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Iterative Methods for Precision Motion Control with Application to a Wafer Scanner System Hoday Stearns Advisor: Professor Masayoshi Tomizuka PhD Seminar Presentation /42

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

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

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Wafer stage test system 4/42

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Overall experimental setup Prototype wafer stage FPGA 7831RRT Target Linear motorInterferometer Motor driver PCI axis board 5/42

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

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

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Repetitive processes wafer die 8/42

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

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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. ILC update law Iterative learning control L: learning filter Q: Q filter Low-pass filter Zero-phase Q 1 : turn learning on Q 0: turn learning off In P-type ILC, L = scalar 10/42

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

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ILC example 12/42

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

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

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

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ILC design for systems with vibrations #1 16/42

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Error sources categorization RepetitiveNon-repetitive Low frequencyForce ripple (< 20 Hz) Table vibration (18 Hz) High frequencyVibration modes of plant (150 Hz) Sensor noise DOB DOB and ILC Special ILC design 17/42 filtering

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

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

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

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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

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

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

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Overall comparison - experiment 24/42 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 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 Conclusions

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

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

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

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

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

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

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

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Then, t est it in the system: Feedforward signal synthesis 32/42 New scan trajectory Synthesize ILC input

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Doesnt require model Doesnt require redoing learning iterations Achieves low tracking error Doesnt require model Doesnt require redoing learning iterations Achieves low tracking error Advantages of proposed method Experimental Results The proposed method achieves performance that is: Similar to ILC, but without need to repeat learning iterations Better than feedforward controller 33/42 RMS error is 33.5% lower than with FF controller

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Iterative tuning of feedforward controllers #3 34/42

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Feedforward signal vs. controller Feedback Controller Feedforward Controller Plant referenceerror measurement Feedback Controller Plant referenceerror measurement ILC feedforward signal Inverse plant structure Disturbance model structure 35/42

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

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

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

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

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

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

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

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

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

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Modelling 45/22

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Trajectory Design 46/22

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Construction of a scan trajectory Position Velocity Acceleration Scanning at constant velocity 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 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

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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.

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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

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DOB Design Solutio n : Use a disturbance observer DOB compensates the force ripple And ILC feedforward signal compensates error due to the trajectory

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Gradient estimate Cost function: The relation of error to the controller is known, so Cost function gradient: CP e[n]r[n] - 51/22 Assume SISO

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Controller Tuning Algorithm Minimize a cost function: Using a gradient-based iterative search k = iteration # = scalar to control step size R = positive definite matrix ρ= controller parameters to be tuned e = tracking error u = control effort 52/22

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Gradient estimate Although are known,are unknown/uncertain because involves plant Gradient can be obtained by passing reference through system twice CP e[n]r[n] - CP 53/22 -

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Experiment Results tune 54/42

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Experiment Results tune 55/42

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Tuning Results Norm of error Evolution of ρ 1, ρ 2 56/42

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Semiconductor manufacturing Moores law Transistor dimension vs. year Courtesy of Intel Courtesy of ASML Photolithography 57/42

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Semiconductor manufacturing Advances in Photolithography Resolution Wavelength Numerical aperture Photolithography 58/42

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Semiconductor manufacturing Wafer stage motion control Ultra-high positioning precision High velocities Synchronization Wafer stage motion control Ultra-high positioning precision High velocities Synchronization Advances in Photolithography Resolution Wavelength Numerical aperture 22 nm Half-pitch 0.55 nm Inter-atom spacing in silicon Advanced control schemes 59/42

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