Integrated Scheduling and Synthesis of Control Applications on Distributed Embedded Systems Soheil Samii 1 , Anton Cervin 2 , Petru Eles 1 , Zebo Peng 1 1 Dept. of Computer and Information Science Linköping University Sweden 2 Dept. of Automatic Control Lund University Sweden
22
Embed
Integrated Scheduling and Synthesis of Control Applications on Distributed Embedded Systems Soheil Samii 1, Anton Cervin 2, Petru Eles 1, Zebo Peng 1 1.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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)