Measurement and Control for High-Speed Sub-Atomic Positioning in - - PowerPoint PPT Presentation

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Measurement and Control for High-Speed Sub-Atomic Positioning in - - PowerPoint PPT Presentation

Sep 13, 2022 46 likes •298 views

Measurement and Control for High-Speed Sub-Atomic Positioning in Scanning Probe Microscopes Andrew J. Fleming and Kam K. Leang Outline Challenges and benefits of feedforward control System inversion Linear dynamics (creep and

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Measurement and Control for High-Speed Sub-Atomic Positioning in Scanning Probe Microscopes

Andrew J. Fleming and Kam K. Leang

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Outline

  • Challenges and benefits of feedforward control
  • System inversion

– Linear dynamics (creep and vibration) – Nonlinearity (hysteresis)

  • Iteration-based feedforward
  • Conclusions
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Key challenges in SPMs using piezoelectric actuators

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Positioning errors effect SPM imaging

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Positioning errors effect SPM fabrication

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Benefits of feedforward control

  • High-bandwidth positioning (compensates for lag)
  • Small tracking error with good models
  • Stable
  • Cost effective (no sensors for feedback)

The feedforward control concept

“ Anticipates ”

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Piezoelectric actuators

Hammerstein-based model for piezoactuators

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What’s the ‘best’ approach?

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  • A1. Model and invert all effects

Nonlinear Linear

  • Creep + Vibration
  • Short-range
  • Low-to-high speed
  • Hysteresis
  • Long-range
  • Low-speed

Short-range, low/high-speed Long-range, low-speed 7

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Short-range, low- and high-speed

Creep model Vibration model 8

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Inversion-based feedforward control: time domain

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(Exact Inversion)

Find input subject to the cost:

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Range: 10 x 10 x 2 µm Resonances: 25 kHz (x), 6 kHz (y), >80 kHz (z) AFM imaging rate: >70 fps (100x100 pixels) w/o FF w/ FF w/FF

High-speed AFM imaging example

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Prandtl-Ishlinskii hysteresis model

Hysteresis curve:

Play operator Sum of basic relays 13

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Advantages of relay-based hysteresis models

  • Inverse model can be obtained from measured input/output data
  • Can be use for real-time feedforward control

1 Hz 14

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Loop due to phase shift 15

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Creep, hysteresis, and vibration compensation

  • Croft et. al., Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application,
  • ASME J. Dyn. Sys. Meas. Cont., 2001

Advantage: offers best performance with good models

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  • A2. Model and invert G(jω), use feedback for H

Advantage: avoids modeling nonlinearity

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  • B1. What if you don’t know the model?

Iteratively find the feedforward input

Advantages

  • Does not require an accurate model
  • Provides high-precision tracking
  • Can be automated, but requires a sensor
  • Stable

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Types of update laws: time-domain

  • 1. System is linear1
  • 2. System is hysteretic2

1Arimoto et. al., 1983; 2Leang and Devasia, 2006

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Frequency domain*

* Wu et. al., 2007

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AFM imaging example

21 1 Hz scanning; 100 iterations

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Conclusions

  • Feedforward control anticipates for deficit performance
  • Feedforward control provides high-bandwidth, high-precision

positioning (compensates for lag) with good models

  • Feedforward-controlled system is stable
  • Feedforward control does not require sensors

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