MECH5675M Vehicle Systems Engineering CubeSat B-Dot Control System Design Term Project Full Mark: 100% (This is 30% of the final mark of the module.) Include all source codes including Simulink block diagrams. Fail to include source codes would cause significant reduction in the marks. Submit your final report in pdf format through the Minerva. The submission link will be activated in April. You are not allowed to discuss or share any codes, program, diagrams, etc, directly related to the term project assignment. Similarities in the programming & diagram are to be checked and copies of any part of source code/diagrams from others are considered as plagiarism. Task #1 [30%] The initial satellite body attitude with respect to the reference frame are given by the following quaternion at time t = 0: and rotates with the constant angular velocity for each body axis as follows: a) Obtain the time history of quaternion from the initial time (t=0) to t = 1000 s. [10%] b) Obtain the time history of roll, pitch and yaw angles in degrees using 123-rotation. [10%] c) Plot the constraint for the quaternion with respect to time and check if it is satisfied the constraint during the whole simulation time interval. [10%] Turn Over Task #2 [30%] For this task, you might use the Modelio software to draw SysML diagram: • Modelio (https://www.modelio.org/) : this is a freeware and can be installed on computer without requiring the admin right. or you could use any drawing software including the drawing tools in MS-Word. Download the following the simulation blocks from the Minerva: i) “constants.m”: the required physical parameters including the satellite moment of inertia, launch date, etc, are defined. You need to update some values in the file to match with the scenario given in here. The file must be called first in the matlab prompt before using the environment simulink block in the next. ii) “environment_model.slx”; the simulink block provides the gravity gradient torque and the geomagnetic field vector in the body frame. a) Draw the internal block diagram (ibd) for the geomagnetic field model implemented in “environment_model.slx”. [15%] b) Draw an internal block diagrams (ibd) of the B-dot controller of a CubeSat to be implemented in Task 3. Note that the B-dot controller does not use any gyroscope measurements. [15%] Turn Over Task #3 [40%] Implement the following simulation blocks where the initial attitude in quaternion and the initial angular rate are given by and there exist only two types of external torques: 1) gravity gradient torque; 2) torque generated by magnetic torquer. Download the following from the Minerva and use them in implementing the simulation blocks: i) “constants.m”: the required physical parameters including the satellite moment of inertia, launch date, etc, are defined. You need to update some values in the file to match with the scenario given in here. The file must be called first in the matlab prompt before using the environment simulink block in the next. ii) “environment_model.slx”; the simulink block provides the gravity gradient torque and the geomagnetic field vector in the body frame. Implement the B-dot Controller using where k and are the control grain and the sampling interval, respectively. Set the sampling interval equal to 0.5 seconds. Use the time-delay block in the simulink to implement the B-dot controller. Restrict the simulink model solver maximum step size less than 0.5s. Turn Over a) Change the control gain k from 10,000 to 100,000. Decide how many k should be tested in the interval. Obtain the settling time for each control gain when the magnitude of angular velocity, ||(t)||, is less than 1o/s. Plot the settling time changes with respect to the control gain. [20%] b) The magnetic torquer specifications are given by: each body-axis direction is equipped with one magnetic torquer; hence total 3 magnetic torquers; each torquer has the number of turns (N) equal to 72, the area of the coil 0.0233m2 and the resistance of the coil (R) is 50Ω. Plot the total magnetic-torquer power consumption from the initial time to the settling time with respect to the same range of the control gains used in a). Use the following formula to calculate the total power consumptions, where ix, iy, and iz are the current for the magnetic torquer in each body coordinates direction: [20%] END OF TASKS Control gain k S e t tl in g t im e Control gain k T o ta l P o w er C o n su m p t i o n s R
