
Embedded Systems  ModelBased Design
Amazing ball (PID control) The device is shown in the picture. The ball position is sensed by a touchscreen placed on top of the plate. The pitch and roll angles are controlled by two servomotors with an integrated controller controlling the plate position by means of mechanical joints. Plant model On the roll and pitch axis, the geometry of the assembly motorplate is shown in figureThe equations of the closed kinematic chain define the relationship between the motor angle alpha and the plate angle theta. (download the pdf document for a full description) Once the theta angle is known, the acceleration on the ball can be computed as the sum of the centrifugal acceleration and the acceleration caused by gravity (assuming rotation without slip).
Document with the description of the assembly and the ball dynamics Controller model The Flex motion board is used to sense the position of the ball using the x,y input from the touchscreen (connected to two ADC channels on the board) and to control the position of the motors on the two axis, using the board PWM outputs.
Simulink model The Simulink model that is provided as part of the examples is shown in the following picture. It includes a model of the balland plate dynamics for the two axis, a 3D renderer of the ball and plate, a 2D scope showing the ball position on the plate and the PID controller.The Simulink model is available from the following link 




