1. Introduction The ball and beam system is one of the most enduringly popular and important laboratory models for teaching control system engineering. It is widely used because it is simple to understand as a system and yet the control techniques studied cover many important lessons and modern design methods. It has a very “important property” – it is open loop unstable. 1. Introduction The ball and beam system is one of the most enduringly popular and important laboratory models for teaching control system engineering. It is widely used because it is simple to understand as a system and yet the control techniques studied cover many important lessons and modern design methods. It has a very “important property” – it is open loop unstable. 2. What it is  A steel ball rolling on the top of a long beam.  The beam is mounted on the output shaft of an electric motor and so the beam can be tilted about its centre axis by applying an electrical control signal to the motor amplifier.  The position of the ball on the beam can be measured using a special light sensor. 2. What it is  A steel ball rolling on the top of a long beam.  The beam is mounted on the output shaft of an electric motor and so the beam can be tilted about its centre axis by applying an electrical control signal to the motor amplifier.  The position of the ball on the beam can be measured using a special light sensor.

m: Mass of the ballu(t) : Force of the drive mechanics g : Gravityl : Radius of force application r : Roll radius of the ballLw : Radius of beam Ib :Inertia moment of the ballx: Ball coordinates with respect to the beam Iw Inertia moment of the beamy: Ball coordinates with respect to the beam M : Mass of the beam ψ : Angle of the ball to the beam b: Friction coefficient of the drive mechanicsa : Angle of the beam to the horizontal K : Stiffness of the drive mechanics