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
Motivation
•
•
Many embedded control systems are distributed
• Typical example: the modern car
Timing delays• System scheduling
Controller design
• Sampling,•computation,
and actuation
• Sharing of computation and communication
resources
• Problem: Degradation of control performance
Plant
Plant
2
Outline
•
Motivation
•
System model
•
Example and problem formulation
•
Scheduling and synthesis approach
•
Experimental results
•
Summary and contribution
3
System model
Plant disturbance v(t)
Internal-state vector x(t)
Output y(t)
Input u(t)
Plant
Measurement noise e(t)
A/D
What is a good sampling period?
D/A
What is a good control law u?
Linear plant model:
• dx(t)/dt = Ax(t) + Bu(t) + v(t)
• y(t) = Cx(t) + e(t)
Controller
Application model:
• Periodic tasks
• Data dependencies
4
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
5
Example: Control of two pendulums
y
y
0.2 m
0.1 m
u
u
1
 0
 0 
x
x
uv


 g / 0.2 0
 g / 0.2
y  1 0 x  e
•
•
•
J = E{y2 + 0.002u2}
Measure the angle y
Stabilize in upright position y=0
Control the acceleration u of the cart
6
Example: Platform
S
S
C
C
A
A
Decide
(1) sampling periods,
(2) design control laws, and
(3) schedule the tasks and messages
7
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)
J1=0.9, J2=2.4, Total=3.3 (achieved for the ideal
runtime scenario: dedicated resources)
8
Example: Scheduling
Sample 20 ms
•
S
S
S
•
•
C
Sample 30 ms
Ideal case
S
• J1=0.9, J2=2.4, Total=3.3
C
C
A
A
S
A
C
10
20
30
Delay distribution
• Application 1: 32, 29, 14
• Application 2: 44, 24
J1=4.2, J2=6.4, Total=10.6
S
S
C
A
40
C
A
A
C
A
50
9
Example: Scheduling
Sample 20 ms
•
S
C
A
•
S
S
•
•
C
A
S
Sample 30 ms
Ideal case
S
• J1=0.9, J2=2.4, Total=3.3
C
A
First schedule
A AJ2=6.4, Total=10.6
S
C
A
• J1=4.2,
A
• Compensate
for
C
S
C theAdelays
C in A
(1440
and 21) 50
10
20 the schedule
30
Delay distribution • J1=1.0, J2=3.7, Total=4.7
• Application 1: 14 (constant)
• Application 2: 18, 24
J1=1.1, J2=5.6, Total=6.7
C
A
10
Example: Change periods
Sample 30 ms
S
S
•
•
Sample 20 ms
S
S
C
C
A
A
Good selection of periods
combined CwithS integrated
C
A
C
A
scheduling and control-law
• With periods 20 ms and 30 ms:
synthesis is important!
C
A
S
A J =3.7,
S
C
A
• J1=1.0,
Total=4.7
2
10
20
30
40
50
Delay distribution
• Application 1: 13, 23
• Application 2: 18
J1=1.3, J2=2.1, Total=3.4 (with delay compensation)
11
Problem formulation
Plant
Plant
Available sampling
periods
Execution-time
specifications
Deadlines
?
Scheduling and synthesis tool
Minimize
w J
i
i
Periods
Control laws
12
Approach (Static-cyclic scheduling)
Select controller periods
Task periods
Schedule the tasks and messages
•
•
•
What if we have
• (CLP)
Geneticpriority-based
algorithm for
ConstraintDelay
logicdistributions
programming
period scheduling?
assignment
Minimize delay and jitter
Synthesize control-laws and
CLP solver ”ECLiPSe”
compute cost
Cost
No
Stop?
Yes
Done!
13
Approach (Priority-based scheduling)
Select task and message priorities
Priorities
No
Schedulable?
•
Yes
Simulate
Run response-time
analysis to obtain
• Genetic algorithm for
worst-case delays
Delaydelays?
distributions priority assignment
• Bounded
• Synthesize
Deadlines met?
control-laws and
compute cost
Cost
Cost
Yes
Stop?
No
14
Average cost improvement [%]
Experimental results
Integrated approach
Isolated scheduling and control-law synthesis
Straightforward period assignment
Number of plants
15
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
16
EXTRA SLIDES
17
Evaluation
Period optimization with
genetic algorithms
Integrated control-law
synthesis and
scheduling
Straightforward period
assignment
Isolated control-law
synthesis and
scheduling
1.
2.
2.
3.
Synthesize
Select
smallest
control-law
periodswith
for all
neglecting
applications
the
implementation
(traditional
design)
Schedule systemaspects
and synthesize
control-laws
”As
as possible”
or ”rate-monotonic”
If notsoon
schedulable,
increase
the period of the
scheduling
application with highest resource demand and
then go back to Step 2
18
Experiments
Integrated control-law
Period optimization with
synthesis and
algorithms
•genetic
Generated
benchmarks with inverted
scheduling
pendulums, servos, and other examples of
unstable plants
Isolatednodes
control-law
•
6
to
45
tasks,
2
to
7
computation
Straightforward period
synthesis and
assignment
scheduling
•
•
•
Straightforward approach as a baseline, JSF
Compute relative cost improvement
• (JSF – J) / JSF
Evaluate each part of the optimization in isolation
19
Average cost improvement [%]
Static-cyclic scheduling
Number of plants
20
Average cost improvement [%]
Priority-based scheduling
Number of plants
21
Average runtime [seconds]
Optimization time
Number of plants
22