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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
2
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
3
Outline
• Motivation
• System model
• Example and problem formulation
• Scheduling and synthesis approach
• Experimental results
• Summary and contribution
4
System model
Linear plant model:
• dx(t)/dt = Ax(t) + Bu(t)
• y(t) = Cx(t)
Internal-state vector x(t)
Input u(t)Output y(t)
Measurement noise e(t)
Plant disturbance v(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)
Controller
A/D D/AWhat is a good sampling period?
What is a good control law u?
5
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
6
Example: Control of two pendulums
u
y
u
y
• Measure the angle y
• Stabilize in upright position y=0
• Control the acceleration u of the cart
0 1 0
/ 0.2 0 / 0.2x x u v
g g
1 0y x e
0.2 m0.1 m
J = E{y2 + 0.002u2}
7
Example: Platform
S
A
C
S
A
C
Decide
(1) sampling periods,
(2) design control laws, and
(3) schedule the tasks and messages
8
Example: Ideal control
S
A
C
S
A
C
• 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)
Sample 20 ms Sample 30 ms
9
Example: Scheduling
S
A
C
S
A
C
S
CS
C S A
S C
S C
A C
A
A
A
20 4010 30 50• Delay distribution
• Application 1: 32, 29, 14
• Application 2: 44, 24
• J1=4.2, J2=6.4, Total=10.6
Sample 20 ms Sample 30 ms• Ideal case
• J1=0.9, J2=2.4, Total=3.3
10
Example: Scheduling
S
A
C
S
A
C
S
CS
C S A
S C
S C
A C
A
A
A
20 4010 30 50
S
CS
C SA
SC
S C
A C
A
A
A
20 4010 30 50• Delay distribution
• Application 1: 14 (constant)
• Application 2: 18, 24
• J1=1.1, J2=5.6, Total=6.7
Sample 20 ms Sample 30 ms
• Compensate for the delays in the schedule (14 and 21)
• J1=1.0, J2=3.7, Total=4.7
• Ideal case
• J1=0.9, J2=2.4, Total=3.3
• First schedule
• J1=4.2, J2=6.4, Total=10.6
11
Example: Change periods
S
A
C
S
A
C
Sample 30 ms Sample 20 ms
S
CS
C SA
S C
C
A
A
A
20 4010 30 50S
C
A
• Delay distribution
• Application 1: 13, 23
• Application 2: 18
• J1=1.3, J2=2.1, Total=3.4 (with delay compensation)
Good selection of periods combined with integrated
scheduling and control-law synthesis is important!
• With periods 20 ms and 30 ms:
• J1=1.0, J2=3.7, Total=4.7
12
Problem formulation
Available sampling periods
Deadlines
Execution-time specifications
Scheduling and synthesis tool
i iw JPeriods
Control laws
?Minimize
13
Approach (Static-cyclic scheduling)
Select controller periods
Task periods
Schedule the tasks and messages
Delay distributions
Synthesize control-laws and compute cost
Stop?No
Yes Done!
Cost
• Constraint logic programming (CLP)
• Minimize delay and jitter
• CLP solver ”ECLiPSe”
What if we have priority-based scheduling?
• Genetic algorithm for period assignment
14
Approach (Priority-based scheduling)
Select task and message priorities
Synthesize control-laws and compute cost
No
Cost
Delay distributions
Schedulable?
Priorities
SimulateYes
Stop?Yes
CostNo
• Run response-time analysis to obtain worst-case delays
• Bounded delays?
• Deadlines met?
• Genetic algorithm for priority assignment
15
Experimental results
Number of plants
Ave
rag
e co
st i
mp
rove
men
t [%
]
Isolated scheduling and control-law synthesisIntegrated approach
Straightforward period assignment
16
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
18
Evaluation
Period optimization with genetic algorithms
Integrated control-law synthesis and
scheduling
Straightforward period assignment
Isolated control-law synthesis and
scheduling
1. Select smallest periods for all applications
2. Schedule system and synthesize control-laws
3. If not schedulable, increase the period of the application with highest resource demand and then go back to Step 2
1. Synthesize control-law with neglecting the implementation aspects (traditional design)
2. ”As soon as possible” or ”rate-monotonic” scheduling
19
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
• Generated benchmarks with inverted pendulums, servos, and other examples of unstable plants
• 6 to 45 tasks, 2 to 7 computation nodes