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Technische Universität München
Multi-Objective Co-Optimization of
FlexRay-based Distributed Control Systems
Debayan Roy1, Licong Zhang1, Wanli Chang2, Dip Goswami3, Samarjit Chakraborty1
1Technical University of Munich,Germany, 2TUM CREATE, Singapore,3Eindhoven University of Technology, Netherlands
RTAS 2016
April 14, 2016
Technische Universität München
Overview
Tc
Ta
FlexRay Bus
ECU
mc
ms
…
…
Scheduler
Scheduler
Ts …
Scheduler
Tc
Scheduler
…
…
FlexRay-based distributed control systems
Co-synthesis of
Control parameters
Platform parameters
Co-optimization of
Overall system performance
Communication cost, i.e., bus utilization
sensors
actuators
Physical System
Co
ntr
olle
r
Ts
Tc
Ta
ms
mc
sensors
actuators
Physical System
Co
ntr
olle
r
Ts
Tc
Ta
ms
mc
sensors
actuators
Physical System
Co
ntr
olle
r
Ts
Tc
Ta
ms
mc
1
Technische Universität München
Introduction
Motivation:
Separation between controller design and implementation is not sustainable
Control theorist says
these are
implementation
details.
Not my problem!
Embedded system
engineer says model
level assumptions
are not satisfied by
implementation
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Introduction
Motivation:
Separation between controller design and implementation is not sustainable
Need for co-design of control and platform parameters
Control theorist and
embedded system
engineer decide on
some common model
level assumptions for
co-design
2
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Introduction
Control theorist and
embedded system
engineer decide on
some common model
level assumptions for
co-design
3
Challenge:
Large design space including control and platform parameters
No standard closed-form optimal control design framework
Platform requires configuration of huge number of parameters
Technische Universität München
Feedback Control Systems
Controller
Plant
SensorActuator
Continuous-time model:
4
Car suspension system
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Feedback Control Systems
Controller
Plant
SensorActuator
Discrete-time model:
Delay ( ) and sampling period ( )
FlexRay bus
E1 E2 E3
Stable
Unstable
1
1
Unit circle
Stability and Pole-Placement
can be
calculated from
and
Closed-loop system poles
determine the system
stability
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Distributed Time-Triggered Control SystemCar Suspension
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Distributed Time-Triggered Control System
Multiple processing units (PUs) connected via a bus
Car Suspension
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Distributed Time-Triggered Control System
Multiple ECUs connected via a bus
Car Suspension
Task model:
Offset
Period
WCET
kth execution start time
kth execution finish time
0t
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FlexRay time is organized as an infinite repetition of series of 64
consecutive cycles (0 ... 63)
FlexRay Communication
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Technische Universität München
FlexRay time is organized as an infinite repetition of series of 64
consecutive cycles (0 ... 63)
FlexRay Communication
Each cycle is of fixed length Tbus and consists of:
Static segment
Dynamic segment
Symbol Window
Network Idle Time
Static Dynamic SW NIT Static Dynamic SIT NIT ........
Ci Ci+1
Slo
t1
Slo
t2
Slo
t3
Slo
t4
Slo
t5
.......
Slo
tN
Min
islo
t(N
+1)
Min
islo
t(N
+2)
Min
islo
t(N
+3)
Min
islo
t(N
+4)
Min
islo
t(N
+5)
.......
Min
islo
t(N
+M
)
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FlexRay frame model
Slot identifier
Base cycle
Repetition rate
FlexRay Communication
cycle
slot
0
1
2
3
4
5
62
63
. . .
1 2 3 4 5 6 7 8 9
kth transmission start time
kth transmission finish time
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Objective Formulation
Overall system performance
Performance metrics like settling time, cost function, etc.
Control performance must satisfy the performance criterion
Normalized control performance
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Objective Formulation
cycle
slot0
1234
5
62
63
1 2 3 4 5 6 7 8 9
Bus utilization
Number of slots used in 64
consecutive cycles
Slots used by a frame is
Fraction of static bandwidth used
Overall system performance
Performance metrics like settling time, cost function, etc.
Control performance must satisfy the performance criterion
Normalized control performance
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Problem Description
10
Given Parmeters:
Plant Model
Performance metric
Required performance
Given Parmeters:
Bus configuration
WCETs
Task mappings
Control Side Platform Side
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Problem Description
10
Given Parmeters:
Plant Model
Performance metric
Required performance
Variables:
Sampling period
Feedback control gain
Feedforward control gain
Variables:
Sensor task
Sensor message
Control task
Control message
Actuator task
Given Parmeters:
Bus configuration
WCETs
Task mappings
Control Side Platform Side
Technische Universität München
Problem Description
10
Given Parmeters:
Plant Model
Performance metric
Required performance
Variables:
Sampling period
Feedback control gain
Feedforward control gain
Objective:
Overall system performance
Objective:
Bus utilization
Variables:
Sensor task
Sensor message
Control task
Control message
Actuator task
Given Parmeters:
Bus configuration
WCETs
Task mappings
Control Side Platform Side
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Control and Platform Interdependence
11
Sampling period
Sensor-to-actuator delay Task schedules
Message schedules
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Control and Platform Interdependence
11
Periodicity constraint
Sampling period of a control
application must coincide with
the periods of the component tasks
and message frames.
Sampling period
Sensor-to-actuator delay Task schedules
Message schedules
Technische Universität München
Control and Platform Interdependence
11
Periodicity constraint
Sampling period of a control
application must coincide with
the periods of the component tasks
and message frames.
Delay constraint
Sampling period
Sensor-to-actuator delay Task schedules
Message schedules
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The Proposed Approach
• Bus configuration• Task Mapping• Task WCETs
• Control performance and gains look-up tables (LUTs)
Prospective Controller Design
Co-Optimization
User Selection
• Pareto Front
Stage 1
Stage 2
• Controllers• Task schedules• Message schedules
• Plant Models• Performance Metrics • Performance Criteria
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The Proposed Approach
Exhaustive search
based optimal
controller design
• Bus configuration• Task Mapping• Task WCETs
• Control performance and gains look-up tables (LUTs)
Prospective Controller Design
Co-Optimization
User Selection
• Pareto Front
Stage 1
Stage 2
• Controllers• Task schedules• Message schedules
• Plant Models• Performance Metrics • Performance Criteria
12
Technische Universität München
The Proposed Approach
• Bus configuration• Task Mapping• Task WCETs
• Control performance and gains look-up tables (LUTs)
Prospective Controller Design
Co-Optimization
User Selection
• Pareto Front
Stage 1
Stage 2
• Controllers• Task schedules• Message schedules
• Plant Models• Performance Metrics • Performance Criteria
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Stage 1: Prospective Controller Design
Exhaustive search
based optimal
controller design
Develop exhaustive search based
optimal control design algorithm
Determine control gains
which optimizes the control
performance to at
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Stage 1: Prospective Controller Design
Optimal control design
Exhaustive search
based optimal
controller design
YES
YES
NO
NO
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Stage 1: Prospective Controller Design
Effect of search granularity
Exhaustive search
based optimal
controller design
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Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
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Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
(C1) Performance requirement
For each control application ,
control performance , must
satisfy the control performance
requirement .
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Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
(C2) Dataflow
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Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
(C3) Non-overalapping tasks
For two tasks mapped on the same
ECU, none of their instances must
overlap in time.
t
t
t
X
where,
or
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Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
(C4) Non-overalapping messages
No two messages must be transmitted
in the same slot of the same cycle.
where,
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Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
(O1) Overall system performance
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Technische Universität München
Stage 2: Co-Optimization
Problem formulation
Constraints
C1: Performance requirement
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
Objectives
O1: Overall system
performance
O2: Bus utilization
(O2) Bus utilization
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Stage 2: Co-Optimization
Pareto front construction
Pareto point is better than any
other point in the design space
in atleast one objective
Discrete values of
Minimum value of
Maximum value of
Minimum difference between
two values of
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Stage 2: Co-Optimization
optCP
depends only on
Solves an ILP problem
Variables:
Objective:
O1: Overall system performane
Constraints:
Objective bound:
C1: Performance requirement
O2: Equality constraint on
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Stage 2: Co-Optimization
findSchedules
Solves a constraint satisfaction problem
Variables:
Task schedules
Message schedules
Constants:
Periods and repetition rates
Periodicity constraint
Constraints:
Delay constraint
C2: Dataflow
C3: Non-overlapping tasks
C4: Non-overlapping messages
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An Example Automotive System
DC Motor
Speed
Control
(DCM)
Cruise
Control 1
(CC1)
Cruise
Control 2
(CC2)
Electronic
Wedge
Brake
(EWB)
Car
Suspension
(CSS)
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Stage 1: Prospective controller design
For each control application
Determine optimal performances at seven possible sampling periods
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An Example Automotive System
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Stage 2: Co-optimization
Pareto front depicts the trade-off between objectives
24 reasonably well-distributed pareto points
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An Example Automotive System
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An Example Automotive System
Simulation validation using SIMTOOLS + MATLAB/SIMULINK
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CC1
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Concluding Remarks
Approach
Design of FlexRay-based distributed control systems
Design objectives
Overall system performance
Bus utilization
Two-stage approach
Exhaustive search based design of prospective optimal controllers
Nested two-layered technique to solve the co-optimization problem
Pareto front depicting the trade-off between objectives is constructed
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Technische Universität München
Concluding Remarks
Approach
Design of FlexRay-based distributed control systems
Design objectives
Overall system performance
Bus utilization
Two-stage approach
Exhaustive search based design of prospective optimal controllers
Nested two-layered technique to solve the co-optimization problem
Pareto front depicting the trade-off between objectives is constructed
Outlook
Incorporate variable sensor-to-actuator delays
Extension to heterogenous systems
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Thank You
Q/A
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