Integrated Scheduling and Synthesis of Control Applications on Distributed Embedded Systems

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Integrated Scheduling and Synthesis of Control
Applications on Distributed Embedded Systems

• Soheil Samii1, Anton Cervin2, Petru Eles1, Zebo
  Peng1

1 Dept. of Computer and Information
Science Linköping University Sweden
2 Dept. of Automatic Control Lund
University Sweden
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Motivation

• Many embedded control systems are distributed
• Typical example the modern car
• Timing delays
• Sampling, computation, and actuation
• Sharing of computation and communication
  resources
• Problem Degradation of control performance

• System scheduling
• Controller design

Plant
Plant
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Outline

• Motivation
• System model
• Example and problem formulation
• Scheduling and synthesis approach
• Experimental results
• Summary and contribution

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System model
Plant disturbance v(t)
Internal-state vector x(t)
Plant
Output y(t)
Input u(t)
Measurement noise e(t)
A/D
D/A
What is a good sampling period? What is a good
control law u?
Controller

• Linear plant model
• dx(t)/dt Ax(t) Bu(t)
• y(t) Cx(t)

• Application model
• Periodic tasks
• Data dependencies

• Linear plant model
• dx(t)/dt Ax(t) Bu(t) v(t)
• y(t) Cx(t) e(t)

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Control performance

• Quadratic cost J E xTQ1x uTQ2u
• Depends on
• the sampling period,
• the control law, and
• the distribution of the delay between sampling
  and actuation of the control signal
• Synthesis of optimal control-law for given
• sampling period and
• constant delay
• Toolbox Jitterbug, developed at Lund University
  in Sweden

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Example Control of two pendulums
0.2 m
0.1 m
J Ey2 0.002u2

• Measure the angle y
• Stabilize in upright position y0
• Control the acceleration u of the cart

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Example Platform
S
S
C
C
A
A
Decide (1) sampling periods, (2) design control
laws, and (3) schedule the tasks and messages
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Example Ideal control
Sample 20 ms
Sample 30 ms
S
S
C
C
A
A

• Control laws synthesized for the constant delays
  of each application (9 and 13)
• J10.9, J22.4, Total3.3 (achieved for the
  ideal runtime scenario dedicated resources)

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Example Scheduling
Sample 20 ms
Sample 30 ms

• Ideal case
• J10.9, J22.4, Total3.3

S
S
C
C
A
A

• Delay distribution
• Application 1 32, 29, 14
• Application 2 44, 24
• J14.2, J26.4, Total10.6

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Example Scheduling
Sample 20 ms
Sample 30 ms

• Ideal case
• J10.9, J22.4, Total3.3

S
S
C
C
A
A

• First schedule
• J14.2, J26.4, Total10.6

• Compensate for the delays in the schedule (14 and
  21)
• J11.0, J23.7, Total4.7

• Delay distribution
• Application 1 14 (constant)
• Application 2 18, 24
• J11.1, J25.6, Total6.7

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Example Change periods
Sample 30 ms
Sample 20 ms
S
S
C
C
A
A
Good selection of periods combined with
integrated scheduling and control-law synthesis
is important!

• With periods 20 ms and 30 ms
• J11.0, J23.7, Total4.7

• Delay distribution
• Application 1 13, 23
• Application 2 18
• J11.3, J22.1, Total3.4 (with delay
  compensation)

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Problem formulation
Available sampling periods
Execution-time specifications
?
Deadlines
Scheduling and synthesis tool
Minimize
Periods
Control laws
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Approach (Static-cyclic scheduling)
Select controller periods
Task periods
Schedule the tasks and messages
What if we have priority-based scheduling?
Delay distributions
Synthesize control-laws and compute cost
Cost
Stop?
Yes
Done!
No
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Approach (Priority-based scheduling)
Select task and message priorities
Priorities
No
Schedulable?
Yes
Simulate
Delay distributions
Synthesize control-laws and compute cost
Cost
Yes
No
Stop?
Cost
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Experimental results
Average cost improvement
Integrated approach
Isolated scheduling and control-law synthesis
Straightforward period assignment
Number of plants
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Summary and contribution

• Problem Sharing of computation and communication
  resources degrades the control performance
• Solution Integrate scheduling with control
  design (period assignment and control-law
  synthesis)
• Contribution
• A tool for such integrated design of distributed
  embedded control systems with
• static-cyclic scheduling or
• priority-based scheduling

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EXTRA SLIDES
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Evaluation
Period optimization with genetic algorithms
Integrated control-law synthesis and scheduling
Straightforward period assignment
Isolated control-law synthesis and scheduling
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Experiments
Period optimization with genetic algorithms
Integrated control-law synthesis and scheduling
Straightforward period assignment
Isolated control-law synthesis and scheduling

• Straightforward approach as a baseline, JSF
• Compute relative cost improvement
• (JSF J) / JSF
• Evaluate each part of the optimization in
  isolation

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Static-cyclic scheduling
Average cost improvement
Number of plants
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Priority-based scheduling
Average cost improvement
Number of plants
22
Optimization time
Average runtime seconds
Number of plants