Self-tuning in master–slave synchronization of high-precision stage systems

For synchronization of high-precision stage systems, in particular the synchronization between a wafer and a reticle stage system of a wafer scanner, a master–slave controller design is presented. The design consists of a synchronization controller based on FIR filters and a data-driven self-tuning approach is used to find the coefficients of these filters. In the context of Lur'e systems, i.e. the reticle stage slave system has a variable gain controller with saturation nonlinearity, a part of the gradients needed for self-tuning is obtained from reconstruction using closed-loop nonlinear models. The remaining part is given by sampled data obtained primarily from time-series measurements. Performance with the synchronization controller is shown to be bounded by a waterbed effect: low-frequency suppression comes at the price of high-frequency amplification. For the considered Lur'e stage systems the ability of the self-tuning to induce improved tracking is discussed in view of this waterbed effect for either simulation results or experimental results.

[1]  Shinji Hara,et al.  Characterization of a complementary sensitivity property in feedback control: An information theoretic approach , 2009, Autom..

[2]  Lucy Y. Pao,et al.  Nonminimum Phase Dynamic Inversion for Settle Time Applications , 2009, IEEE Transactions on Control Systems Technology.

[3]  Henk Nijmeijer,et al.  Self-tuning of a switching controller for scanning motion systems , 2012 .

[4]  Johan A. K. Suykens,et al.  Robust Nonlinear H Synchronization of Chaotic Lur'e Systems , 1997 .

[5]  Marcel François Heertjes,et al.  Data-based control tuning in master-slave systems , 2012, 2012 American Control Conference (ACC).

[6]  Okko Bosgra,et al.  Fixed Structure Feedforward Controller Design Exploiting Iterative Trials: Application to a Wafer Stage and a Desktop Printer , 2008 .

[7]  Niels van Dijk,et al.  Combined input shaping and feedforward control for flexible motion systems , 2012, 2012 American Control Conference (ACC).

[8]  Richard H. Middleton,et al.  A survey of inherent design limitations , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[9]  Koichi Sakata,et al.  Master-slave synchronous position control for precision stages based on multirate control and dead-time compensation , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[10]  M.K. Jouaneh,et al.  Input Shaping Using Finite Impulse Response Filters , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[11]  Hans Butler,et al.  Position Control in Lithographic Equipment [Applications of Control] , 2011, IEEE Control Systems.

[12]  R. Kamidi,et al.  Data-based feed-forward control in MIMO motion systems , 2008, 2008 American Control Conference.

[13]  N. K. Poulsen,et al.  Improving Convergence of Iterative Feedback Tuning , 2009 .

[14]  Chunhong Wang,et al.  Optimal synchronous trajectory tracking control of wafer and reticle stages , 2009 .

[15]  Guanghong Duan,et al.  Cross-coupling control for synchronized scan of experimental wafer and reticle stage , 2006 .

[16]  Jesse B. Hoagg,et al.  Nonminimum-phase zeros - much to do about nothing - classical control - revisited part II , 2007, IEEE Control Systems.

[17]  Maarten Steinbuch,et al.  Advanced Motion Control: An Industrial Perspective , 1998, Eur. J. Control.

[18]  Okko H. Bosgra,et al.  LPV control for a wafer stage: beyond the theoretical solution , 2005 .

[19]  M. Tomizuka,et al.  Iterative learning control design for synchronization of wafer and reticle stages , 2008, 2008 American Control Conference.

[20]  R. Pintelon,et al.  On the equivalence of z-domain and s-domain models in system identification , 1996, Quality Measurement: The Indispensable Bridge between Theory and Reality (No Measurements? No Science! Joint Conference - 1996: IEEE Instrumentation and Measurement Technology Conference and IMEKO Tec.

[21]  B. Francis,et al.  A lifting technique for linear periodic systems with applications to sampled-data control , 1991 .

[22]  Andrew G. Alleyne,et al.  A Cross-Coupled Iterative Learning Control Design for Precision Motion Control , 2008, IEEE Transactions on Control Systems Technology.

[23]  K. Y. Zhu,et al.  Optimal Synchronization Control of High-Precision Motion Systems , 2006, IEEE Transactions on Industrial Electronics.

[24]  M Maarten Steinbuch,et al.  Advanced motion control , 2003 .

[25]  Shen Tielong,et al.  A Switching Control Scheme for the Synchronization of Serially Connected Multi-Stage System , 2006, 2007 Chinese Control Conference.

[26]  Johan A. K. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems with Time-Delay , 2001, Int. J. Bifurc. Chaos.

[27]  Tsu-Chin Tsao,et al.  Control of a dual stage actuator system for noncircular cam turning process , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[28]  H. Butler,et al.  Position control in lithographic equipment , 2013 .

[29]  J. Freudenberg,et al.  Right half plane poles and zeros and design tradeoffs in feedback systems , 1985 .

[30]  C. Mohtadi.  Bode's integral theorem for discrete-time systems , 1990 .

[31]  Rick H. Middleton,et al.  Trade-offs in linear control system design , 1991, Autom..

[32]  Diego Eckhard,et al.  Optimizing the convergence of data-based controller tuning , 2009 .

[33]  Mf Marcel Heertjes,et al.  Minimizing cross-talk in high-precision motion systems using data-based dynamic decoupling , 2011 .

[34]  Jie Chen,et al.  Logarithmic integrals, interpolation bounds, and performance limitations in MIMO feedback systems , 2000, IEEE Trans. Autom. Control..

[35]  L.Y. Pao,et al.  The effect of nonminimum-phase zero locations on the performance of feedforward model-inverse control techniques in discrete-time systems , 2008, 2008 American Control Conference.

[36]  J. Suykens,et al.  Robust nonlinear H/sub /spl infin// synchronization of chaotic Lur'e systems , 1997 .