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1. Liu, B.Y. Motion control of a contactless stage:.

Degree: 2015, Delft University of Technology

In the manufacturing process of flat panel displays (FPD), such as the making of the photomasks and the lithographic process of the glass substrates, the demand for a larger but thinner substrate is increasing. Consequently, the moving stage of these manufacturing machines become larger in size and heavier in weight. The high velocity and acceleration specifications for positioning a moving stage of several tons will require much more power and higher power rate output than any usual positioning tasks. One solution to eliminate the moving mass of the stage is to use a contactless stage. A contactless positioning stage which is capable of controlling a 100 mm wafer in three in-plane degrees of freedom has been developed successfully in the Mechatronic System Design group of the Precision and Microsystems Department. The deployed controller on the contactless stage is a decoupled three-loop Single Input Single Output (SISO) cascaded controller designed by classical loop shaping methods. An initial study shows that the in-plane rotational DoF is disturbed when the center of mass of the wafer is moved from the center of the concatenated air actuators and the planar translational axes are accelerating or decelerating. In addition, the power spectral densities of the measured pressure signals indicate that a high power pressure disturbance affects each control pressure channel. Therefore, the contactless positioning stage should be treated as a Multi Input Multi Output (MIMO) system and controlled with control schemes tailored to the wafer dynamics and the spectrum of disturbances as a potential alternative positioning mechanism at nano/micro levels. In this thesis, the goal is to develop a three in-plane degrees of freedom, multivariable model of the contactless stage, and identify its dynamics or estimate its parameters. With a determined control configuration, design and develop control schemes on the contactless stage that achieves a positioning specification with sub-micrometer precision when performing positioning tasks similar to an industrial precision positioning stage used in FPD manufacturing. With a cascaded control scheme, the dynamics of the contactless stage consist of pressure dynamics and wafer dynamics. The pressure dynamics of the air channels are identified by the Closed-loop Multivariable Output Error Subspace (CL-MOESP) algorithm first. Then the wafer dynamics are modeled from the Newton-Euler equations and the model parameters with disturbance forces in plane are estimated with an extended Kalman filter. Both dynamic models are validated by the comparisons of the frequency response functions (FRFs) of the derived models with the measured FRFs of the system. The pressure and position control problems are formulated with the required performance specifications. Then, both the pressure and position controller are synthesized using pole placement with sensitivity function shaping techniques. With high bandwidth inner pressure loops, a MIMO triangular controller is designed to control the positions… Advisors/Committee Members: Verhaegen, M., Van Ostayen, R., Van der Veen, G., Vuong, P..

Subjects/Keywords: contactless; positioning

University of Technology in [5]. A conceptual diagram of the contactless actuator is… …adopted in precision machines, a contactless actuator is proposed by van Ostayen at Delft… 

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APA (6th Edition):

Liu, B. Y. (2015). Motion control of a contactless stage:. (Masters Thesis). Delft University of Technology. Retrieved from

Chicago Manual of Style (16th Edition):

Liu, B Y. “Motion control of a contactless stage:.” 2015. Masters Thesis, Delft University of Technology. Accessed March 23, 2019.

MLA Handbook (7th Edition):

Liu, B Y. “Motion control of a contactless stage:.” 2015. Web. 23 Mar 2019.


Liu BY. Motion control of a contactless stage:. [Internet] [Masters thesis]. Delft University of Technology; 2015. [cited 2019 Mar 23]. Available from:

Council of Science Editors:

Liu BY. Motion control of a contactless stage:. [Masters Thesis]. Delft University of Technology; 2015. Available from: