While taking ME 4012: Modeling and Control of Motion Systems, I worked with Mesum, Martha, and Mannan to mathematically model and balance a Reuleax triangular prism on an inherently unstable edge. The system contained a prismatic body with nominal depth and a reaction wheel powered by a DC motor. The DC inrunner motor, acquired from a combat robot, was powered by a 6s Lipo battery. During testing, the motor's RPM capability posed a significant controls challenge due to dead spots present at low current inputs and low RPMs.
An IMU measured the body's angle about it's vertex. The Teensy corrected the angle's error with respect to the vertical axis (parallel to gravity) by sending an output PWM to the motor. In turn, the reaction wheel rotates to apply a torque opposing the body's rotation. Several mechanical challenges were solved by leveraging 3-D printing. For instance, the friction between the ground and triangle's frame was initially insufficient, so a fuzzy-skin attachment to the vertex prevented slippage.
Finally, a variety of PI, PD, PID, loop-shaping, and state-space controllers were modeled and tuned on System Controller Designer on MATLAB. After modeling and experimenting, a promising set of PID parameters became apparent, as shown in the video below.