Design, modeling and control of a 3 degree-of-freedom positioning system for high-precision 3D inline-metrology

This paper presents the mechatronic design and control of a 3 degree-of-freedom (3-DoF) precision positioning system for high-precise optical 3D inline-metrology based on a dual-stage approach. It overcomes limitations of common optical 3D measurement systems due to motion blur by precisely positioning measurement systems on a metrology platform with respect to a (moving) measurement sample and additionally extends their measurement range. A comprehensive mathematical model of the system is derived and simplified to linear models suitable for classical linear control design methods. Using a modal analysis approach for system decoupling, a decentralized control scheme with individual Single-Input Single-Output controllers is developed for precisely controlling the metrology platform position in 3 DoFs. Experimental measurements on the prototype system demonstrate a maximum measurement error resulting from the positioning system of down to $7.5\mu m$ to $12.3\mu m$ (rms) during platform motion of up to 100 mm/s over a large inspection area (0.7 m × 0.5 m), as well as 147 nm (rms) error during static positioning.