Modeling, Simulation, and Control of Digital Clay Mod

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Modeling, Simulation, and Control of Digital
ClayModélisation, Simulation, et Control de
lArgile Numérique

• PFE Final Presentation

Students Stephen ASKINS Samuel DESSOLIN
Project Directors Monsieur André BARRACO (ENSAM,
Paris) Doctor Wayne BOOK (GATech, Atlanta)
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Modeling, Simulation, and Control of Digital Clay

• NSF funded haptics research project at GATech
  Digital Clay
• Haptics Interfacing with a computer through
  touch by transmitting or sensing forces.
• Carried out as PFE at ENSAM/Paris as a result of
  collaboration through GTL Program.

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General Introduction to Digital Clay

• Novel distributed input/output device with
  continuously variable surface.
• To operate like clay
• Surface shaped by user è computer model shape
  mode.
• Computer model è surface assumes shape display
  mode.
• Computer model è surface assumes feel impedance
  mode.
• Fluidically actuated.
• Applications design, art, education.

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Digital Clay Architectures

• Currently no fixed design for digital clay, in
  process of making these decisions.
• Possible architectures
• Bed of Nails.
• Bellows.
• Distributed architecture.

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PFE

• Part of Digital Clay project
• Beginning of a 5-year project.
• Members of Controls Group, lead by Dr. Book.
• Far from other teams involved ? few
  communication.
• Modeling, Simulation, and Control
• No concrete values or even the kind of structure
  used
• ? be as general as possible.
• ? use logical numbers, see their influence.

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General Approach

• Assumptions Fluidic cells, changing size, 2-
  or 3-D network, membrane

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Cell Modeling

• Using MATLAB/Simulink.
• Goals
• Translate phenomena and physical laws into block
  diagrams.
• Build the base of a general model of Digital
  Clay.
• Steps
• Conventional model.
• Dual Mass model.
• Results and comparisons.

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Cell Assumptions

• Kinetic mass variable mobile submitted to
  forces.
• Hydraulic flow due to pressure difference,
  conservation of mass, incompressible fluid.
• Consider height limitation.

• Fexternal divided in 2 effects
• Squeezing due Fmin.
• Pushing due to (Fmax-Fmin).
• Pcell in equilibrium with Fsqueezing and Fc.

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Conventional Model
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Dual Mass Model
Only small difference in acceleration when
unanchored.
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Conclusions

• Conventional Model (Fave) and Dual Mass Model
  perform equivalently on tests so far.
• Different satisfying tests Display mode, Shape
  mode.
• Continue using both models for verification.

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Membrane Modeling

• Using ANSYS Finite Element Code.
• Membrane advantages
• Better visual and tactile effects.
• Enclose device space.
• Goals
• Feed MATLAB network model with analytical
  formula.
• Build Analytical Models by identification.
• Steps
• Linear Analysis and Linear Analytical Model.
• Nonlinear Analysis and Nonlinear Analytical Model.

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Linear Analysis and Linear Analytical Model
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Nonlinear Analysis

• Nonlinearity due
• Geometry of load.
• Material type.

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Nonlinear Analysis

• Example

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Nonlinear Analytic Model
Only 1 type of bar
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Conclusions

• Linear Model
• First step.
• Useful for MATLAB network model.

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General Modeling
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Network Modeling

• Use piston-ram cell.
• Bed of nailsarchitecture
• Single layer.
• Grid pattern.
• Conventional model sufficient.
• Form 36-cell device.
• Cover with membrane.

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Creating Network

• All as single Simulink Model file.
• Using subsystems for simplifying.
• Work intensive
• Both creating and editing these block diagrams
  can be difficult and error prone.
• Possibility of automating this process using
  MATLAB commands.
• Possibility for at most 100 cell networks in pure
  simulink format.
• Attempt at discretizing using MATLAB code failed.

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Network Testing (Uncontrolled)
Results for Single Frozen Cyl
Results for Single Forced Cyl

• Tested with various inputs to verify expected
  behavior and find bugs in block diagram.
• These results show speed of response for
  unpressurized cell.

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Control Implementation

• Proportional
• Standard first implented.
• On/Off
• Simplest allows 2 state valves.
• Neighbor Influenced
• Proportional but with gain dependent on expected
  resistance from membrane.
• May be useful given importance of membrane to
  cell response.
• PID (proportional integrator derivative)
• Standard control improvement.
• No need or advantage seen
• not shown

General Control
Controls Implemented
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Examples of Control Tests

• Shown with Proportional Control
• Kc 100
• Time scale 5s
• Only limiting factor for forming shapes is
  saturation of pressure against membrane

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Control Results Proportional

• Results shown for K 25 100 500 and 10000 on
  scale of 3s.
• Even as gain is increased so that system
  approaches speed capacity negligible overshoot
  seen.
• System, as modeled, very stable probably no need
  for complex control for forming shapes.

Effect of Reducing Gain
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Control Results On/Off

• Because of stability at high gains, On/Off
  (equiv. to K ) deemed possible.
• Even w/ dead zone on order of 1x10-5 m we see
  only small over shoot and fast settling
• RTmax .104s.
• Advantage valves need not be continuous
• ie. solenoid style valves.

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Control Results Neighbor Influenced

• Based on equation
• Adjust gain based on stretch on membrane
• Only adds to Kn for Herrors such that membrane
  resists cell movement.
• Some advantage seen, but currently no great
  advantage over raising gain in overall
  performance.

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Conclusions

• Cell Modeling
• Two models developed which should be useful for
  simulating most digital clay architectures and
  will hopefully require little modification for
  adapting to real actuators.
• Membrane Modeling
• Limiting factor in having useful ANSYS results is
  displacements achieved.
• New analytical model would be useful.

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Conclusions

• Network Modeling
• Demonstrated capability of all Simulink devices
  on order of 50 to 100 cells, though tedious.
• Showed difficulties in employing MATLAB m-files.
• Control
• We note that the Bed of Nails Architecture
  appears inherently easy to control.
• Cannot offer conclusions on more complex
  architectures.

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Next Steps

• To be continued in GATech as MS thesis.
• Cell Modeling
• Extension of movements in horizontal directions
  ? 3-D.
• Membrane Modeling
• Get larger vertical displacements in Nonlin Ana
  if possible.
• Try a different approach of curve fitting.
• Network Modeling
• Simulate with nonlinear springs (hyperelastic
  bars).
• Build a multiple levels structure.
• Generate models with MATLAB commands.