The key to successfully balancing the ball on the platform is a well designed controller.

In order to analytically design a full state controller, we needed to fist create a dynamic system model. Next, we linearized the system at the opperating point. Finally, we used pole placement to find the controller gains for our full state controller. Once all of our tasks were functioning we used these gains as a starting point for tuning our controller. We first started by trying to balance the platform in a horizontal position without the ball on it by only adjusting the controller gains for the platform angular position and velocity. We repeatedly doubled the angular velocity gains untill the platform began to oscillate. Then we increased the angular velocity gain until the oscillation was significantly reduced. Next, we placed the ball on the touch panel and increased the ball position gains until the system became unstable and then reduced the position gains slightly. As the nex step, we increased the ball velocity gains until we couldn't see any noticable bost in the system performance. Form there we experimented with incrementally increasing and decreasing the ball position and velocity gains to see if we could improve the system's performance.

You will find all related system calculations at the following links:

These calculations were derived throughout the quarter from our homework assignemnts.