Transcript Control Reconfigurable Distribuido

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
External
Fault Tolerance
Module
Plant
"Smart" Sensor
Fault Tolerance
Module
"Smart"Actuator
Controller
Classic approximation based upon
Queues
Sensors
Messages
Queue
Plant
Time Delays associated
to perturbated external
processes.
Controller
Actuators
Messages
Queue
Codesign Strategy
External
Event
Scheduler Proposal
In here
Reconfiguration
takes place
No
SCHEDULLING
EVALUATION
Yes
No
Stability
Test
Valid Scheduler
Yes
Reconfiguration
Proposal
Time Delays
Evaluation
What is the studied iteraction
External Factor to request
reconfiguration
First Reconfiguration Stage
No
(Rejection of the
proposed P lan)
Reconfiguration
Request P lan
Yes
Validation P lan
Valid P lan
Database
Bus Controller
Node
Computer Network
(Sensor Netw ork)
Control Law
Node
(If the P lan
is valid
The related Control Law
is chosen)
Selection of the
Related Control
Law
Control Laws
Database
Second Reconfiguration Stage
Time Delays Managment
Lost Queue
Sender/ Sensor
ts
Time
Tj+1
Tj
tc
Controller
tc
Time
tqa
tqs
ta
Receiv er/Actuator
Time
Time Spent by Queuing
Inter-Communication
Partial adds of transmissiontimes
Sender/ Sensor
ts
Time
tqc
tc
Controller
Time
tqa
tqs
ta
Receiv er/Actuator
Time
Time Spent by Queuing
Inter-Communication
t sc  t s  tqs
tca  tc  tqc  tqa
Time Delays Management
considering local faults
Sensor I
Time
Sensor II
Time
Sensor III
Time
Decision
Maker
Control
Algorithm
Control
Algorithm
Time
Time
Time Managment considering
different scenarios
Sensor 1
Sensor 2
Sensor 3
Fault Module
Control
Actuator
Not expected Process
Not expected Process
Agente 1
Agente 2
Agente 3
Actuator
…Considering several
communication stages
Deadline
Sensor 1
Operating Systems
Software
Application
Sensor 2
Sensor 3
Controller
Actuator
Actuador
Actuator
Involved
Processes onto
the Event
Communiaction Network
Deadline
Deadline
Partial Time Adding as the definition
of particular scenarios
sensors
controllers
actuators
Total time Consumed by system
tt j
T
Time
Where the delays come from?
From Process of Concurrency managment
ci  ci
U 
1
Pi
i 1
N
Where Ci is the processor consumed time
ci 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
R j : ifx1 k isAj1andx2isAj2 then xk  1  Aj xk   B juk 
n
v j k    w ji k 
i 1
w ji  Aij xi k 
xk  1 
 v k A xk   B uk 
m
j
j
j
j 1
m
 v k 
i
i 1
The Related approximation to the
state space representation
The discret plant considering time delays:
l
xk  1  Axk    Bik u k  i 
i 0
B   k exp( AT   )Bd
k
i
tik1
ti
where l=1 due to maximum time delay is one.
The related approximation
amongst time delays and faults
p
N
M
i
τ j1
i
τj
B   i Bi  
i 1
j1
a
p
t τ 
e
dτ
Control design following a predictive approach
1
ui  ( S Q Si  R ) SiQ ( w  pi )
T
i
The recursive horizont
development
S =  S Np
S N p1 1 
1

S
S Np
S N P1 1
N p 2 1
1






S N p 2 1 
 S Np2
s j = y0
j  nd
,






S Np  N 
2
c 
0
Na
s j =  ai S j i +  Bip
i=1
Na
Nb
j=1
j=1
Nb
i=1
pi =  a j pi  j +  b j B jp uk  j  nd + i + c
j > nd
Time Delays Diagram
k
l
Sampling Period k
Horizonts Na y Nb
nd
Na
Nb
time
As in terms of Feedback
Control Loop
 Ω (y ,u )S
N
u k  =
i
'
T
k ,i
Q S k ,i + R

1

S k ,i Q (w  pk ,i )
i=1
N
 Ω (y ,u
i
'
)
i=1


N
Di (y ,u ' ) a i xk + Bip


i=1


xk +1 =

N
i=1
N
 D (y ,u
i
i=1


S k ,i Q (w  pk ,i ) 

N

Ωi (y ,u ' )


i=1

 Ωi (y ,u ' ) SkT,iQ Sk ,i + R
'
)

1
Following an Optimization Procedure to
tune the related Control Law
NB
NA
J =  B ref k  Cx(k  1 ) +  δk uk 
k=1
p
k
2
2
k=1
2
N
1


 N
p
Di (y ,u ' )a i x k  2 + Bi u k  2   N A   Ωi (y ,u ' )S kT Q S k + R  S k Q (w  p k

Np

 + δ  i=1
J =  Bkp  ref k  C i=1
k
N
N

 

k =1
k =1
Di (y ,u ' )
Ωi (y ,u ' )





i=1
i=1




)




2
The related Numeric Optimization
NB
J
p
= 2 Bk ref k  Cx(k  1 )
p
Bk
k=1
NA
J
= 2 δk uk 
δk
k =1
N

 N

p






D
(y
,
u
)
a
x
k

2
+
B
u
k

2
D
(y
,
u
)
x(k

2
)




i
Np


i

'
i
i

'
J
 i=1

= 2C  Bkp  ref k  C i=1
N
N



ai
k =1
D
(y
,
u
)
D
(y
,
u
)


i

'
i

'



i=1
i=1



….The related Numeric
optimization
N



p






D
(y
,
u
)
a
x
k

2
+
B
u
k

2




i
Np

i

'
i
J
p
i=1
 Cu(k  2 ) 
=
2
B
ref

C

k
N
k

 N

B ip
k =1
D
(y
,
u
)
D
(y
,
u
)

i

'

  i   ' 
i=1

 i=1

 N

p






a
x
k

2
+
B
u
k

2

Nx
(
k

1
)
 i

Np
i
J

= 2C  B kp ref k  Cx( k  1)  i=1
N


Di
k =1
Di (y ,u ' )



i=1


1
 N T



S
Q
S
+
R
S
Q
(w

p
)

Nu
(
k
)



NA
k
k
k
k
J

= 2 δk u(k ) i=1
N


 i
k =1
Ω
(y
,
u
)

i

'


i=1


Where the related optimized
parameters are…
y 2
u
y 
y 2  Np






y

c
u

c


Di
y

c
y

c
ij 
'
ij
  

ik 
ik  
  


=

2
exp
exp


  
  σ y   σ u
y 2

   σ iky
cijy
k 1  σ ik 
j
=
1,
j

k
ij
ij
 
 
  
 
Np
 u '  cik u
Di
= 2 
u
 σ u 2
cij
k 1 
ik
Np
   u '  cik u
exp  
   σ iku
  




2




2




  y  c y 2  u  c u
 Np

exp    y ij     ' u ij

 j=1, j k
  σ ij   σ ij






2




Cases of Study
 AIRPLANE
 THREE BANDS
 MAGNETIC LEVITATOR
 HELICOPTER
System Simmulation considering
aerodynamic modelling
Satel l i te di s h
Data
Data
Data
Three Bands Case Study
Conveyor belt 1
Conveyor belt 2
s11
MC
MC
MC
s12
s13
MC
MC
MC
s110
MC
s21
s22
MC
Conveyor belt 3
MC
s23
MC
MC
s210
s31
MC
MC
s32
MC
MC
MC
Controlle r
s33
s310
Bus Controlle r
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 algorithm
Related to based period and the
increment of possible uncertainties
Preliminar Results from the
control Point of View
Multi-Variable Case Study
Helicopter
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