# Modelling of a Controlled Cart on a Horizontal Pivoting Beam

Use Newtons Law to derive equations of motion for the system. This should be converted into transfer functions for input into MATLAB/SIMULINK.

The system consists of a motorised trolley on a see-saw (see attached figure). The trolley motor is to be controlled and eventually the trolley must balance the beam. A potentiometer senses the angle of the beam at the centre, and relates this to the required direction of travel for the trolley.

To re-iterate, full derivation of equations of motion (Newton) and their corresponding transfer functions are needed.

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... is the acceleration of gravity and I is the angula inertia of system.

If you decompose the weight force, you obtain the torque force W*cos(O) and the moving cart force W*sin(O). this force changes the cart position at a velocity ...