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Design of FIU FUNSAT System: Attitude Control for the 3U CubeSat Pradeep Shinde, Elijah Newman, Ibrahim Tansel, Sabri Tosunoglu Department of Mechanical and Materials Engineering Florida International University, 10555 West Flagler Street Miami, Florida 33174 [email protected], [email protected], [email protected], [email protected] ABSTRACT CubeSats are inexpensive, versatile, light in weight and make for a very good resource when desired an inexpensive way to collect data in space. One of the subsystems of the CubeSat, which is very important and often times determines whether a mission will fail or not, is the attitude control system. Standard size of 3U CubeSat is 10 cm x 10 cm x 30 cm. Given such small dimensions, traditional ways of control are not feasible and thus the necessity for smaller components and parts arise. With this in mind, magnetic torque bars are a relatively new invention that, when mounted on the satellite’s frame has the ability to create torques. They consist of a metal rod usually wrapped in copper wire to create an electromagnet. The magnetic field created by the electromagnet will try to align itself with the earth’s magnetic field which creates the torques. This paper presents a simple design for a torque rod developed intended to be implemented on Florida International Universities’ RoarSAT. Keywords Attitude control, Attitude determination, CubeSat, 3U, FUNSAT 1. NOMENCLATURE µ τ V M B Core Radius, m Core length, m Permeability of Free Space, H/m Relative Permeability of Core, H/m Torque, Nm Voltage, V Current, A Wire Resistivity, / Solenoid Resistance, Wire Length, m Core Length, m Demagnetizing Factor Coil Turns Total Moment, Nm Magnetic Field, T p m P F f Momentum, Mass, Power, W Force, N Frequency, Hz / 2. INTRODUCTION CubeSat’s have grown in popularity in recent years. This is due to their small size, light weight, low cost and their ability to transport a variety of payloads. Because of this, it is necessary to miniaturize components, which includes the attitude control system (ACS). Full-scale satellite attitude control systems, in general are too large or too expensive to be installed in the CubeSat’s [1]. In recent years, the use of magnetic torque bars (aka magnetorquers) and small sized reaction wheels, have been explored in the application of controlling these small space vessels [2, 3, 4]. The work of A magnetic torque bar as referred to in this paper, is a current carrying solenoid with a magnetic-material core, which, when a current is passed through, it produces a resulting torque. While this is the type of torquer that will be elaborated on, there are two other primary ones; the air coil torquer and the permanent magnet. The air coil is a planar enclosed current carrying coil; similar to the first torquer it creates a moment when a current is sent through it. The third is the permanent magnet, which by interaction with earth’s magnetic field creates a magnetic moment; however, there is no simple way of controlling its magnitude and direction. With this in mind, the electromagnetic torquer remains the most feasible given that they require the least amount of power and have the ability to be adjusted based on requirements. While the produced torque is small, the satellite will be operating at LEO, and the necessary minimal torque is therefore justified. This paper has organized as follows: Section 3 summarizes the architecture od the attitude control system, its mission goals in respect with RoarSAT, theoretical calculation Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 266 procedures, orbital parameters, design specifications and proposed design. The equations used for the theoretical calculations are from the work of Bauer, W., and Gary D. [5] and Mehrjardi, Mohamad Fakhari, and Mehran Mirshams [6]. Section 4 discusses the proposed attitude control system with the cost and weight budget of the proposed system. In section 5 conclusions are made and future considerations are proposed. Followed by the acknowledgement and references in sections 6 and 7 respectively. and z directions). This component will be controlled by an ATmega328 single chip host controller. The responsibility of the sun sensor is to keep track and measure the position of the sun with respect to the satellite. It works by letting light into the chamber of the sensor which strikes lightsensitive cells. With a reference centerline, a refraction angle can be measure using the chamber height. Because 3. ATTITUDE CONTROL SYSTEM An attitude control system can be divided and distinguished as individual counterparts, i.e. attitude determination (AD) and the actual attitude control (AC). These counterparts each have their own components and specifications, and in combination they form a complete attitude control system. Upon initial launch and release into orbit, the satellite will be tumbling about all axes in an uncontrolled manner. It is the responsibility of the ACS to correct this and then orient the satellite in a specific direction based on the predetermined requirements. Accounting for the fact that there has been a plethora of research in the field encompassing concepts, manufacturing and testing of such systems, this paper presents a basic but highly effective design to be implemented on Florida International University’s RoarSAT. An AD system can be made using a variety of sensors. The idea is to measure variables that allow the onboard computer to develop a matrix which describes the motion about all axes of the satellite at a specific moment. The computer then uses this to generate a correction matrix to be implemented by the AC. A correction matrix after launch will be generated instantly by the satellite, however all other maneuvers that are mission specific will be sent from earth for the satellite to keep its path. The next step is to implement the AC. Like AD, there are numerous ways to make and implement attitude control. Typically, larger space vessels and satellites use thrusters, however, given the constraints, magnetic torque bars will be employed on each principal axis. Each torque bar will have the ability to produce a torque which in turn acts on the satellite to change its direction. However, the produced force is limited and remains a function of the electromagnetic core and the specifications of the coil. 3.1 Attitude Determination The purpose of the AD system is to establish the satellites orientation and position at a given moment. To do this, the LSM9DS0 sensor board (Figure 1) will be used in conjunction with a sun sensor (Figure 2) to determine the acceleration, orientation, magnetic field and position with respect to the sun. This sensor board is a SIP containing a 3D accelerometer, 3D gyroscope and a 3D magnetometer (3D in this case represents a sensor measurement in the x, y Figure 1. LSM9DS0-9DOF Sensor the light cells operate on the photoelectric effect, the photons are converted into electrons and then into a digital signal to be read by the host controller. In different AD systems implemented on other satellites, sensor selection can be different. This is usually dependent on mission objective and any constraints presented during the design, construction and fabrication process for the vessel. One application that has been explored during the process of developing this proposal is the observation of earth through a long optical lens. The payload would also include a thermal camera and the main purpose would be to gather weather data and thermal images that can help predict cloud height amongst other things. With this endeavor, it is not necessary to keep and maintain very accurate pointing coordinates, and it would be a waste of power if that were attempted. This means that there is a tolerance that is acceptable; a reasonable degree of inaccuracy to which the satellite can point without compromising the mission objective. However, if a high degree of accuracy was desired, using reaction wheels and or control moment gyros in combination with the magnetorquors would allow for a much better degree of accuracy. The reaction wheels and or the gyros would act as the main source for attitude control, the torquers would then be a secondary means-useful for desaturation and despinning the satellite after launch into orbit. However, it is important to note that the addition of these components add to the total weight resulting in increased costs. Figure 2. Sun Sensor Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 267 3.2 Attitude Control Magnetic torquers work through interaction of the satellite’s magnetic field with earth’s magnetic field. With each coil, when current flows through the loop it creates an electromagnet. With each of the torque bars placed and oriented along different axes, the corresponding directions of the magnetic fields will be different. By determining a value for the current flowing through the loops based on voltage and resistance, a magnetic field for each torque bar can easily be calculated. The magnitude and direction of earth’s magnetic field will also vary, and maintaining that the satellite is in a LEO, the earth’s magnetic field is still strong enough to create a torque on the satellite thus changing its direction. 3.3 Velocity Calculations Given a maximum force that each torquer is required to produce, the equations below outline the requisite steps needed to obtain a final design. First, a period must be defined. When launched into space, depending on the altitude of the orbit the satellite will take, the period will vary and therefore this must be the first parameter defined as this affects all further calculations. The frequency ‘ ’ is calculated using (1) where ‘T’ is the period. 1 (1) The angular velocity is then calculated using (2) and velocity using (3) where ‘c’ is defined as the radius of orbit. 2 (2) (3) Momentum equations relate the mass and velocity of an object. With this, the required force needed to shift the satellite can be calculated. (4) A velocity vector relationship (Figure 3) can then be developed to calculate the velocity difference needed to shift the satellite θ degree in pre-specified time frame, which would then be resubstituted into (4) to obtain the design force that each torquer would need to produce. vi θ vdifference summarizes the orbital information operating at 600km above the surface of the earth. Table 1. Orbital Parameters Orbital Radius 6971 km Orbital Time 1 h, 36 m, 41 s Period 5801 s 1.723841 Frequency 1.083121 Angular Velocity Velocity 10 Hz rad/s 7.55 km/s Momentum 30200 kg-m/s In the design of the attitude control system for RoarSAT mission, a standard scenario was considered. Change in momentum required for one-degree change in angular rotation in one particular direction was determined. Table 2 summarizes the parameters obtained to be used in the design of the torquers. Table 2. Design Parameters 1 Degree Rotation Initial Momentum 30200 kgm/s Required Change in Velocity 131.78 m/s Required Change in Momentum 527.14 kgm/s 3.4 Torquer Calculations Torquer system is designed in the following sequence to generate desired control on attitude of the satellite. First, as designed parameters, a wire length and core radius will be defined from which the number of loops is calculated using equation (6). (6) 2 It is then necessary to obtain a value for the total resistance of the wire. Equation (7) shows the resistance calculation and finally a current is obtained using (8). (7) (8) It is necessary to calculate a demagnetization factor which accounts for the stray field produced by the magnetization of the cylindrical core. This is given by (9). 4 ln vf 10 1 (9) 4ln Figure 3. Velocity Vector tan θ (5) RoarSAT’s mission focusses on Earth’s ground surveillance from 600km above the Earth’s surface. Table 1 Finally, a magnetic field and moment for the satellite can be calculated using (10) and (11) respectively. 1 Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. (10) 268 1 (11) 1 1 With the calculated moment and magnetic field, the torque produced is given by (12). 1 (12) Applying these equations for a torquer core of perm alloy and a copper solenoid, the values obtained are as follows. Table 3. Torquer Specifications Core Length 0.09 m Core Radius 0.002 m Demagnetization Factor 0.005586028 Wire Resistivity 1.68E-08 Relative permeability 75000 Wire Length 100,m Number of Turns 7957 Wire Resistance 3.44 Ω/m Wire Gauge 40 Coil Layers 6.96 Magnetic Field 0.2311258 T Magnetic Moment 0.208828 N-m Torque 0.048265 N-m Force 24.133 N Table 3, above shows the torquer specifications of the proposed design. For the proposed torquer design, the generated force at the end of the torque bar can be found around 24 N. With this generated force and change in momentum required for one-degree change in angular rotation of the RoarSAT, total time required can be found using the equation (13) below. For the current design total time of around 21.84 seconds was found to change the attitude of the RoarSAT by one-degree change in angular rotation. (13) ∆ ∆ Alternatively, a power and voltage can be defined as designed parameters, from which the total circuit resistance and wire length can be calculated. This is given by (14) and (15) respectively. permalloy core with 4 mm diameter and 9 cm length and 40-gauge copper coil with 100 m in length was proposed. With the design presented, the force produced by the attitude control system was ~24 N, and the time required to change the RoarSAT’s attitude by one-degree change in angular rotation is ~22 seconds assuming there are no external forces that act on the satellite and no interruptions in its flight path. The power consumption of the proposed design is found to be 0.0465 W, based on the 4 V supply from the on-board power system. Total cost and weight estimate of the attitude control system is another primary aspect in terms of determining the feasibility of the system for the required mission. Total cost of the proposed system is $2135 whereas the weight of the system is around 41 g, as can be seen from Table 4, below. Table 4. Cost and Weight Estimate Component Cost Weight LSM9DS0 $40 4g Sun Sensor $2000 5g Perm alloy Rod x3 $70 30 g 40ga Copper Wire (300m) $25 1.5 g Total $2135 40.5 g It is to be noted that there is only one sun sensor used in the proposed design due to the high cost of the sensor. Ideally, six of these sensors should be used on each face of the structure. However, using only one sun sensor RoarSAT team is proposing the cost efficient system. Use of only one sun sensor will require initial alignment of the sun sensor in the direction of the sun. Initial alignment will be conducted by continuously changing the attitude of the RoarSAT in search of the sun in all three directions, by receiving the output from the sun sensor. This will consume more time during the initial alignment, however it will save $10,000 on the additional five sensors cost. 5. CONCLUSION 4. DISCUSSION Light weight, low power and cost effective RoarSAT attitude control system has been conceptually designed for complicate mission demands. The design presented makes use of a perm alloy rod, 9cm in length and having a diameter of 4mm. It is wrapped in 40-gauge copper wire forming approximately 7 copper layers of coil with a combined total of 7957 turns. The proposed design precisely shows around 22 seconds required to change onedegree angular rotation of RoarSAT. The proposed system weighs around 41 g, consumes around 0.0465 W and costs $2135. The paper presents two alternative methods of designing the attitude control system in the earlier section. The first one with wire and core as design parameters where as the second one is the voltage and power available as the design parameters. First method of design was elaborated in the paper. For the RoarSAT’s attitude control system The proposed design is only left to be tested. For further development, the present design can be optimized with the trade off between the weight, power consumption and attitude control time. Another improvement can be done by reducing the components cost, specifically the cost of the sun sensor, by replacing the sun sensor with light sensor for (14) (15) Following this, the procedure highlighted above would then be applied and carried through the same way to ultimately obtain a design force and time required for the precise control of the RoarSAT’s attitude. Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 269 the required wavelength and use of more complex programming. 6. ACKNOWLEDGMENTS RoarSAT development is conducted as a part of the FUNSAT 2015-2017 competition organized by NASA’s Florida Space Grant Consortium (FSGC). Therefore, the authors acknowledge the financial support and motivation provided by FSGC. The authors also acknowledge the support received from the Department of Mechanical and Materials Engineering (MME) of Florida International University (FIU). Authors extend their thanks to the reviewers for many useful comments which helped to greatly improve the paper. The authors finally wish to thank the members of the Near Earth Explorers (NEE) Student Club at FIU for the continuation of the present work towards building and testing of the proposed attitude control system. 7. REFERENCES [1] Y.W. Jan and J. C. Chiou. (2005, Feb.). Attitude control systemfor ROCSAT-3 microsatellite: a conceptual design. Acta Astronautica. [Online]. 56(4), pp. 439–452. Available: http://www.sciencedirect.com/science/article/pii/S009457650 4002231 [2] G. P. 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(2010, Apr.). Design and Manufacturing of a Research Magnetic Torquer Rod. Presented at Fourth International Conference on Experimental Mechanics. [Online]. Available: http://proceedings.spiedigitallibrary.org/proceeding.aspx?arti cleid=775628 Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 270