Control of a multi-axis platform for metrological purposes using differential flatness

Positioning and tracking devices with micrometer range and sub-micrometer resolution are becoming of special interest in recent years for an extending range of applications including metrological devices, manipulators and mechanization systems both in research and high precision industries (for example, semiconductors). The control of these systems is not an easy task because of its normally high stiffness and the coupling existing between the different degrees of freedom. The present work proposes a control strategy based on differential flatness for static positioning and dynamic trajectory tracking with a platform of three degrees of freedom. The system uses piezoelectric actuators and is specially conceived for metrological devices, which do not suffer important external loads. The proposed method permits to decouple the design of a closed loop control for each degree of freedom and calculates an open loop command directly from the trajectory definition in the three degrees of freedom. The performance of the controller has been experimentally checked both in positioning and tracking applications.