing bottom part is 58.9 mm with a external diameter of just 60 mm. However, due to the 3D printing process a flat side is required to lie the air bearing, increasing the size in one of the axes by 6.2 mm, as depicted in Figure 3. A configuration of three rows of holes was found to work efficiently for the developed uir bearing even though no further analysis and optimization were conducted. The first ‘ow only contains the center hole whilst the second and the third rows contain 9 and 19 1oles, respectively. Each hole has a diameter of 1 mm. The angle of the holes with respect to he horizontal plane are 90 deg, 105 (or 15) deg and 120 (or 30) deg for the first, the second ind the third row. The number of holes for each row is selected so that the air bearing is yperational while not presenting imbalances. However, the configuration of the air bearing will be further studied and optimized in future designs. Table 3 summarizes the main characteristics of the bottom part of the air bearing platform.
Table 3. Air bearing—bottom part. The top part of the air bearing is shown in Figure 4. The ABS rectangle plate was also 3D-printed with dimensions 14.4 cm x 14.4 cm x 5.1 cm. The strength combined with the ower density of ABS compared to this of aluminum allows for less mass and, as a result, ower moment of inertia, while improving the maneuverability of the system. Low printing velocity, heated bed and raft are used to ensure the minimum thermal strain and avoid warping. The diameter of the 3D-printed air bearing at its highest point is 60 mm. The printing accuracy is 0.15 mm, so the surface is slightly finished using only P2000 sandpaper. Alternatively, an acetone steam bath can also be used for smoothing. Each CMG is fixed on he plate using two M5 bolts.
Table 3. Air bearing—bottom part. The top part of the air bearing is shown in Figure 4. The ABS rectangle plate was also 3D-printed with dimensions 14.4 cm x 14.4 cm x 5.1 cm. The strength combined with the ower density of ABS compared to this of aluminum allows for less mass and, as a result, ower moment of inertia, while improving the maneuverability of the system. Low printing velocity, heated bed and raft are used to ensure the minimum thermal strain and avoid warping. The diameter of the 3D-printed air bearing at its highest point is 60 mm. The printing accuracy is 0.15 mm, so the surface is slightly finished using only P2000 sandpaper. Alternatively, an acetone steam bath can also be used for smoothing. Each CMG is fixed on he plate using two M5 bolts.
Table 4. Measurement cases. The microcontroller is programmed in C. Both channels of each encoder are exploited to calculate the gimbal angles through interrupt pins. The IMU is utilized in PC mode, while a low-pass filter is used to eliminate the measurements noise. A set of one hundred samples is used for bias correction, while no temperature compensation is needed. The [MU sensor operates for about 30s and negligible temperature change is observed in this time period. However, the built-in functions found in the LSM9DS1 library allow for the magnetic data compensation by temperature, setting the first bit of the CTRL_REG1_M register to 1, in case there is a considerable temperature change. Different measurements were obtained by the IMU sensor to define the attitude of the platform while it is stationary. six different cases were examined, depending on whether both the gyroscope and the magnetometer of the IMU are exploited to define the yaw angle. Table 4 explains each case.
Table 4. Measurement cases. The microcontroller is programmed in C. Both channels of each encoder are exploited to calculate the gimbal angles through interrupt pins. The IMU is utilized in PC mode, while a low-pass filter is used to eliminate the measurements noise. A set of one hundred samples is used for bias correction, while no temperature compensation is needed. The [MU sensor operates for about 30s and negligible temperature change is observed in this time period. However, the built-in functions found in the LSM9DS1 library allow for the magnetic data compensation by temperature, setting the first bit of the CTRL_REG1_M register to 1, in case there is a considerable temperature change. Different measurements were obtained by the IMU sensor to define the attitude of the platform while it is stationary. six different cases were examined, depending on whether both the gyroscope and the magnetometer of the IMU are exploited to define the yaw angle. Table 4 explains each case.
Figure 4. Top part of air bearing. The hemispherical top part of the 3D-printed structure was locked in horizontal position preventing the system from rotating about the roll and the pitch axes using a thin bolt (Figure 5) which enters the center hole of the air bearing.
Figure 4. Top part of air bearing. The hemispherical top part of the 3D-printed structure was locked in horizontal position preventing the system from rotating about the roll and the pitch axes using a thin bolt (Figure 5) which enters the center hole of the air bearing.
Figure 6. Yaw measurements for (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, (e) Case 5, (f) Case 6. The minimum standard deviation is 0.0973 deg and it is presented for case 3, where only the gyroscope is used, after bias correction and low-pass filtering. An angle drift of 0.0124 deg/s is achieved in this case and it is the minimum of all cases. Thus, the attitude determination is provided only by the gyroscope data and the low pass filter is given by
Figure 6. Yaw measurements for (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, (e) Case 5, (f) Case 6. The minimum standard deviation is 0.0973 deg and it is presented for case 3, where only the gyroscope is used, after bias correction and low-pass filtering. An angle drift of 0.0124 deg/s is achieved in this case and it is the minimum of all cases. Thus, the attitude determination is provided only by the gyroscope data and the low pass filter is given by
vhere G,, is the filtered gyroscope value at " iteration, Gi" is the gyroscope measurement srovided by the IMU after the bias correction at n‘” iteration. fg denotes the smoothing actor and it is equal to 0.25 for this experimental setup. The loop cycle is selected to be 0.05 as this is the maximum time period needed to collect the input data from the IMU, execute Jl the required calculations and write the output data to an SD memory card connected to he native SD Card port of the microcontroller. A flow diagram of the air bearing operation yrocesses that take place is presented in Figure 7. At first, the SD card is prepared, and a warning message is shown if the initialization has failed. The definition of input, output and interrupt pins follows in order to control the gimbals as presented in the next step. Due to the nature of the encoders, it is possible to achieve only a relative gimbal angle value. This limitation requires the initialization of the gimbals angles to the preferred values in the beginning. Afterwards, the establishment of I?C communication takes place that allows to read the data from the IMU and the sensor is
vhere G,, is the filtered gyroscope value at " iteration, Gi" is the gyroscope measurement srovided by the IMU after the bias correction at n‘” iteration. fg denotes the smoothing actor and it is equal to 0.25 for this experimental setup. The loop cycle is selected to be 0.05 as this is the maximum time period needed to collect the input data from the IMU, execute Jl the required calculations and write the output data to an SD memory card connected to he native SD Card port of the microcontroller. A flow diagram of the air bearing operation yrocesses that take place is presented in Figure 7. At first, the SD card is prepared, and a warning message is shown if the initialization has failed. The definition of input, output and interrupt pins follows in order to control the gimbals as presented in the next step. Due to the nature of the encoders, it is possible to achieve only a relative gimbal angle value. This limitation requires the initialization of the gimbals angles to the preferred values in the beginning. Afterwards, the establishment of I?C communication takes place that allows to read the data from the IMU and the sensor is
Table 5. Sizing details. The numerical results of the sizing analysis are presented in Table 5
Table 5. Sizing details. The numerical results of the sizing analysis are presented in Table 5
Figure 9. Angular velocity for rotating a deg in t, s.
Figure 9. Angular velocity for rotating a deg in t, s.
Table 6. Experimental details. Figures 10 and 11 present the experimental results for the 180 deg manoeuvre. The theoretical data, also shown in each figure, are obtained using the moment of inertia of the system about the vertical axis as measured by the CAD model of Figure 1a and is equal In order to validate the operation of the ACS, two different experiments are conducted. In the first, the platform has to complete an 180 deg manoeuvre about the yaw axis as expressed by the q° = [0,0,0,1]". In the second, a 90 deg manoeuvre about the same axis is commanded as given by the quaternion q° = [0.7071,0,0, 0.7071]. It is assumed that the system has reached the steady state when the attitude error ae; remains below a preset threshold for a given time tss. The parameters Kp, K; and K,, denote the contro gains. Initially, the selection of a high Ky gain leads to a highly oscillatory response and K; can be used to correct the steady-state error. K,, is then tuned to reduce the overshoots and converge faster to the desired attitude. The values of the parameters used in the experiments are presented in Table 6.
Table 6. Experimental details. Figures 10 and 11 present the experimental results for the 180 deg manoeuvre. The theoretical data, also shown in each figure, are obtained using the moment of inertia of the system about the vertical axis as measured by the CAD model of Figure 1a and is equal In order to validate the operation of the ACS, two different experiments are conducted. In the first, the platform has to complete an 180 deg manoeuvre about the yaw axis as expressed by the q° = [0,0,0,1]". In the second, a 90 deg manoeuvre about the same axis is commanded as given by the quaternion q° = [0.7071,0,0, 0.7071]. It is assumed that the system has reached the steady state when the attitude error ae; remains below a preset threshold for a given time tss. The parameters Kp, K; and K,, denote the contro gains. Initially, the selection of a high Ky gain leads to a highly oscillatory response and K; can be used to correct the steady-state error. K,, is then tuned to reduce the overshoots and converge faster to the desired attitude. The values of the parameters used in the experiments are presented in Table 6.
Figure 10. (a) Attitude error and (b) angular velocity of the platform for 180 deg maneuver. to J = 0.00283 commanded at state, as defined only 3.7 s. This also in Figure and it follows the theoretical angular velocity profi 51.38 deg/s at is observed in the response due to of 1.5 deg tight the cluster are presented in Figure 1 a, Figure 11b, = 1.6s. The mean angular velocity throug deg/s. The experimental results differ slightly from the theore the low-pass fi However, the system is capable of completing the command y following the theoretical profile. The gim Figure 1 Both minimum and steady-state values of each gimbal are MAE for this experiment for gimbal as derived by 5 sets of measuremen 3.3122 deg and 1.7429 deg. angles 61, 62, 63, 64, atti ts are 4.1654 deg, 4.5314 d nt. ed ba 1c and Figure tud kgm*. Figure 10a illustrates that the system immediately responds to the titude as it begins to rotate about the positive yaw of the axis. The steady previously, is reached at about t = 20 s and the rising time of the system is indicates that the platform has gained a high angular velocity, as shown Ob. The maximum angular velocity achieved is 53.47 deg/s at t = 1.9 s e, which presents a maximum value of he whole manoeuvre is 8.32 tical and a minor time delay ter used to eliminate the sensor noise. maneuver with an accuracy angles of the four CMGs in 1d, respectively. shown in Table 7. The average e error and angular velocity, eg, 7.9983 d eg, 15.3848 deg,
Figure 10. (a) Attitude error and (b) angular velocity of the platform for 180 deg maneuver. to J = 0.00283 commanded at state, as defined only 3.7 s. This also in Figure and it follows the theoretical angular velocity profi 51.38 deg/s at is observed in the response due to of 1.5 deg tight the cluster are presented in Figure 1 a, Figure 11b, = 1.6s. The mean angular velocity throug deg/s. The experimental results differ slightly from the theore the low-pass fi However, the system is capable of completing the command y following the theoretical profile. The gim Figure 1 Both minimum and steady-state values of each gimbal are MAE for this experiment for gimbal as derived by 5 sets of measuremen 3.3122 deg and 1.7429 deg. angles 61, 62, 63, 64, atti ts are 4.1654 deg, 4.5314 d nt. ed ba 1c and Figure tud kgm*. Figure 10a illustrates that the system immediately responds to the titude as it begins to rotate about the positive yaw of the axis. The steady previously, is reached at about t = 20 s and the rising time of the system is indicates that the platform has gained a high angular velocity, as shown Ob. The maximum angular velocity achieved is 53.47 deg/s at t = 1.9 s e, which presents a maximum value of he whole manoeuvre is 8.32 tical and a minor time delay ter used to eliminate the sensor noise. maneuver with an accuracy angles of the four CMGs in 1d, respectively. shown in Table 7. The average e error and angular velocity, eg, 7.9983 d eg, 15.3848 deg,
Figure 11. Gimbal angles for 180 deg manoeuvre, (a) 61, (b) 62, (c) 53, (d) 64.
Figure 11. Gimbal angles for 180 deg manoeuvre, (a) 61, (b) 62, (c) 53, (d) 64.
Table 7. Gimbal angle values for 180 deg maneuver.
Table 7. Gimbal angle values for 180 deg maneuver.
Figure 12. (a) Attitude error and (b) angular velocity of the platform for 90 deg maneuver Figures 12 and 13 present the results for the 90 deg maneuver. It is observed that he system follows the theoretical attitude and attitude velocity profile as in the previous -xperiment. A maximum angular velocity of 32.8 deg/s is presented and the platform “completes the maneuver at about t = 17 s. However, the rising time is only 3.25 s while 10 oscillations are observed, which denotes that the system responds immediately and 1pproaches the desired angle fast. Table 8 presents the minimum and steady-state values »f each gimbal. The average MAE for the 90 deg manoeuvre for gimbal angles 61, 62, 63, 64, ittitude error and angular velocity, as derived by 5 sets of measurements, are 12.877 deg, 7.5154 deg, 10.7191 deg, 6.6816 deg, 2.5545 deg and 1.6842 deg. 8. 4 8. 4 gS
Figure 12. (a) Attitude error and (b) angular velocity of the platform for 90 deg maneuver Figures 12 and 13 present the results for the 90 deg maneuver. It is observed that he system follows the theoretical attitude and attitude velocity profile as in the previous -xperiment. A maximum angular velocity of 32.8 deg/s is presented and the platform “completes the maneuver at about t = 17 s. However, the rising time is only 3.25 s while 10 oscillations are observed, which denotes that the system responds immediately and 1pproaches the desired angle fast. Table 8 presents the minimum and steady-state values »f each gimbal. The average MAE for the 90 deg manoeuvre for gimbal angles 61, 62, 63, 64, ittitude error and angular velocity, as derived by 5 sets of measurements, are 12.877 deg, 7.5154 deg, 10.7191 deg, 6.6816 deg, 2.5545 deg and 1.6842 deg. 8. 4 8. 4 gS
Figure 13. Gimbal angles for 90 deg maneuver, (a) 61, (b) 62, (c) 63, (d) d4.
Figure 13. Gimbal angles for 90 deg maneuver, (a) 61, (b) 62, (c) 63, (d) d4.
Table 8. Gimbal angle values for 90 deg maneuver. Two main differences are noticed in the gimbal angle profiles of both experiments in comparison to the theoretical profiles. The first is that the minimum values of all four gimbal angles are larger than the expected values. This error is caused by various fabrication and assembly imperfections that lead to a non-ideal system. The 3D-printed air bearing naturally introduces a torque error to the rotating platform due to non-zero friction between the upper and the bottom part of the air bearing. In addition, static and dynamic imbalances from flywheels and CMGs along with small torques caused from cables and aerodynamic drag degrade the performance of the air bearing. It has been observed that these manufacturing flaws have a similar effect to increasing the moment of inertia of the rotating platform to J = 0.00323 kgm?. The results obtained via calculations are a better fit to the theoretical results obtained by this moment of inertia for every gimbal in the cluster, as well as the angular velocity, compared to the results obtained for the initially estimated moment of inertia of J = 0.00283 kgm?. The percentage difference of the MAE values for these two moments of inertia denote that there is a 1.71% increase only in the first gimba which is a minor change compared to the decrease in the rest of the examined parameters as shown in Table. 9.
Table 8. Gimbal angle values for 90 deg maneuver. Two main differences are noticed in the gimbal angle profiles of both experiments in comparison to the theoretical profiles. The first is that the minimum values of all four gimbal angles are larger than the expected values. This error is caused by various fabrication and assembly imperfections that lead to a non-ideal system. The 3D-printed air bearing naturally introduces a torque error to the rotating platform due to non-zero friction between the upper and the bottom part of the air bearing. In addition, static and dynamic imbalances from flywheels and CMGs along with small torques caused from cables and aerodynamic drag degrade the performance of the air bearing. It has been observed that these manufacturing flaws have a similar effect to increasing the moment of inertia of the rotating platform to J = 0.00323 kgm?. The results obtained via calculations are a better fit to the theoretical results obtained by this moment of inertia for every gimbal in the cluster, as well as the angular velocity, compared to the results obtained for the initially estimated moment of inertia of J = 0.00283 kgm?. The percentage difference of the MAE values for these two moments of inertia denote that there is a 1.71% increase only in the first gimba which is a minor change compared to the decrease in the rest of the examined parameters as shown in Table. 9.
Table 9. MAE values for two different moments of inertia. The second difference is that the steady-state value of 64 and 6) for the first and th econd experiment, respectively, deviate from the theoretical ones. Positioning the fou “MGs in the platform is achieved manually through 3D-printed holes left intentionall or bolt tightening, and slight asymmetries may affect the performance of the simulato Vloreover, in the concept of a low-cost CMG cluster, the selected gimbal motors preser ome backlash. In combination with their non-zero stall voltage, a dead zone is admitted fc ow speeds. As shown also in Figure 8, PWM signals below 40 are considered and handle is zero to prevent the gimbal motors from stalling. These motor imperfections do not affec he flywheel motors since they operate at a constant velocity. Another hardware-relate: imitation is that the gimbals are oriented manually to their initial positions because onl elative encoders are employed. Thus, minor misalignments among the initial gimbal angle nay provoke the experimental gimbal angles values to deviate from the theoretical ones Despite the limitations discussed above and the extremely low cost of 400 €-360 € fc
Table 9. MAE values for two different moments of inertia. The second difference is that the steady-state value of 64 and 6) for the first and th econd experiment, respectively, deviate from the theoretical ones. Positioning the fou “MGs in the platform is achieved manually through 3D-printed holes left intentionall or bolt tightening, and slight asymmetries may affect the performance of the simulato Vloreover, in the concept of a low-cost CMG cluster, the selected gimbal motors preser ome backlash. In combination with their non-zero stall voltage, a dead zone is admitted fc ow speeds. As shown also in Figure 8, PWM signals below 40 are considered and handle is zero to prevent the gimbal motors from stalling. These motor imperfections do not affec he flywheel motors since they operate at a constant velocity. Another hardware-relate: imitation is that the gimbals are oriented manually to their initial positions because onl elative encoders are employed. Thus, minor misalignments among the initial gimbal angle nay provoke the experimental gimbal angles values to deviate from the theoretical ones Despite the limitations discussed above and the extremely low cost of 400 €-360 € fc
Table 10. Micro/nano-satellites with CMGs.
Table 10. Micro/nano-satellites with CMGs.
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