multi-objective co-optimization of flexray-based...

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


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


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

2


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


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


Feedback Control Systems

Controller

Plant

SensorActuator

Continuous-time model:

4

Car suspension system


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

5


Distributed Time-Triggered Control SystemCar Suspension

6


Distributed Time-Triggered Control System

Multiple processing units (PUs) connected via a bus

Car Suspension

6


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

6


FlexRay time is organized as an infinite repetition of series of 64

consecutive cycles (0 ... 63)

FlexRay Communication

7


FlexRay time is organized as an infinite repetition of series of 64

consecutive cycles (0 ... 63)


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

)

7


FlexRay frame model

Slot identifier

Base cycle

Repetition rate


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

8


Objective Formulation


Performance metrics like settling time, cost function, etc.

Control performance must satisfy the performance criterion

Normalized control performance

9


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


Performance metrics like settling time, cost function, etc.

Control performance must satisfy the performance criterion

Normalized control performance

9


Problem Description

10

Given Parmeters:

Plant Model

Performance metric

Required performance

Given Parmeters:

Bus configuration

WCETs

Task mappings

Control Side Platform Side


Problem Description

10

Given Parmeters:

Plant Model

Performance metric


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



Problem Description

10

Given Parmeters:

Plant Model

Performance metric


Variables:

Sampling period

Feedback control gain

Feedforward control gain

Objective:


Objective:

Bus utilization

Variables:

Sensor task

Sensor message

Control task

Control message

Actuator task

Given Parmeters:

Bus configuration

WCETs

Task mappings



Control and Platform Interdependence

11

Sampling period

Sensor-to-actuator delay Task schedules

Message schedules



11

Periodicity constraint

Sampling period of a control

application must coincide with

the periods of the component tasks

and message frames.

Sampling period


Message schedules



11


Sampling period of a control

application must coincide with

the periods of the component tasks

and message frames.

Delay constraint

Sampling period


Message schedules


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

12



Exhaustive search

based optimal

controller design




Co-Optimization

User Selection

• Pareto Front

Stage 1

Stage 2



12






Co-Optimization

User Selection

• Pareto Front

Stage 1

Stage 2



12


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

13



Optimal control design

Exhaustive search

based optimal

controller design

YES

YES

NO

NO

13



Effect of search granularity

Exhaustive search

based optimal

controller design

13


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

14



Problem formulation

Constraints


C2: Dataflow



Objectives

O1: Overall system

performance

O2: Bus utilization

(C1) Performance requirement

For each control application ,

control performance , must

satisfy the control performance

requirement .

14



Problem formulation

Constraints


C2: Dataflow



Objectives

O1: Overall system

performance

O2: Bus utilization

(C2) Dataflow

14



Problem formulation

Constraints


C2: Dataflow



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

14



Problem formulation

Constraints


C2: Dataflow



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,

14



Problem formulation

Constraints


C2: Dataflow



Objectives

O1: Overall system

performance

O2: Bus utilization

(O1) Overall system performance

14



Problem formulation

Constraints


C2: Dataflow



Objectives

O1: Overall system

performance

O2: Bus utilization

(O2) Bus utilization

14



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

15



optCP

depends only on

Solves an ILP problem

Variables:

Objective:

O1: Overall system performane

Constraints:

Objective bound:


O2: Equality constraint on

15



findSchedules

Solves a constraint satisfaction problem

Variables:

Task schedules

Message schedules

Constants:

Periods and repetition rates


Constraints:

Delay constraint

C2: Dataflow



15


An Example Automotive System

DC Motor

Speed

Control

(DCM)

Cruise

Control 1

(CC1)

Cruise

Control 2

(CC2)

Electronic

Wedge

Brake

(EWB)

Car

Suspension

(CSS)

16


Stage 1: Prospective controller design

For each control application

Determine optimal performances at seven possible sampling periods

17



Stage 2: Co-optimization

Pareto front depicts the trade-off between objectives

24 reasonably well-distributed pareto points

18




Simulation validation using SIMTOOLS + MATLAB/SIMULINK

19

CC1


Concluding Remarks

Approach

Design of FlexRay-based distributed control systems

Design objectives


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

20


Concluding Remarks

Approach

Design of FlexRay-based distributed control systems

Design objectives


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

20


Thank You

Q/A

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