3DOF Ball on Plate Using Closed Loop Stepper Motors

The ball on plate problem consists of a flat plate on which a ball needs to be positioned. Ball positioning is only achieved through unstable equilibrium where any small changes in the plate angle will result in the continual acceleration of the ball until it leaves the plate. Such a system presents an interesting controls problem as closed loop control is needed for stable ball positioning on the plate. A good approximation for controlling the balls motion is to decouple the x and y directions on the plate. This allows for two separate independent control loops. One loop controls the x-location of the ball and another controls the y-location. Each control loop for the x and y axis consists of two parts; an inner control loop and an outer loop. The inner loop is responsible for running the stepper motors in closed loop for angle control. Motor angle is obtained from quadrature encoders on each stepper motor. A set angle for the stepper motors is provided from the outer loop and the difference between the set angle and measured angle drives the stepper motor angular velocity.”