Quality-Driven Synthesis of Embedded
Multi-Mode Control Systems
Soheil Samii1, Petru Eles1, Zebo Peng1, Anton Cervin2
1 Dept. of Computer and
Information Science
Linköping University
Sweden
2 Dept. of Automatic Control
Lund University
Sweden
Motivation
Plant
Plant
 Number of modes = 2Number of control loops
Plant
Cannot afford the synthesis time
Plant
 Cannot store all controllers and schedules
2
Outline
 System model and control performance
 Example and problem formulation
 Synthesis approach
 Experimental results
3
System model
Plant disturbance v(t)
Internal-state vector x(t)
Output y(t)
Input u(t)
Plant
What is a good sampling period?
A/D
Measurement noise e(t)
D/A
What is a good control law u?
Controller
Linear plant model:
• dx(t)/dt = Ax(t) + Bu(t) + v(t)
• y(t) = Cx(t) + e(t)
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 schedule (delays between sampling and
actuation)
5
Synthesis of a mode (DATE’09)
Scheduling and synthesis tool
Minimize
J
i
Periods
Control laws

6
Example
Plant 1
Plant 3
Plant 2
S
S
C
S
A
A
C
10
S
20
C
C
30
J1 = 3.0
J2 = 1.2
J3 = 2.2
A
A
40
7
Example
Plant 1
Plant 3
Plant 2
S
S
C
S
A
A
C
10
S
20
C
C
30
A
J1 = 3.0
J2 = 1.2
A
40
8
Example
Plant 1
Plant 3
Plant 2
Previous case:
J1 = 3.0
J2 = 1.2
S
C
S
C
10
A
J1 = 1.6
J2 = 1.4
A
20 22
9
Example
J1 = 3.0
J2 = 1.2
J3 = 2.2
1
J1 = 1.6
J2 = 1.4
1
Cumulative cost of all
modes: 19.6
2
1
J1 = 1.6
2
1
3
3
2
3
J1 = 3.0
2 J3 = 2.2 3
J2 = 1.2
J3 = 2.2
10
Problem formulation
 Inputs:
 Multi-mode control system (architecture, tasks,
plants)
 Available memory on each computation node
 Outputs:
 Schedules and controllers for some modes
 Cost to minimize:
 Cumulative cost of each functional mode
11
Some modes are
functionally excluded
Synthesis approach
J1 = 2.5
1
2
J2 = 1.5
J4 = 2.0
3
4
J1 = 2.3J1 = 2.0
J1 = 2.0 J2 = 1.8
4
3
4
2 3
1
2
1
2
1
3
J2 = 1.2J3 = 2.2
J4 = 1.2 J4 = 1.3
 =Synthesis
versus
Impr. =Impr.
12.5%
16.0% time Impr.
= quality
20.0%
Impr. = 11.4%
1
1
2
1
 Parameter λ (20% in our example)
3
2
2
3
1
4
3
2
4
3
4
4
4
J1 = 1.2
J4 = 1.2
Require at least λ = 20% improvement
Impr. = 40%
Impr. = 0%
12
Synthesis approach
Cost = 23
Mem = 18
1
1
2
1
3
1
2
1
3
Cost = 23
2
4
3
Mem = 20
2
4
2
3
1
1
Cost = 19
Mem = 20
3
4
4
2
2
3
4
3
4
4
 ILP formulation
1
2
3
4
13
Synthesis approach
1
1
1
2
1
2
1
1
3
3
2
2
4
2
3
2
4
3
1
1
3
4
3
4
2
2
3
4
3
4
4
4
14
Cost improvement [%]
Experiments – Synthesis Quality
λ = 0%
λ = 10%
λ = 30%
λ = 50%
Number of control loops
15
Runtime [seconds]
Experiments – Synthesis Time
λ = 0%
λ = 10%
λ = 30%
λ = 50%
Number of control loops
16
Summary and Contribution
 Two important problems in synthesis of multimode control systems
 Time complexity (offline)
 Memory complexity (online)
 Contribution:
 Synthesis tool with performance/time/memory
trade-off
17