Applied System Identification for a Four Wheel Reaction Wheel Platform By Seth Franklyn Silva At the California Polytechnic State University, San Luis Obispo there is a four-wheel reaction wheel pyramidal simulator platform supported by an air-bearing. This simulator has the current capability to measure the wheel speeds and angular velocity of the platform, and with these measurements, the system identification process was used to obtain the mass properties of this simulator. A handling algorithm was developed to allow wireless data acquisition and command to the spacecraft simulator from a “ground” computer allowing the simulator to be free of induced torques due to wiring. The system identification algorithm using a least squares estimation scheme was tested on this simulator and compared to theoretical analysis. The resultant principle inertia about the z-axis from the experimental analysis was 3.5 percent off the theoretical, while the other inertias had an error of up to 187 percent. The error is explained as noise attributed to noise in the measurement, averaging inconsistencies, low bandwidth, and derivation of accelerations from measured data.

The Pyramidal Reaction Wheel Platform, or PRWP, is used to simulate three-axis controls in a torque free space-like environment. The primary purpose of the system will be to evaluate the effects of conjoining sensors to maximize pointing accuracy. Furthermore, the system will incorporate a star tracker in conjunction with a Simulated Star Field (SSF) to better estimate the PRWP orientation. For the sake of this document, however, the goal is to implement a gyroscope, wheel rate sensors, and a make-shift accelerometer—to the PRWP—and integrate a controls algorithm such that three-axis controls are achieved for the PRWP. Three sensors were either better integrated into the system or added altogether. Tachometers were created as a form of hardware circuitry to measure each wheel rate with an accuracy of approximately 2.5 Hz (nearly 15 radians per second). The TAC board circuitry converted each motors encoder output into a speed by use of a frequency to voltage converter. Additionally, although three gyroscopes had been implemented previously, the system was better incorporated into the model such that it was directly transformed via a ROBOSTIX ADC converter before being relayed to SIMULINK via a Bluetooth link. The MEMS gyroscopes allowed for very accurate rate measurements—with a minimum resolution of approximately 0.25 radians per second. Finally, a makeshift accelerometer was incorporated into the system for the purpose of system identification. The accelerometer was incorporated into the system by utilizing a discrete time derivative of the gyroscope readings. However, thankfully a system of two accelerometers can be later utilized to achieve an accuracy of approximately 6 degrees per second-second in the x-axis and 2-3 degrees per second-second in the y- and z-axes. A controls test was performed where the starting location was qo=[0, 0, sqrt(2)/2, sqrt(2)/2] and the target location was qc=[0, 0, 0, 1]. At 80 seconds, the pointing accuracy was 70 degrees around the target and the system was unable to settle during the 80 second trial. The inaccuracy was because of the low frequency of operation of the system—1 Hz. Additionally, the platform reacts slowly to sensor readings and commands. The coupling of these issues causes the pointing accuracy to high. Furthermore, through experimental testing, the maximum wheel rate was found to be approximately 6400 RPM at a duty cycle of 50% at an 8000Hz PWM application due to the Pololu MD01B design limitations: low voltage range (up to 16V), low limit current limiter (5A), and high susceptibility to overheating for large currents.