Synchronization of State Based Control Processes with Delayed and Asynchronous Measurements

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Synchronization of State Based Control Processes
with Delayed and Asynchronous Measurements

• Haitham Hindi
• Lara Crawford
• Markus Fromherz
• Palo Alto Research Center
• (formerly known as Xerox PARC)

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Outline

• Context Motivation
• Distributed, networked, cooperative control
• Modular reconfigurable printing
• Overview of technical challenges remedies
• Network delays
• Distributed sensing and actuation
• Focus on controller state synchronization
  techniques
• Embedded systems issues implementation
• Goal share some hard-learned lessons simple
  powerful tricks from the trenches

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High-End Printing system

• A complex multi-function device
• variety of operations
• complex interactions
• real-time, high-speed operations
• Control software ensures performance and
  correctness

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Modularity, Reconfigurability, Distributed Control
Control
Ca. 1990 monolithic system, central control
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Hierarchical Networked Paper Path Control Problem

• Distributed system
• Sheet moved by multiple nips
• Sheet sensed by multiple sensors
• Asynchronous measurements
• Due to different length modules noise
• Network delays
• Nips (rollers) sensors communicate across
  network via sheet controller
• Synchronization
• clock
• controller state

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3DOF Nip Controller

• Nip controller computes nip motor control command
  u
• Keeps sheet (red) following interpolated way
  point curve (blue), in presence of process
  sensor noise
• Uses feedforward (for ref. tracking), feedback
  (for noise rejection) and lead (look ahead) ? 3
  degrees of freedom

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Handling Asynchronous Detection

• Sheet is detected when edge crosses sensors
• Irregular sensor crossing times cause
  asynchronous detection
• Handled via standard time-varying Kalman filter

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Network Delays
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Handling Random DelaysTime Stamping Delay
Equalization
Network
Delay Equalizer
SensorMgr
MC
Physical System
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Asynchronous Controller Performance

• Good tracking of way point trajectory
• Arrival window error approx. 4mm ?
  15msec_at_0.3m/sec
• Peak control (nip speed and acceleration) within
  specs
• Asynchronous detection cause approx factor of two
  error over synchronous

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Distributed Coordination Network Delays

• Multiple nips joining leaving network
  communication delays
• ? need careful synchronization technique
• Solution nip-to-nip handoff implemented by
  embedding continuous LQG controller in discrete
  finite state machine (FSM)
• FSM has 4 functions off, synch., compute, and
  drive

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Notation

• Think of controller on each nip as separate
  process
• Processes p0,,pn-1 run the controller
  recursion
• xi(t1) f(xi(t),yi(t-d),t) xi(0)
  xi0
• ui(t) g(xi(t),yi(t-d),t)
• xi state
• ui control output
• yi measurement input yi,
• d known fixed integer delay
• Same f g for all nips and all sheets

pi
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Synchronized Processes

• Suppose processes p0,,pn-1 driven by same
  measurements and same initial condition, ie
• xi0 x0 8 i
• yi(t) y(t) 8 i,t,
• then the processes all run the same recursion
• x(t1) f(x(t),y(t-d),t) x(0) x0
• u(t) g(x(t),y(t-d),t).
• Definition such a set of processes, where the
  x(t) and u(t) are identical for all time, as
  synchronized.

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Problem Statement

• Given (1) f, g, and d
• (2) p0,,pn-1 running
  synchronized
• (3) t d, starting time for
  new process pn
• (4) d-sample delay in any
  message pi ! pj
• Goal synchronize new process pn, to p0,,pn-1,
  
• for all time t t'
• for any state recursion functions f
  and g
• Specifically, is there some start-up messaging
  protocol which will do the job?

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Solution

• Note performing d iterations of the state
  recursion
• x(t'-d1) f(x(t'-d),y(t'-2d),t'-d)
• x(t'-d2) f(x(t'-d1),y(t'-2d1),t'-d
  1)
• x(t') f(x(t'-1),y(t'-d-1),t'-1)
  .
• ) only need y(t'-2d),,y(t'-d-1) and x(t-d) to
  compute x(t)
• Requires sending nothing more recent than d time
  samples ago!
• Protocol to synchronize with p0,,pn-1 8 t
  t, pn must
• from time (t-d) start receiving measurements y
• at time t have x(t-d) and instantly forward
  propagate to x(t')
• From t onwards, to remain synchronized, pn
  only needs to receive the
• same measurements y as p0,,pn-1.
• Used in many distributed applications computer
  games, data bases

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Results Nip Coordination via FSM

• Results
• As sheet passed on from nip to nip, all nips
  touching sheet (blue) produce the same control
  signal (red)
• As soon as nip finishes moving sheet, nip free to
  process other sheets
• Status
• Implemented code in embedded processors
• Demonstrated on real prototype hardware

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Conclusion

• Covered some useful techniques for distributed
  coordinated networked control
• Time stamping delay equalization
• Time varying Kalman filter estimation
• Controller state synchronization (Hand-off)
• Clock synchronization (phase locked loop not
  covered in this talk)
• Showed how controller state synchronization can
  be accomplished by embedding dynamic controller
  in Finite State Machine (FSM) which handles
  synchronization
• Extremely simple when formulated and implemented
  precisely and correctly
• These 4 simple yet powerful techniques provide a
  good basic tool set for tackling distributed
  networked control applications
• Golden Rules from The Trenches
• Always try the easiest thing first!
• Have faith in your equations!
• Always pick feasibility over optimality