Model-based mechanical and control design of a three-axis platform

In recent times, the interest from scientific and industrial community for the micrometric range has observed an important growth. The advances in microelectronics or the research on microbiology are just two examples of fields requiring technologies capable of assuring accurate displacements in that range. The present work focuses on the mechanical and control design of a micrometer range positioning and tracking platform using mathematical models. In a first phase, these models permit to identify the relationship between the dynamic performance of the structure and the mechanical properties of the elements that compose it. At the very beginning of the design, this information is used for the development of the different parts of the platform. Afterwards, once an initial design is finished and 3D models are available, the design is refined using finite element tools. In parallel to the mechanical design, the knowledge of the system embodied in the mathematical model is profited in the design of a control strategy for tracking and positioning. The proposed control strategy combines a linear controller based on differential flatness with a hysteresis compensator for correcting this nonlinear effect of the piezoelectric actuators. In the present paper, the mathematical derivation of the system model, its application to the design and validation of the platform and the final closed loop experimental evaluation are described.