Design and performance simulation of a satellite momentum exchange actuator

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1 Australian Journal of Mechanical Engineering ISSN: (Print) (Online) Journal homepage: Design and performance simulation of a satellite momentum exchange actuator Abolfazl Shirazi & Mehran Mirshams To cite this article: Abolfazl Shirazi & Mehran Mirshams (2016) Design and performance simulation of a satellite momentum exchange actuator, Australian Journal of Mechanical Engineering, 14:1, 1-9, DOI: / To link to this article: Published online: 18 Nov Submit your article to this journal Article views: 405 View related articles View Crossmark data Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at

2 Australian Journal of Mechanical Engineering, 2016 VOL. 14, NO. 1, Design and performance simulation of a satellite momentum exchange actuator Abolfazl Shirazi and Mehran Mirshams Space Research Laboratory, Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran ABSTRACT The attitude determination and control subsystem is tasked with identifying the location and the orientation of the satellite at all times during the mission. Momentum exchange actuators such as reaction wheels are mounted on the satellites to transfer some of their torque, turning them through its centre of mass along each of three axes. In this paper, the design process of a momentum exchange actuator is presented, which has been designed and manufactured in Space Research Laboratory. This device named as RW2000 is the engineering model of reaction wheel for the satellite control simulator. In this approach in designing, design parameters related to the manoeuvrability of the system are considered as the inputs of the design process. After presenting the overall concept of the design process along with constrains, the general analysis of the actuator s performance is investigated and the related equations are derived. Using the derived equations, the design process is developed. Finally, the engineering model of reaction wheel is designed using the proposed algorithm. The results of the performance test of the manufactured actuator accredit the accuracy and the correctness of the proposed design algorithm. ARTICLE HISTORY Received 1 April 2014 Accepted 30 June 2014 KEYWORDS Momentum; reaction wheel; attitude control; simulator; design process; satellite; actuator 1. Introduction Accurate and effective control of spacecraft is a significant challenge due to the inherent nonlinearity of their dynamics in orbital missions. Attitude determination and control subsystem is an important part of the satellite system and the performance life of the spacecraft is related to this subsystem (Fortescue, Stark, and Swinerd 2011). Accuracy and stability in attitude manoeuvres are the main factors in designing this subsystem. There are some limitations in this design process like the overall weight and the overall power consumption of the actuators. Therefore, choosing proper attitude actuators is an important challenge which leads us to have acceptable accuracy and manoeuvrability in addition to minimum weight, minimum power consumption and maximum reliability. Reaction wheels are momentum exchange devices which are used for attitude stabilization and attitude manoeuvres in satellites (De Ruiter, Damaren, and Forbes 2013). In momentum exchange devices, a free rotating mass attached to the satellite has the ability to change the angular momentum of the whole satellite which results in an attitude manoeuvre or the attitude stability against disturbance torques in space (Wie 2008). Many space related laboratories focus on designing attitude actuators in recent years and various organizations have attempted to design reaction wheels for different types of satellites. Sinclair Interplanetary has developed a low-cost scalable reaction wheel for nanosatellites in collaboration with University of Toronto s Space Flight Laboratory (Werremeyer et al. 2012). SunSpace is another organization which has manufactured a reaction wheel that can be controlled by current or by speed through a serial RS485 interface (Engelbrecht 2005). Recent studies concern the design process of reaction wheels not only for single-axis control, but for using in combinations with different types of actuators such as magnetorquers (Polites, Kalmanson, and Mangus 2008). In order to develop, improve and carry out operational tests of actuators and attitude control algorithms in experimental framework, the 3-DOF spacecraft simulator has been developed as part of a research programme on spacecraft multi-body rotational dynamics and control, by the technical team in Space Research Laboratory (Mirshams and Taei 2009). This test-bed is used to explore various issues and concepts in spacecraft dynamics and control. The main components of this facility are spherical air-bearing, three-axial sensor, battery, onboard processor, reaction wheels and cold gas thrusters. All of these subsystems have been designed and manufactured in Space Research Laboratory. The main project challenges were air-bearing design, high-efficiency actuators, CONTACT Abolfazl Shirazi 2015 Engineers Australia ashirazi@mail.kntu.ac.ir

3 2 A. Shirazi and M. Mirshams may vary in different cases. Availability of bearing in reaction wheel manufacturing process limits the maximum rotational speed. In fact, maximum rotational speed is related to the type and the quality of the bearing used in reaction wheels. Also, the type of the motor that is available for the manufacturing group limits the control torque. In the design process, each of these limitations should be stated according to the requirements. Figure 1. Spacecraft control simulator (HOJJAT100). remote communications, high-frequency data collection, optimal control algorithm and manufacturing of main subsystems (Mirshams, Vahid, and Taei 2010). This simulator is illustrated in Figure 1. The design process of reaction wheel, which is going to be presented in this paper, is an improved algorithm which has been used in manufacturing several classes of reaction wheels such as RW1800 and RW1900 for the introduced control simulator. However, the design process that is about to be presented in this paper is completely general and can be used in designing reaction wheels for any control simulators or satellites. The overall concept of the design algorithm for a reaction wheel is to manufacture an actuator that is capable of rotating the simulator or the satellite based on momentum exchanging. The design process is based on a single-axis attitude manoeuvre. The actuator must be able to rotate the simulator within a specific range in a limited time. In this paper, the preliminary analysis of the reaction wheel performance is investigated as the first step and the related equations are derived. In this phase, the equations of attitude manoeuvre of simulator are derived based on using reaction wheels. The next phase is developing the design process based on the derived equations. This phase is divided into several steps and some of the steps should be followed iteratively in order to satisfy requirements and limitations. This phase would be the main contribution of this research. After developing the design process of reaction wheels, the engineering model of reaction wheel named RW2000 is designed using the proposed algorithm and finally the correctness of this process is validated by testing the performance of the manufactured reaction wheel in an attitude manoeuvre of the control simulator. There are many limitations in the design process of a reaction wheel such as maximum nominal rotational speed, control torque, dimensions, weight and material. Each of these limitations is related to a parameter which 2. Mathematical modelling of attitude manoeuvre The parameters, which are involved in the design process of a reaction wheel, must be defined before the development of the design algorithm. The main parameters are the moment of inertia of simulator (I S ), actuator s moment of inertia (I W ), total deviation of simulator at the end of the attitude manoeuvre (Δθ S ), attitude manoeuvre total time (t max ), the control torque of reaction wheel (T), the power consumption of reaction wheel (P) and the maximum rotational speed of reaction wheel (ω max ). In this phase, the equations which state the relations between the design parameters are derived. Single-axis attitude manoeuvre is based on the conservation of the angular momentum when a single reaction wheel is used as an actuator. The system consists of two main bodies including the reaction wheel and the simulator. If the disturbances are neglected, the conservation of angular momentum equation will be governed as Equation (1) (Hibbeler 2010). Ḣ S = Ḣ W (1) In this equation, Ḣ S and Ḣ W are the time rates of angular momentum changes of simulator and reaction wheel, respectively. Considering a classic attitude manoeuvre for the simulator can lead us to the fact that the rotational speed of reaction wheel and simulator is equal to zero at the beginning and the end of the attitude manoeuvre. Therefore, by integrating both sides of the conservation of angular momentum equation, the following equation is obtained. I S ω S (t) = I W ω W (t) (2) In this equation, I S and I W are the moment of inertia of the simulator and the reaction wheel, respectively. Also, ω S (t) and ω W (t) are the angular velocities of the simulator and the reaction wheel, respectively, as a function of time. The angular velocity changes of the simulator and the reaction wheel can be divided into three time steps during the attitude manoeuvre. The first and last time steps represent the times when the reaction wheel increases and decreases its speed, respectively, while the second time step is the time when the wheel rotates with no angular acceleration. The rotational speed at the second time step may not be constant due to disturbance torques and other factors. By considering such a profile for the

4 Australian Journal of Mechanical Engineering 3 attitude manoeuvre, these changes in angular velocity of the wheel will be as follows. ω w (t) = ω w1 (t) 0 < t < ω w2 (t) < t < + t 2 ω w3 (t) + t 2 < t < + t 2 + t 3 (3) Expanding and integrating Equation (2) yields Equation (4) as follows. Δθ s = I [ +t 2 w ω I s w1 (t)dt + 0 ω w2 (t)dt + 3. Design algorithm of momentum exchange actuator The final goal of this research is to design a reaction wheel that is capable of rotating the simulator by its rotational speed at a limited time using the proposed design algorithm. There is a characteristic for the reaction wheel which conveys its ability to rotate another body in the attitude manoeuvre. The moment of inertia of the system, total attitude manoeuvre time and the total deviation of +t 2 +t 3 +t 2 ] ω w3 (t)dt (4) Equation (4) states a relation between the total deviation of the simulator and the rotational speed of the reaction wheel along with moment of inertias. Note that the integrator in the left-hand side of above equation is replaced by the equivalent term which shows the area under the plot of the angular velocity changes of the reaction wheel according to Equation (3). The parameters, t 2 and t 3 are the time limits in Equation (3). The parameters and t 3 are not exactly equal because the reaction wheel uses its maximum capability to reach its maximum rotational speed at the beginning of the manoeuvre as soon as it receives the command, but the decreasing rate of the rotational speed needs less control torque. Although there is a small difference between these two time limits, this difference can be neglected as it has a very neglectful effect on the results. Such differences is determined and analysed in preliminary design and detail design stage. As the work in this paper is in conceptual design stage, such concerns are not considered in design approach. The equation of control torque can be used in preliminary analysis of the attitude manoeuvre of the simulator. Equation (5) shows the relation between the control torque and other parameters in each time limit. the system are the design parameters which should be defined in developing the design process. Other parameters such as the power consumption, maximum rotational speed and the control torque are the requirements in the design process. The batteries which are the power supplier in the simulator have limited power supply for the reaction wheel. Therefore, there is a maximum value for allowable power consumption of the reaction wheel in the design process. Similarly, the type of the bearing used in the manufacturing of the reaction wheel limits the maximum rotational speed. Also, the motor type used for rotating the reaction wheel limits the control torque. Finally, the output of the design process will be the moment of inertia of the reaction wheel along with the possible suggestions for its dimensions and material. Figure 2 illustrates the overall concept of the design process. Three main assumptions are considered for developing the design process. First, all of the disturbance T i = I w ω wi (t) (5) Using Equation (5), the control torque of each time limit can be obtained. It is clear that the control torque in the second time limit (t 2 ) is zero if the rotational speed of the reaction wheel assumed to be constant. The power consumption of the reaction wheel in each time limit can be obtained by the following equation. P i = I w ω wi (t)ω wi (t) (6) If a unique value for the parameters and t 3 along with the same rotational speed gradient of the wheel are assumed in the first and last time steps, the control torque and the power consumption of the reaction wheel in these two time limits will be equal. Figure 2. Actuator design process concept.

5 4 A. Shirazi and M. Mirshams torques are neglected due to their small value in comparison to the reaction wheel torque. Second, the angular acceleration of the reaction wheel is assumed to be constant during the increment or reduction of the reaction wheel rotational speed. Third, all of the frictions in the rotation of the reaction wheel are neglected. According to these assumptions, it can be concluded that the two time limits and t 2 are equal. Rewriting Equations (4) (6) along with these assumptions will result a group of equations which can be solved simultaneously. The input variables such as I S, Δθ S, t max are known, while I W,, t 2, t 3 are unknown. Also, the two parameters ω maxw, P are the requirements which should be satisfied. Resolving the equations for the unknown parameters will result the following equations. t max P t 2 max P2 2ω maxw (Δθ s )I s P I (7) w = t max P = t 3 = t 2 = ω 2 maxw t 2 max P2 2ω maxw (Δθ s )I s P (8) In these equations, ω maxw is the maximum is rotational speed of the wheel and t max is the total time. It is clear that Equation (7) has a solution if and only if the following inequality is satisfied. The constraint in Equation (10) shows the minimum required power supply of the reaction wheel for the desired attitude manoeuvre. Equation (7) shows the required moment of inertia of the reaction wheel as a function of the power consumption and maximum rotational speed. Using this equation, the required moment of inertia of the reaction wheel can be plotted as a function of power consumption and different values of maximum rotational speed. An example of this surface is illustrated in Figure 3. The design process can be started at this point. The batteries used in the simulator as the power supplier for the reaction wheel create a safe area in Figure 3. In this area, the power consumption of the reaction wheel is lower than the critical value that is limited by the batteries. This area can be called as Design Area in the figure which is bounded by a minimum value of the power consumption according to Equation (10). 2P t 2 max P2 2ω maxw (Δθ s )I s P P P min > 2ω maxw (Δθ s )I s t 2 max (9) (10) Figure 3. Required moment of inertia as a function of power and speed. Regarding Figure 3, it can be concluded that by choosing high maximum rotational speed for the reaction wheel, the minimum power consumption required for the attitude manoeuvre is increased. Also, in constant power consumptions, small moment of inertia is needed for the reaction wheel as the maximum reaction wheel speed increases. It should be emphasized that different input values may result in high power consumptions which may not be in the design area according to the limitation of the power consumption. Another observation in Figure 3 is the points with the same moment of inertia. It can be seen that for some input values, there may be some points in the design area which results a unique moment of inertia and the power consumption for the reaction wheel, but two different values can be assumed for the maximum rotational speed. Using Equations (5) and (6), the control torque of the reaction wheel can be calculated as a function of power consumption and the maximum rotational speed. The reaction wheel torque should be calculated before finalizing the values of the power consumption and the maximum rotational speed. It should be verified that whether the required control torque of the reaction wheel is appropriate with the motor type of the reaction wheel or not. At this point, a method for determining the moment of inertia of the reaction wheel can be defined. The overall algorithm of reaction wheel design process is illustrated in Figure 4. The input variables are known at the beginning of the design process. Therefore, the surface that illustrates the changes of moment of inertia can be plotted according to Equation (7). The design area will be defined according to the maximum allowable power consumption of the reaction wheel, which depends on the type of batteries used in simulator. Then, the maximum rotational speed will be specified according to the bearing type of the reaction wheel. The design point will be selected and the

6 Australian Journal of Mechanical Engineering 5 Figure 4. The overall algorithm of reaction wheel design process. moment of inertia along with the power consumption of the reaction wheel can be obtained. Consequently, the required control torque of the reaction wheel can be obtained. If the value obtained for the required control torque is more than the maximum allowable value, the design process should be restarted and another design point must be selected. This iterative process continues until all the values satisfy their requirements. After finalizing the parameters, the moment of inertia of reaction wheel is known. At this point, the physical properties of the reaction wheel can be defined according to the obtained moment of inertia. There may be many methods for specifying the physical properties of the reaction wheel in order to satisfy the obtained moment of inertia. 4. RW2000 design process The reaction wheel that is going to be designed is an engineering model of reaction wheel named RW2000 that is expected to be used as an actuator for attitude manoeuvres in the presented attitude control simulator in Space Research Laboratory. This attitude control simulator imposes specific requirements and limitations for the reaction wheel designing. According to the design process, which is presented previously, the reaction wheel is going to be designed at different steps. The inputs of the design process are specified according to the desired attitude manoeuvre. Designing a reaction wheel, which is capable of rotating the attitude control simulator π radians within less than 60 s, is desired. Moreover, the moment of inertia of attitude control simulator in Space Research Laboratory (HOJJAT100) on the favourable axis is 5 kg m 2. The limitations and requirements for designing the reaction wheel are specified. Generally, the available bearing that is going to be used in reaction wheel manufacturing can make the reaction wheel rotate with the maximum rotational speed of 150 Hz. This limitation is subjected to our current technology available in manufacturing group at Space Research Laboratory. Also, the batteries used in the attitude control simulator as the power supplier for the reaction wheel can supply the maximum of 15 W energy for the reaction wheel. Finally, the available motor that is going to be used in manufacturing the reaction wheel can provide the maximum control torque of 0.05 N m. Note that the safety margin is properly considered in defining these limitations. The required moment of inertia as a function of power consumption for different maximum rotational speeds according to Equation (7) is plotted as follows. The design area is specified according to the maximum power consumption. The design point is selected and the parameters related to this design point are illustrated in Figure 5. The required control torque regarding the selected point is 0.03 N m. Clearly, the calculated control torque satisfies the requirement. Note that, this value is the final result that is obtained after some iteration.

7 6 A. Shirazi and M. Mirshams Figure 5. Changes of required moment of inertia of RW2000. Table 1. Characteristics of RW2000 at the end of design process. Figure 6. Overall shape of RW2000. Parameter Quantity Maximum rotational speed 125 Hz Theoretical nominal torque 0.03 N m Mass (rotating part) 0.8 kg Overall dimension Ø mm Moment of inertia (rotating mass) kg m 2 Mechanical power 12 W According to Equations (8) and (9), the first and last time limits will be s, while the second time limit is 39.3 s. Clearly, the summation of the time limits will be the total time of the attitude manoeuvre. The physical characteristic of the reaction wheel such as geometry, dimensions and material according to the moment of inertia of the reaction wheel can be specified at this step. This step does not have a unique process and any procedure for specifying the physical characteristics of the reaction wheel may be used as a new self initiated manner. In the current design, there are no special requirements in determination of the physical properties of the reaction wheel. However, the physical characteristics of the reaction wheel based on minimizing the weight of the reaction wheel are going to be specified. In this case, the weight distribution of the reaction wheel is determined so that the overall weight reaches its minimum possible value besides the satisfaction of the desired moment of inertia with an acceptable safety margin. Therefore, two different materials are used. Phosphor bronze is used as the dense material in the border of the reaction wheel and Aluminium is used as the light material in the centre of the reaction wheel. Proper dimension is specified for each part in order to satisfy the desired moment of inertia of the reaction wheel with an acceptable safety margin. The overall shape that is considered for the reaction wheel is shown in Figure 6. The overall dimension which is considered for the selected shape is 100 mm 62 mm which provides the moment of inertia of kg m 2 for the wheel. The final characteristics of the reaction wheel are shown in Table Performance simulation of RW2000 Advanced simulation of reaction wheel performance is developed in order to make sure that the wheel can operate properly during the attitude manoeuvre with regard to actual reaction wheel control law. More details are included in this kind of simulation. PID control method is used for the wheel as it can be applied to various versions of such systems. Controller is designed based on worst-case scenario for the uncertainty in the wheel. Limitations and requirements such as power consumption and maximum rotational speed of the wheel are considered. Simulation block diagram of system and reaction wheel performance in a single-axis attitude manoeuvre are illustrated in Figures 7 and 8, respectively. Deviation of the system with regard to the simulation block diagram of reaction wheel performance is analysed. Result is depicted in Figure 9.

8 Australian Journal of Mechanical Engineering 7 Figure 7. Overall simulation block diagram of single-axis attitude manoeuvre. Figure 8. RW2000 performance simulation block diagram. Figure 9. Simulator deviation angle in attitude manoeuvre. Figure 11. Momentum exchange actuator with protective cap. Figure 10. Engineering model of reaction wheel (RW2000). The changes of system deviation angle indicate that the controller parameters are well defined as the wheel response is appropriate with regard to the desired attitude manoeuvre regarding the assumed manoeuvrability. 6. Performance test and validation The engineering model of reaction wheel is manufactured after finalizing its characteristics using the proposed design process. Figures 10 and 11 show this actuator after the manufacturing process. The real characteristics of the wheel can be measured and compared with the theoretical values which were obtained in the design process. By this comparison, the correctness of the proposed design process can be investigated. In addition to physical properties measurements, functional and performance test is done on the reaction wheel according to ECSS standard. The reaction wheel is mounted on the attitude control simulator in Space Research Laboratory and several attitude manoeuvres have been adjusted as depicted in Figure 12.

9 8 A. Shirazi and M. Mirshams Figure 12. RW2000 mounted on the attitude simulator. Figure 13. Rotational speed changes of RW2000 in attitude manoeuvre. Table 2. Performance test results of RW2000. Parameter Quantity Maximum rotational speed Hz Power (standby) 0.76 W Power (nominal speed) W Power (maximum torque) W Maximum control torque N m The test results are illustrated in Table 2. Comparing the real power consumption of W with the theoretical power consumption of 12 W, which is obtained in the design process, can lead us to the fact that the power consumption of actuator is in the safe range. Also, it can be seen that the proposed design process can be trusted in estimating power consumption of the actuator in the attitude manoeuvre. The rotational speed variation and the torque variation of the wheel during the attitude manoeuvre are shown in Figures 13 and 14 respectively. The attitude manoeuvre is established based on constant torque in the first and last time limit and constant rotational speed at the second time limit regarding the assumptions in the design process. Analysing Figure 13 with regards to Equation (3) shows the accomplishment of the manufacturing process of the actuator with regard to the initial assumptions. The changes in control torque and rotational speed in the attitude manoeuvre are nearly the same as they are in the design process. It can be observed that there is a small fault in these changes at two times (t = 10 s, t = 50 s) during the attitude manoeuvre. These undesirable changes occur in the times when the actuator is about to change its rotational profile from constant rotational speed to constant rotational acceleration and vice versa. The probable reason for these small undesirable changes can be the error in reaction Figure 14. Control torque changes of RW2000 in attitude manoeuvre. wheel controller performance, encoder fault or the sensor tolerance (Leite, Da Fonseca Lopes, and Kuga 2006). The presented design algorithm is an improved process that is enhanced for designing RW2000 in conceptual design stage. Earlier classes of reaction wheels which were designed based on case studies are compared with RW2000 in Table 3. Regarding Table 3, the enhancement of the proposed design algorithm is concluded. It can be observed that while earlier classes of reaction wheels are heavier and require more power, newly designed reaction wheel is lighter and has less power consumption. Comparing maximum rotational speeds also reveals that RW2000 uses high rotational speed instead of having high weight and moment of inertia in providing required angular momentum in attitude manoeuvres. Therefore, the advantage of RW2000 in performance and power consumption in comparison to earlier versions of reaction Table 3. Comparison of different classes of reaction wheels. Actuator model name Mass (kg) Maximum rotational speed (Hz) Maximum power (W) Voltage (v) RW RW RW

10 Australian Journal of Mechanical Engineering 9 wheels shows the effectiveness of the presented design process. 7. Conclusions In this paper, the design process of an engineering model of reaction wheel named RW2000 is presented. This actuator is used in the attitude control simulator at Space Research Laboratory. Constraints on power, torque and speed are included in the analysis. The proposed design process is a general algorithm for designing reaction wheels. Several performance tests of the manufactured reaction wheel have been conducted. The results are presented at the end of this research. These results validated the accuracy and the correctness of the proposed design process. Applying additional requirements and limitations to the proposed design process is the main further work for this research. In the other word, the presented design process can be improved based on other limitations and requirements which may be crucial in some cases according to the desired attitude manoeuvre of attitude control simulator or the satellite. Other constraints like lubrication, which can impact not only the design process but also the performance, can be investigated in further works. Disclosure statement No potential conflict of interest was reported by the authors. Notes on contributors Abolfazl Shirazi received his BS and MS degrees in Aerospace Engineering from K.N. Toosi University of Technology, Iran, in 2010 and 2012, respectively. He is presently the head of Technology and Manufacturing Group in Space Research Lab at K.N Toosi University of Technology, Iran since He has academic experience in space engineering with specialization on reaction wheels and attitude control simulators as well as spacecraft guidance and control. He is also the teaching assistant at K.N. Toosi University of Technology in several courses such as Advanced Orbital Mechanics and Spacecraft Dynamics and Control. Mehran Mirshams received the BS degree in Mechanical Engineering from the Isfahan University of Technology, Iran in 1992 and the MS and PhD degrees in Aerospace Engineering from Moscow Aviation Institute MAI, Russia in 1994 and 1999, respectively. He is presently an associate professor and head of the Space Research Lab www. spacerl.com at Aerospace Faculty, K.N. Toosi University of Technology, Tehran, Iran, since His PhD research involved optimum conceptual design of satellites. His research focuses on the spacecraft s system engineering design methodologies, spacecraft and its subsystem s simulators and recently the new educational plans and pedagogical methods for engineering students. In this way, he has published some papers about spacecraft and its subsystems design and simulations. References De Ruiter, A. H. J., C. Damaren, and J. R. Forbes Spacecraft Dynamics and Control. New York: J. Wiley. Engelbrecht, J. A. A User s Manual for the Reaction Wheel and Gyroscope SunSpace Subsystem. Matieland, South Africa: SunSpace. (SS ). Fortescue, P. W., J. Stark, and G. Swinerd Spacecraft Systems Engineering. New York: J. Wiley. Hibbeler, R. C Engineering Mechanics: Dynamics. 12th ed.. Upper Saddle River, NJ: Prentice Hall. Leite, A., R. V. Da Fonseca Lopes, and H. K. Kuga Model-Based Fault Detection on a Reaction Wheel. In Brazilian conference on dynamic, control and their application, Guaratingueta, SP, Brazil, May Mirshams, M., and H. Taei A 3-DoF Satellite Simulator Design and Development. In 60th International Astronautical Congress. Daejeon, Republic of Korea. Mirshams, M., M. A. Vahid, and H. Taei A Systems Engineering Tool for Satellite Simulator Design. In ASME th Biennial Conference on Engineering Systems Design and Analysis, Istanbul, Turkey, July Polites, M., J. Kalmanson, and D. Mangus Solar Sail Attitude Control using Small Reaction Wheels and Magnetic Torquers. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 222 (1): Werremeyer, M., S. Clark, N. Fitz-Coy, J. Liou, M. Sorge, M. Voelker, R. Kelley, and T. Huynh Design and Fabrication of Debrisat A Representative LEO Satellite for Improvements to Standards Satellite Breakup Models. In Paper presented at 63rd International Astronautical Congress, 1 12, Naples, Italy, July Curran Associates, Inc. Wie, B Space Vehicle Dynamics and Control, Second Edition. Reston, VA: American Institute of Aeronautics and Astronautics.