Network Control Systems using Scheduling Strategies

Dr. Héctor Benítez Pérez

IIMAS UNAM

Objectives of NCS and Reconfigurable Control

To modify the control law based upon external factors such as Time Delays

Take into account time delays based upon the distributed system communication.

Being capable to keep an efficient response even though there is a fault and local time delays.

Objectives of NCS and Reconfigurable Control

To study dynamic schedulling in Real-Time considering how to manage processes, their communication and the related reconfiguration.

To study the dynamic effects of the computer network onto the control law.

Areas of Study

To Model Real-Time Systems

To model stochastic behaviour using TKS

To study the iteraction amongst dynamic systems and complex computer systems.

Classic Configuration

"Smart" Sensor

"Smart"Actuator

ControllerPlant"Smart" Sensor

Fault ToleranceModule

External Fault Tolerance

Module

Classic approximation based upon Queues

Messages Queue

Sensors Plant

Messages Queue

Controller

Actuators

Time Delays associated to perturbated external

processes.

Codesign Strategy

SCHEDULLING EVALUATION

StabilityTest

Time DelaysEvaluation

Valid Scheduler

Reconfiguration Proposal

Yes

NoYesNo

Scheduler Proposal

External Event

In here Reconfiguration

takes place

What is the studied iteraction

Reconfiguration

Request Plan

Validation Plan

Valid Plan

Database

Bus Controller

Node

Control Law

Node

Selection of the

Related Control

Law

Database

Control Laws

Computer Network

(Sensor Network)

Yes

(If the Plan

is valid

The related Control Law

is chosen)

No

(Rejection of the

proposed Plan)

First Reconfiguration Stage

Second Reconfiguration Stage

External Factor to requestreconfiguration

Time Delays Managment

ts

tc

ta

Sender/ Sensor

Receiver/Actuator

Controller

Time

Time

Time

Time Spent by QueuingInter-Communication

tqa

tqs

tc

T jT j+1

Lost Queue

Partial adds of transmission-times

ts

tc

ta

Sender/ Sensor

Receiver/Actuator

Controller

Time

Time

Time

Time Spent by QueuingInter-Communication

tqa

tqs

tqc

qaqccca

qsssc

tttt

ttt

Time Delays Management considering local faults

Time

Time

Time

Time

TimeControlAlgorithm

ControlAlgorithm

DecisionMaker

Sensor I

Sensor III

Sensor II

Time Managment considering different scenarios

Sensor 1

Sensor 3

Sensor 2

Not expected Process

Not expected Process

Fault Module

Actuator

Control

Actuator

Agente 3

Agente 2

Agente 1

…Considering several communication stages

Communiaction Network

Ope

ratin

g S

yste

ms

Sof

twar

e A

pplic

atio

n

Deadline Deadline Deadline

Sensor 1

Actuator

Controller

Sensor 3

Sensor 2

ActuadorActuator

Involved Processes onto

the Event

Partial Time Adding as the definition of particular scenarios

sensors

controllers

actuators

Total time Consumed by system

TimeT

jtt

Where the delays come from?From Process of Concurrency managment

11

N

i i

ii

Pcc

U

Where Ci is the processor consumed time

ic It is the uncertainty associated to the consumed time

Where the delays come from?From Process of Concurrency managment

Schedulling distributed processes using Neural Networks such as ART2A.

Processes schedulling based upon the worst case scenario under dynamic conditions.

Process managment optimization considering the communication period modification

It is of particular interes to manages the computer network system through

Communication Frecuencies

Fuzzy Approximation to the plant

kuBkxA1kxthenisAandxisAkifx:Rjjj22j11j

kxAw

kwkv

iijji

n

ijij

1

m

ii

m

jjjj

kv

kuBkxAkv

kx

1

11

The Related approximation to the state space representation

The discret plant considering time delays:

BdTAB

ikuBkAxkx

ki

ki

t

t

ki

l

i

ki

1

)exp(

10

where l=1 due to maximum time delay is one.

The related approximation amongst time delays and faults

N

1i

M

1j

τ

τ

τta

ii

p i

1ji

j

p

dτeBB

)()( 1iii

Tii pwQSRSQSu

Control design following a predictive approach

The recursive horizont development

,

SSS

SSS

SS=S

cN2NpN2Np

N1NpN

N1Np

p

Pp

p

1

11

1

2

12

10

dj nj=s 0y d

Na

=i

Nb

=i

piijij n>jB+Sa=s

1 1

Na

=j

Nb

=jd

pjjjiji c+i+njkuBb+pa=p

1 1

Time Delays Diagram

l

k Na Nbnd

time

Sampling Period k

Horizonts Na y Nb

As in terms of Feedback Control Loop

N

=ii

N

=iikikik

Tiki

)u,(yΩ

)p(wQSR+SQS)u,(yΩ=ku

1'

1,,

1

,,'

N

=ii

N

=iN

=ii

N

=iikikik

Tiki

pii

)u,(yD

)u,(yΩ

)p(wQSR+SQS)u,(yΩB+kxa)u,(yD

=+kx

i

1'

1

1'

1,,

1

,,'

'

1

Following an Optimization Procedure to tune the related Control Law

AB N

=kkk

N

=kk

pk uδ+)Cx(krefB=J

1

2

1

21

2

1

1'

1

1

'

1

2

1'

1' 22

Ap i N

=kN

=ii

N

=ikkk

Tki

k

N

=kN

=ii

N

=i

pii

kpk

)u,(yΩ

)p(wQSR+SQS)u,(yΩδ+

)u,(yD

kuB+kxa)u,(yDCrefB=J

The related Numeric Optimization

BN

=kk

pkp

k

)Cx(krefB=J

1

12B

AN

=kkk

k

uδ=δJ

1

2

N

=ii

N

=iiN

=kN

=ii

N

=i

pii

kpk

i )u,(yD

)x(k)u,(yD

)u,(yD

kuB+kxa)u,(yDCrefBC=

aJ p i

1'

1'

1

1'

1' 222

2

….The related Numeric optimization

N

=ii

N

=kN

=ii

N

=i

pii

kp

p

)u,(yD

)Cu(k

)u,(yD

kuB+kxa)u,(yDCrefB=

B

J p i

k

i

1'

1

1'

1' 2

222

N

=ii

N

=i

piN

=kk

p

i )u,(yD

kNxkuB+kxakCxrefBC=

D

Jip

k

1'

1

1

)1(22)1(2

AN

=kN

=ii

N

=ikkk

Tk

ki )u,(yΩ

kNu)p(wQSR+SQSkuδ=

J

1

1'

1

1)(

)(2

Where the related optimized parameters are…

pN

=j

N

k

i

σ

cu

σ

cy

σ

cy

σ

cy=

c

D p

kj 1,

2

uij

uij'

2

yij

yij

2

yik

yik

12y

ik

yik

yij

expexp2

pN

=j

N

k

i

σ

cu

σ

cy

σ

cu

σ

cu=

c

D p

kj 1,

2

uij

uij'

2

yij

yij

2

uik

uik'

12u

ik

uik'

uij

expexp2

Cases of Study

AIRPLANE

THREE BANDS

MAGNETIC LEVITATOR

HELICOPTER

System Simmulation considering aerodynamic modelling

Data Data Data

Satellite dish

Three Bands Case Study

MC

MC

MC

MCMC

MCMC

MC

MCMC

MCMC

MCMC

MCMC

Controller Bus Controller

Conveyor belt 1

Conveyor belt 2

Conveyor belt 3

s11

s12 s1

3

s110

s21s2

2 s23

s210

s310

s31 s3

2s3

3

Magnetic Levitation Case Study

Magnetic Levitation Case Study

Magnetic Levitation Case Study

Processes management in closed distributed systems enviroment

Agent Integration

The use of schedulling to define process behaviour

Preliminar Results

Modifying conditions on the scheduling algorithmRelated to based period and the increment of possible uncertainties

Preliminar Results from the control Point of View

Multi-Variable Case StudyHelicopter

Preliminar Results from the control Point of View

Preliminar Results

The Designed Algorithms

Different models based upon schedulling algorithm following an optimization procedure.

Designing a control strategy following bounded time delays.

Conclusions

The Reconfiguration as a strategy to keep certain efficiency even in the case of a fault scenario.

To understand time delays as result of reconfiguration procedure.

Acknowledgments

Dr. Jorge Ortega Arjona Miguel Palomera Pérez Oscar Alejandro Esquivel Paul Erick Mendez Monroy Dr. Antonio Menendez Leonel de Cervantes Dr. Pedro Quiñones Reyes Magali Arellano Angel Garcìa Zavala William Sanchez Dr. Eduardo Pérez

The use of schedulling to define process behaviour