The purpose of this project was to create a test environment that can be used to test different controllers and their robustness. In this report, the equations of motion were derived using kinematics, with attitude quaternions, and spacecraft dynamics, with angular velocity and acceleration. The equations were combined and placed into the form of a linearized state-space equation. The different control methods being investigated, Linear Quadratic Regulator (LQR) for the reaction wheel model, and the Bdot with bias controller, were explained and the block diagram for each was shown. To setup the test, the tolerances for the roll, pitch, and yaw, and their rates, were taken from the mission requirement for the ESSENCE mission. The attitude tolerance being ±0.5deg and the angular rates requirement being ±0.05deg/s. Then the test setup was further explained. The test is broken up into different scripts and steps:
1. Main run function for simulation. Initializes simulation parameters.
2. Build state-space equation and calculate constant gain matrix.
3. Randomize initial conditions and pass onto simulation.
4. Post-processing and plot generation.
5. Statistics generation.
This robust testing environment was used to test 5 different controllers for the reaction wheel model. Each controller was tested for 200 different simulations, in which the initial attitude, initial angular rates, and the center of mass were randomized. The first controller was successful for 198/200 simulations, where the only failure came from over-saturating the reaction wheels. The next three controllers had a perfect record and were successful for all 200 simulations each. The last controller, had only 71 successful simulations in the set, and a sample of one of the failed simulations was further investigated to see how it failed.