Self Balancing Stick
For our Dynamics final project, Daniel Daughtery and I decided to build a self balancing stick. We couldn't use a classical PID controller because of the nature of using reaction wheels. Not only is it necessary to set the angle of stick to 90 degrees, but it is also necessary to set the velocity of the reaction wheels to zero in order to avoid saturation, which occurs when the reaction wheels reach their maximum velocity, and control authority is lost because no further torque can be extracted. To do this, we used two PD controllers, one to control the position of the stick itself, and the other to control the setpoint of the stick in order to drive the velocity of the reaction wheels to zero.
Controller Diagram
The stick was originally designed with a fixed IMU and with non-encoded reaction wheels. This proved unusable because the vibration of the wheels required filtering of the IMU to such a degree that the lag caused by the filtering made control of the system impossible. Thus, the IMU was then suspended by rubber fixturing to minimize vibrations. We were also unable to correlate the ESC pwm amount to an acceleration, since we didn't know the current velocity of the wheels. We then modified the design to use two IR sensors on the motors as encoders.
Lag caused by heavy IMU filtering