Elsevier

Mechatronics

Volume 83, May 2022, 102733
Mechatronics

Frequency response data-based peak filter design applied to MIMO large-scale high-precision scan stage

https://doi.org/10.1016/j.mechatronics.2021.102733Get rights and content

Abstract

A large-scale high-precision scan stage is important equipment in the industrial productions of micro-fabrication such as flat panel display (FPD) lithography systems. Designing controllers for multi-input multi-output (MIMO) systems is time-consuming and needs experience because of the interaction between each axis and many controller tuning parameters. The aim of this study is to develop a peak filter design method based on frequency response data to reduce repetitive disturbance. This data-based approach does not use the model and only uses the frequency response data of the controlled system and the disturbance spectrum calculated from the scanning error data (Contribution 1). The peak filter is designed by convex optimization and satisfies robust stability conditions for six-degree-of-freedom systems (Contribution 2). The control performance of the designed peak filter is experimentally demonstrated with an industrial MIMO large-scale high-precision scan stage in reducing the scanning error of the main stroke of the translation along the x-axis (Contribution 3).

Introduction

Large-scale high-precision scan stages have an important role in industries such as manufacturing semiconductors and flat panel displays (FPD). To improve the throughput and the product quality, fast and precise positioning control is required, and these specifications become severe year by year because of the growing need for TVs, PCs, and smartphones [1].

The large-scale scan stage has several challenges in position control such as low resonance modes because of the low stiffness and many disturbances because of the wide scan range [2]. The large-scale scan stage is typically controlled with two-degree-of-freedom (DOF) control with a feedforward controller for reference tracking such as a perfect tracking control based on a multirate feedforward control [3], [4] and a feedback controller for disturbance rejection. In the scan region, the reference trajectory of the high-precision scan stage is with constant velocity without acceleration, and the feedback controller plays a major role in tracking control performance.

Classical scan stages move along (x,y,θz)-axes, and the interaction between each axis is ignored, and a single-input single-output (SISO) decentralized control is commonly employed. However, in these applications, the high-precision scan stages are supported by the magnetic force or air pressure and moving in 6-DOF with (x,y,θz,z,θx,θy)-axes to reduce disturbances by the friction and the vibration from the ground and to improve tracking performance, and they become multi-input multi-output (MIMO) systems [5], [6], [7], [8]. The controller design of the MIMO systems has several challenges such as stability analysis in a coupled system between each axis, modeling of MIMO systems, and enormous tuning parameters of the controllers. Especially, improving the tuning method of the controller parameters is important for the cost of time and effort of on-site control engineers.

Based on these challenges in designing the feedback controller, several data-based controller design approaches with an optimization method are proposed, such as genetic algorithm [9], Nelder–Mead method [10], particle swarm optimization [11], loop shaping method [12], bundle method [13], [14], sequential linearization method [15], [16], [17], [18] using concave–convex procedure [19].

Among these methods, the sequential linearization method using the concave–convex procedure has an advantage in monotonic convergence to a saddle point or a local optimum and suits for controller design. Other methods also need the parametric model of the controlled system. The precise modeling is difficult when the system is complicated such as MIMO systems.

In this study, the sequential linearization method using the concave–convex procedure is used with the frequency response data of the controlled system and disturbance spectrum to design the optimal feedback controller.

The disturbance spectrum during the scanning motion with constant velocity has a repetitive characteristic such as a motor cogging and has a large amplitude in a certain frequency.

The repetitive control approaches are presented to reject the periodic disturbances [20], [21], [22]. They reject the disturbance on not only main disturbance frequency but also harmonic ones. The experimental setup in this study does not have a characteristic of harmonic disturbance frequencies, and the repetitive control approaches are not suitable for it.

Previous researches show that repetitive disturbance can be effectively rejected by a peak filter, which is the same as inverse notch filter in other literature, with the same resonance frequency, and it is applied in several industrial products such as hard disk drives [23]. However, in the application of the high-precision scan stage, the repetitive disturbance rejection by a peak filter has not been reported in the literature.

Since the peak filter has a large gain at a certain frequency, it may easily deteriorate the closed-loop stability due to the interaction. Moreover, the combination of the controller parameter can blow up in such a multi-axis system. Hence, the heuristic tuning approach [24] depends on experiences and efforts, and it is not the optimal solution. To address this problem, the frequency response data-based peak filter design method considering both the SISO robust stability condition and the MIMO stability condition is proposed in this study.

The optimal disturbance filter design method is also presented [25]. However, the peak filter is designed with nonlinear optimization procedure not with convex optimization. The convergence of the nonlinear optimization procedure is not monotonic and it could take a long time for the optimization. Therefore, the data-based peak filter design method with convex optimization suitable to industrial applications is proposed in this study.

The proposed peak filter design method has an advantage in convex optimization without parametric modeling. The control performance of the designed peak filter is experimentally demonstrated with an industrial MIMO large-scale high-precision scan stage in reducing the scanning error of the main stroke of the translation along the x-axis. This study consists of mainly these three following contributions:

Contribution 1

The optimization problem of data-based peak filter design for the MIMO system is formulated.

Contribution 2

The data-based peak filter design method with convex optimization is presented.

Contribution 3

The designed peak filter is validated in the experiment with the industrial MIMO large-scale high-precision scan stage.

Section snippets

Problem formulation

In this section, the control problem is formulated.

Data-based design method of peak filter with convex optimization

In this section, the data-based peak filter design method is formulated as a convex optimization problem. The proposed method is formulated to design the peak filters for the MIMO controlled system in each axis, independently.

Experimental validation

In this section, experimental validation is conducted. The aim of this study is to develop a peak filter design method based on frequency response data. The control performance of the designed peak filter is experimentally demonstrated with an industrial MIMO large-scale high-precision scan stage in reducing the scanning error of the main stroke of the translation along the x-axis.

Conclusion

The frequency response data-based peak filter design in this study enables reducing tracking errors in the scanning motion. The main underlying idea of this study is the combination of the frequency response data-based design approach with convex optimization and the robust design method of the MIMO controlled systems.

The effectiveness of the designed peak filter is demonstrated in the experiment with the industrial MIMO large-scale high-precision scan stage. The disturbance spectrum of the

CRediT authorship contribution statement

Masahiro Mae: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization. Wataru Ohnishi: Software, Formal analysis, Writing – review & editing. Hiroshi Fujimoto: Conceptualization, Supervision, Project administration. Koichi Sakata: Validation, Formal analysis, Writing – review & editing, Project administration. Atsushi Hara: Conceptualization, Resources, Funding acquisition.

Masahiro Mae received the B.E. and M.S. degrees from The University of Tokyo in 2018 and 2020, respectively.

He is currently working towards the Ph.D. degree in the Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo.

He is also a research fellow (DC2) of Japan Society for the Promotion of Science from 2021.

His research interests are in control engineering, precision motion control, multirate control, and multi-input multi-output

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  • Masahiro Mae received the B.E. and M.S. degrees from The University of Tokyo in 2018 and 2020, respectively.

    He is currently working towards the Ph.D. degree in the Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo.

    He is also a research fellow (DC2) of Japan Society for the Promotion of Science from 2021.

    His research interests are in control engineering, precision motion control, multirate control, and multi-input multi-output systems.

    He is a student member of the Institute of Electrical and Electronics Engineers, the Institute of Electrical Engineers of Japan, and the Society of Instrumental and Control Engineers.

    Wataru Ohnishi received the B.E., M.S., and Ph.D. degrees from the University of Tokyo, Japan in 2013, 2015, and 2018, respectively.

    Presently, he is an assistant professor with the Department of Electrical Engineering and Information Systems, Graduate School of Engineering, the University of Tokyo.

    His research interest includes high-precision motion control.

    He is a member of the Institute of Electrical and Electronics Engineers and the Institute of Electrical Engineers of Japan.

    Hiroshi Fujimoto received the Ph.D. degree in the Department of Electrical Engineering from the University of Tokyo in 2001.

    In 2001, he joined the Department of Electrical Engineering, Nagaoka University of Technology, Niigata, Japan, as a research associate. From 2002 to 2003, he was a visiting scholar in the School of Mechanical Engineering, Purdue University, U.S.A. In 2004, he joined the Department of Electrical and Computer Engineering, Yokohama National University, Yokohama, Japan, as a lecturer and he became an associate professor in 2005. He had been an associate professor of the University of Tokyo from 2010 to 2020 and became a professor from year 2021.

    He received the Best Paper Awards from the IEEE Transactions on Industrial Electronics in 2001 and 2013, Isao Takahashi Power Electronics Award in 2010, Best Author Prize of SICE in 2010, The Nagamori Grand Award in 2016, and First Prize Paper Award IEEE Transactions on Power Electronics in 2016.

    His interests are in control engineering, motion control, nano-scale servo systems, electric vehicle control, motor drive, visual servoing, and wireless motors. Dr. Fujimoto is a senior member of IEE of Japan and IEEE. He is also a member of the Society of Instrument and Control Engineers, the Robotics Society of Japan, and the Society of Automotive Engineers of Japan.

    He is an associate editor of IEEE/ASME Transactions on Mechatronics from 2010 to 2014, IEEE Industrial Electronics Magazine from 2006, IEE of Japan Transactions on Industrial Application from 2013, and Transactions on SICE from 2013 to 2016. He is a chairperson of JSAE vehicle electrification committee from 2014 to 2020 and a past chairperson of IEEE/IES Technical Committee on Motion Control from 2012 to 2013.

    Koichi Sakata received the B.S., M.S., and Ph.D. degrees in the Department of Physics, Electrical and Computer Engineering from Yokohama National University, Japan in 2006, 2008, and 2011, respectively.

    He was a research student in the University of Tokyo, Japan during April 2010 to March 2011.

    He was also a research fellow (DC2) of Japan Society for the Promotion of Science during April 2009 to March 2011.

    Since April 2011, he has been with Nikon Corporation.

    His interests are in motion control and nano-scale servo control.

    He works on the design of a motion control and high-precision servo control of large-scale stage.

    He is a member of the Institute of Electrical and Electronics Engineers and a senior member of the Institute of Electrical Engineers of Japan.

    Atsushi Hara received the B.S. and M.S. degrees in mechanical engineering from Kyushu Institute of Technology, Kitakyushu, Japan, in 1998 and 2001, respectively.

    Since 2001, he has been with the Precision Equipment Company, Nikon Corporation, Yokohama, Japan.

    He is currently working on the mechanical design and high-precision control for large-scale stages.

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