1 / 59

Iterative Methods for Precision Motion Control with Application to a Wafer Scanner System

Iterative Methods for Precision Motion Control with Application to a Wafer Scanner System. Hoday Stearns Advisor: Professor Masayoshi Tomizuka PhD Seminar Presentation 2011-05-04. 1 /42. Semiconductor manufacturing. Photolithography. Advances in Photolithography. Resolution.

jasper-daniel
Download Presentation

Iterative Methods for Precision Motion Control with Application to a Wafer Scanner System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Iterative Methods for Precision Motion Control with Application to a Wafer Scanner System HodayStearns Advisor: Professor Masayoshi Tomizuka PhD Seminar Presentation 2011-05-04 • 1/42

  2. Semiconductor manufacturing Photolithography Advances in Photolithography Resolution Courtesy of ASML Wavelength Numerical aperture • 2/42

  3. Semiconductor manufacturing Courtesy of IEEE Spectrum 22 nm Half-pitch 0.55 nm Inter-atom spacing in silicon • Wafer stage motion control • Ultra-high positioning precision • High velocities • Synchronization Advanced control schemes • 3/42

  4. Wafer stage test system • 4/42

  5. Overall experimental setup Prototype wafer stage Interferometer Linear motor PCI axis board Motor driver FPGA 7831R RT Target • 5/42

  6. Challenges in precision tracking Decrease tracking error Reference Command tracking error measure position vibrations disturbances sensor noise Error while accelerating • 6/42

  7. Baseline controller design • Feedback control … • Feedforwardcontrol … Feedforward control … • Uses a-priori information • Improves transient response • Trajectory dependent • a-causal • Uses sensor measurements • Increases robustness • Trajectory independent • Limited to being causal Feedforward Controller Feedforward control design + reference error Feedback Controller + Plant measurement + - • 7/42

  8. Repetitive processes wafer die • 8/42

  9. Repetitive processes wafer Information from past runs is used to improve future runs Iterative learning control (ILC) die Iteratively update a feedforward signal Iterative feedback tuning (IFT) Iteratively update a controller parameters • 9/42

  10. Iterative learning control • Improves performance of systems that operate repetitively over a fixed time interval • Updates a feedforward signal iteratively based on the tracking error signal of previous runs. L: learning filter ILC update law • In P-type ILC, L = scalar Q: Q filter • Low-pass filter • Zero-phase • Q ≈ 1 : turn learning on • Q ≈ 0: turn learning off • 10/42

  11. Iterative learning control Advantages: • Simple to implement • Effective • Data-driven method • Does not change feedback loop ILC is effective at reducing error due to : • Repetitive disturbances • Trajectory disturbances sensor noise vibrations Error while accelerating • 11/42

  12. ILC example • 12/42

  13. ILC considerations ILC design should satisfy the following considerations: Asymptotic performance Transient performance Robustness • 13/42 Stability

  14. ILC challenges Vibrations ILC design for systems with vibrations #1 Nonrepetitive High frequency • ILC can only compensate for repetitive disturbances • Difficult to design ILC algorithms with robust performance at high frequencies • 14/42

  15. ILC challenges New Trajectories Apply ILC Trajectory 1 Tracking error ILC signal ? ? • When trajectory changes, learning must be restarted from scratch Feedforward signal recalculation method Feedforward controller iterative tuning Tracking error ILC signal Trajectory 2 #2 #3 • 15/42

  16. #1 ILC design for systems with vibrations • 16/42

  17. Error sources categorization DOB and ILC filtering DOB Special ILC design • 17/42

  18. First try: P-type ILC P-type ILC, Q filter with 250 Hz cutoff Q filter function: Learning turned on in frequency bands where Q ≈ 1 Learning turned off in frequency bands where Q ≈ 0 Large learning transient • 18/42

  19. First try: P-type ILC P-type ILC, Q filter with 250 Hz cutoff P-type ILC, Q filter with 100 Hz cutoff Transient eliminated Worse peak error • 19/42

  20. P-type ILC with notch Q filter P-type ILC, Q filter with 250 Hz cutoff P-type ILC, Q filter with 250 Hz cutoff and notch at 150 Hz Transient eliminated P-type ILC, Q filter with 250 Hz cutoff and dynamic notch • 20/42

  21. Notch L filter P-type ILC, Q filter with 250 Hz cutoff Notch L filter, Q filter with 250 Hz cutoff Dynamic notch L filter, Q filter with 250 Hz cutoff • 21/42

  22. Frequency shaped L filter P-type ILC, Q filter with 250 Hz cutoff Frequency-shaped L filter, Q filter with 250 Hz cutoff L filter shape Notch L Frequency shaped L • 22/42

  23. Model-inverse L filter Model-inverse L, Q filter with 250 Hz cutoff • 23/42

  24. Overall comparison - experiment Conclusions • Time-varying filters (Q and L) can give better performance than fixed filters • For L, choosing a filter can give better performance than choosing a scalar Frequency shaped L filter gives 42.2% improvement over P-type 250 Hz cutoff Dynamic notch L filter gives 28.3% improvement over P-type 250 Hz cutoff • 24/42

  25. Stability of designed ILC P-type 100 Hz cutoff P-type 250 Hz cutoff Frequency shaped L The lowest is ILC with frequency- shaped L Stability condition • 25/42

  26. Performance of designed ILC P-type 100 Hz cutoff P-type 250 Hz cutoff Frequency shaped L The lowest is ILC with frequency- shaped L Asymptotic error equation • 26/42

  27. #2 Feedforward signal generation for new trajectories via ILC • 27/42

  28. ILC for feedforward signal generation Apply ILC Trajectory 1 Tracking error ILC signal ? ? Tracking error ILC signal • Develop a method for generalizing ILC results to other scan trajectories Trajectory 2 • 28/42 A learned ILC signal is limited to a single trajectory. If trajectory is changed, ILC signal must be relearned.

  29. Construction of a scan trajectory Scanning at constant velocity Position Constant acceleration • Specify • scan length, • velocity limit, • acceleration limit • Time-optimal trajectory • Polynomial spline Velocity Acceleration • 29/42

  30. Construction of a Scan Trajectory + • 30/42 Notice that acceleration is superposition of 4 shifted and scaled step signals

  31. Feedforward signal analysis ILC feedforward inputsignal is also a superposition (assume no disturbances) + = ILC input for Traj 1 decomposition Learned signal Base feedforward signal acausal part • 31/42

  32. Feedforward signal synthesis New scan trajectory Synthesize ILC input Then, test it in the system: • 32/42

  33. Experimental Results • RMS error is 33.5% lower than with FF controller • The proposed method achieves performance that is: • Similar to ILC, but without need to repeat learning iterations • Better than feedforward controller Advantages of proposed method • Doesn’t require model • Doesn’t require redoing learning iterations • Achieves low tracking error • 33/42

  34. #3 Iterative tuning of feedforward controllers • 34/42

  35. Feedforward signal vs. controller ILC feedforward signal + reference error Feedback Controller + Plant measurement + - Inverse plant structure Feedforward Controller Disturbance model structure + reference error Feedback Controller + Plant measurement + - • 35/42

  36. Iterative Controller Tuning Iterative Feedback Tuning • IFT is an iterative method of tuning controller parameters • Minimizes a cost function • Descent algorithm search • Gradient direction estimated from experimental data • No model of the plant is needed for optimization ρ= controller parameters to be tuned = scalar to control step size k = iteration # R = positive definite matrix • 36/42

  37. Feedforward controller 1 Inverse model structure For reducing error due to trajectory Peak error decreased 95% • 37/42

  38. Force ripple • Force Ripple is a periodic disturbance that arises in linear permanent magnet motors due to imperfections Force Ripple • 38/42

  39. Feedforward controller 2 Force ripple compensator For reducing error due to force ripple disturbance tune tune Feedforward signals • 39/42

  40. Comparison of ILC and IFT • ILC: • Most effective • Simpler computation • No assumptions of model structures Time plot of error • IFT: • Applicable for new trajectories • Performance can be improved by increasing controller complexity • 40/42

  41. Conclusion • 41/42 Iterative methods for high precision position control ILC design for systems with vibration ILC feedforward computation for scan trajectories Iterative feedforward controller tuning

  42. Thank you MSC Lab Professor Tomizuka Precision motion control group • 42/22

  43. Repetitive Processes Silicon wafer 300mm diameter Die Changing every year • 43/22

  44. Repetitive Processes Silicon wafer 300mm diameter International Technology Roadmap for Semiconductors Die • Translates to: • high tracking precision (error <1nm) • high repeatability • high scanning speeds Changing every year • 44/22

  45. Modelling • 45/22

  46. Trajectory Design • 46/22

  47. Construction of a scan trajectory Scanning at constant velocity Position Constant acceleration • Specify • scan length, • velocity limit, • acceleration limit • Time-optimal trajectory is unique • It is polynomial spline • The continuous-time trajectory is determined analytically then sampled Velocity Acceleration

  48. Thesis contributions Applying ILC for high precision control of systems with vibrations Making ILC tuning results applicable to multiple trajectories Compensating for force ripple disturbance through IFT.

  49. Experiment One complication: force ripple Force ripple is NOT LTI so it cannot be scaled and time-shifted. Nor is force ripple disturbance always the same : it depends on the reference trajectory

  50. DOB Design Solution: Use a disturbance observer DOB compensates the force ripple And ILC feedforward signal compensates error due to the trajectory

More Related