Flatness based control of a ball in tube system

This paper deals with the derivation and the implementation of a flatness based control for a nonlinear ball in tube system as a testbed. For this purpose the system equations are quoted, considering that the system properties are changing in dependence on a positive or a negative fan acceleration. The proof for the ball position as chosen output shows that the system has the attribute flat. On the basis of this proof a precontrol law is calculated, in order to track the output to a predefined reference trajectory exactly, in case of an ideal model and non-occurring disturbances. Within the whole feedforward control the nonlinear static gain of the DC motor is taken into account by the use of an inverse measured characteristic. The feedforward control is combined with a state feedback and an integral controller. The control quality of the closed-loop system is evaluated with a setpoint transition in form of three different trajectories. In this evaluation the performance is compared using the control concept with and without the integral controller. Concluding the disturbance rejection of the ball in tube system is examined.