This design project simulates and controls a beam and ball system. A ball rolls on a pivoting beam. The beam is connected through DC motor through a linkage arm. The objective is to create an output feedback control system. The project simulates the system using Matlab and Simulink.

Ball and beam geometry

The physical system consists of coupled linkages and a free-to-roll ball. The linkage motion is nonlinearly coupled to the gear angle. The beam has a length of 1 meter. The gear arm has a radius of 0.03 meters, and the linking arm has a length of 0.2 meters. The ball is steel with a radius of 15 millimeters. The system has 2 energy storage components: beam inertia and ball inertia. System control is allowed through a voltage input into the DC motor, which provides a torque applied at the gear arm. The gear arm motion is harmonic; the gear can go past topdead-center in the straight up and down positions.

The document is available here.