Post on 26-Jun-2020
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Time-Delay Systems forNetworked Control problems
Networks such as Internet or Wireless 802.11 present great advantages forflexible and low-cost networking. However, they are not as reliable as CANs,and integrating them in control applications, while preserving someperformance, constitutes an interesting challenge.
It will be explained how using delay models allows for catching many of theeffects introduced by the presence of such unreliable networks in the controlloops (such as variable transmission times, lost packets, non-uniformscheduling and sampling).
Various theoretical techniques allow for analyzing the resulting models. Some ofthem need the delays to be constant, which can be obtained by using waitingstrategies involving buffers and leading to time-driven solutions. Some othertolerate fast varying delays and allow for event-driven, faster solutions.Two experimental cases, remote control with state prediction and bilateralteleoperation over Internet, will illustrate the talk.
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Time-Delay Systems forNetworked Control problems
Jean-Pierre Richard
http://researchers.lille.inria.fr/~jrichard
jean-pierre.richard@ec-lille.fr
CEIT’2015 – Tlemcen – May 2015
EMETTEUR 00 MOIS 2011
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
The team(permanent staff)
LOTFI DENIS THIERRY WILFRID ANDREY J.-PIERRE ROSANE GANG ALEX NICOLAI CHRISTOPHE LAURENTIU ANNEMARIE
BELKOURA EFIMOV FLOQUET PERRUQUETTI POLYAKOV RICHARD USHIROBIRA ZHENG KRUSZEWSKI CHRISTOV FITER HETEL KOKOSY
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
• Motivation and examples
• Modelling
• Sampling and delay
• A crude example
• Control : to buff, or not to buff? A selection of results
• Conclusions
• Motivation and examples
• Modelling
• Sampling and delay
• A crude example
• Control : to buff, or not to buff? A selection of results
• Conclusions
OverviewOverview
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Tele surgery: the Lindbergh operation, 07/09/2001
Constant RTT< 200 msecDistance:17 000 km
Com. cost ≈ 160k$/month
« The only restriction to the development of long-distance tele-surgery has to do, still today, with itscost. For tele-surgery, you must use a transcontinental ATM line, that you have to book during 6monthes, at the price of about 1 million dollars. » Prof. J. Marescaux, Le Monde, January 6, 2010
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
otherexamples…
Bilateral Teleoperation
Avoiding electrical cabling
Remote Monitoring
Robot collaboration
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
and an example from everyday life…
Natural loop of audio-phonatory control
TO BE OR NOT TO BE, THAT IS THE QUESTION: WHETHER
‘TIS NOBLER IN THE MIND TO SUFFER THE SLINGS AND ARROWS OF OUTRAGEOUS FORTUNE. OR TO
TAKE ARMS AGAINST A SEA OF TROUBLES, AND BY OPPOSING,
END THEM? TO DIE: TO SLEEP; NO MORE; AND BY A SLEEP
TO SAY WE END
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
and an example from everyday life…
Networked loop of audio-phonatory ctrl
G…
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Some surveys…• Control methodologies in Networked Control Systems
Y. Tipsuwan, M.Y. Chow, Control Eng. Practice 11, 1099-111, 2003
• Networked Control System: a brief survey T.C. Yang, IEE Proc. Control Theory Appl., 153 (4), 2006
• Control over Wireless Networks K.H. Johansson, 25th Benelux Meeting on S&C, The Netherland, 2006
• A survey of recent results in Networked Control SystemsJ.P. Hespanha, P. Naghshtabrizi, Y. Xu, Proc. of the IEEE, 95 (1), 2007
• Trends in Networked Control SystemsS. Zampieri, 17th IFAC World Congress, Seoul, 2008
• A switched system approach to exponential stabilization through com. network A.Kruszewski, WJ.Jiang, E.Fridman, J.P.Richard, A.Toguyeni, IEEE CST, 20 (4) 2012
nice (wrt 2007)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
not forgetting…
C. Canudas de Wit, T. Divoux, P. Fraisse, D. Georges, J.P. Georges, G. Juanole, A. Lelevé, F. Lepage, F. Michaut, G. Mouney, W. Perruquetti,
J.P. Richard, E. Rondeau, O. Sename, A. Seuret, E. Wittrant.
2007
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
• Motivation and examples
• Modelling
• Sampling and delay
• A very basic example
• Control : to buff, or not to buff? A selection of results
• Conclusions
Overview©
jea
n-pi
erre
.ric
hard
@ec
-lille
.fr
Single-loop NCS
Tipsuwan 2003
Tipsuwan 2003
What about multi-loop?
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Yang 2006
Multiple-loop NCS according to [Yang 2006]:
Yang 2006
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Multiple-loop NCS according to [Hespanha 2007]:
Hespanha 2007
Hespanha 2007
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Single-loop NCS.
Measurement
channel
1 - Controller 2 - PlantActuating
channel
Network
… the talk will be limited to this case, too.
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Single-loop NCS
Measurement
channel
1 - Controller 2 - PlantActuating
channel
Network
Types of networks:
�dedicated (ControlNet, DeviceNet) : frequent transmission of small packets � guaranteed time but €�Ethernet, wifi : rare transmission of bigger packets � no guarantee for delay but €
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Effects of the network on the closed-loop control
IssueTranslation in control terms
ConcernedNot
concerned
limited bandwidth
quantification, quantité d’info par seconde limitée (Shannon, maximum bit rate)
systèmes à ressources énergie limitée (UAVs, réseaux de µ-capteurs ou de µ-actionneurs…)
envoi par paquets type Inter/Ethernet, Bluetooth… 1 bit ou 300 � idem ATM=384, Ethernet>368, Bluetooth>499
sampling, coding, scheduling, transmission, asynchronism
retards variables,estimés si modèle ou time-stamps
systèmes à transmission par paquets
réseau spécialisé (ControlNet, DeviceNet)
non partagé
packet losseséchantillonnage asynchrone, retard variable
sans fils, UDP
protocoles type TCP (mais peu utile : perte de temps pour infos périmées)
out-of-sync clocks
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Effects of the network on the closed-loop control
IssueTranslation in control terms
ConcernedNot
concerned
limited bandwidth
quantification, limited quantity of info per second (Shannon, maximum bit rate)
limited energyresource systems(UAVs, WSN, µ-sensorsor µ-actuators, aerosp…)
packet-transmiss. type Inter/Ethernet, Bluetooth… 1 bit or 300 � idemATM=384, Ethernet>368, Bluetooth>499
sampling, coding, scheduling, transmission, asynchronism
retards variables,estimés si modèle ou time-stamps
systèmes à transmission par paquets
réseau spécialisé (ControlNet, DeviceNet)
non partagé
packet losseséchantillonnage asynchrone, retard variable
sans fils, UDP
protocoles type TCP (mais peu utile : perte de temps pour infos périmées)
out-of-sync clocks
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Effects of the network on the closed-loop control
IssueTranslation in control terms
ConcernedNot
concerned
limited bandwidth
quantification, limited quantity of info per second (Shannon, maximum bit rate)
limited energyresource systems(UAVs, WSN, µ-sensorsor µ-actuators, aerosp…)
packet-transmiss. type Inter/Ethernet, Bluetooth… 1 bit or 300 � idemATM=384, Ethernet>368, Bluetooth>499
sampling, coding, scheduling, transmission, asynchronism
variable delays,estimated if there is a model, or time-stamps
packettransmission systems
dedicated and unshared netw. (ControlNet, DeviceNet)
packet losseséchantillonnage asynchrone, retard variable
sans fils, UDP
protocoles type TCP (mais peu utile : perte de temps pour infos périmées)
out-of-sync clocks
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Effects of the network on the closed-loop control
IssueTranslation in control terms
ConcernedNot
concerned
limited bandwidth
quantification, limited quantity of info per second (Shannon, maximum bit rate)
limited energyresource systems(UAVs, WSN, µ-sensorsor µ-actuators, aerosp…)
packet-transmiss. type Inter/Ethernet, Bluetooth… 1 bit or 300 � idemATM=384, Ethernet>368, Bluetooth>499
sampling, coding, scheduling, transmission, asynchronism
variable delays,estimated if there is a model, or time-stamps
packettransmission systems
dedicated and unshared netw. (ControlNet, DeviceNet)
packet lossesasynchronoussampling, variable delay
wireless, UDP-like protocols
TCP-like protocols(but generally useless: time wasting for outdatedinfo)
out-of-sync clocks
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Effects of the network on the closed-loop control
IssueTranslation in control terms
ConcernedNot
concerned
limited bandwidth
quantification, limited quantity of info per second (Shannon, maximum bit rate)
limited energyresource systems(UAVs, WSN, µ-sensorsor µ-actuators, aerosp…)
packet-transmiss. type Inter/Ethernet, Bluetooth… 1 bit or 300 � idemATM=384, Ethernet>368, Bluetooth>499
sampling, coding, scheduling, transmission, asynchronism
variable delays,estimated if there is a model, or time-stamps
packettransmission systems
dedicated and unshared netw. (ControlNet, DeviceNet)
packet lossesasynchronoussampling, variable delay
wireless, UDP-like protocols
TCP-like protocols(but generally useless: time wasting for outdatedinfo)
out-of-sync clocks delays (at least) internetcontrol-dedicatednetw. (CAN bus…)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
In such a framework, let’s show we have the equation:
transmission + sampling + packet loss = 1 delay .transmission + sampling + packet loss = 1 delay .transmission + sampling + packet loss = 1 delay .transmission + sampling + packet loss = 1 delay .
Measurement
channel
1 - Controller 2 - PlantActuating
channel
Network
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Transmission delays
RTT (40km)Mean = 82 msMaxi = 857 msMini = 1 ms
Lille-Lens (France, 40 km) – Source: PhD WJ. Jiang 2008
To give an idea on the delay variation…
France - France
one week of RTT…
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
One week of RTT…
Tunis-Lille (1640 km) – Source: S. Belhaj, ENSIT 2009
Transmission delays
To give an idea on the delay variation…
RTT (1640km)Maxi = 415 msMini = 70 ms
RTT (1640km)Maxi = 415 msMini = 70 ms
France – North-Africa
one week of RTT…
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Transmission delays
unshared CAN 2m: 200 µsec
bluetooth 2m: 40 msec
Internet: 100-400 msec
orbital stations: 0.4-7 sec
underwater 1.7km: >2 sec
To give an idea on the delay variation…
Other RTT approximated values
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
• Motivations and examples
• Modelling
• Sampling and delay
• A very basic example
• Control : to buff, or not to buff? A selection of results
• Conclusions
Overview
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
ContinuousProcess
Computer
A/DConverter
D/A Converter+ ZoH
x(t) x(nT)
u(t)=u
Aperiodic sampling
u*(nT)n
ContinuousProcess
Remote(or non prioritary)
Computing
A/DConverter
D/A Converter+ZoH
x(t)
u(nT(t))communication network
(or task scheduling,or packet loss...)
Sampling via Delay / 1
A
Integration, z-transform, everything’s ok, etc.
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Sampling via Delay / 2Time-varying sampling:� any consequence?
[Zhang, Branicky, Phillips. - IEEE Ctrl.Syst.Mag. 2001]
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Sampling via Delay / 3Time-varying sampling:� any consequence?
[Gu, Kharitonov, Chen - Birkhauser 2003]
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Sampling via Delay / 4
Models for aperiodic sampling
Hybrid / Impulsive syst.Input-Output approach
Input delay systems
"Tutorial on Arbitrary and State-Dependent Sampling "C. FITER, H. OMRAN, L. HETEL, J.P. RICHARD
European Control Conf., Strasbourg, France, 2014
"A robust stability framework for time-varying sampling"C. FITER, L. HETEL, W. PERRUQUETTI, J.P. RICHARD
Automatica, 45: 56-64, 2015.
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Input delay systems
Mirkin TAC 07, Fujioka Aut 09, Kao ACC 14
Omran-Hetel-Richard-Lamnabhi ECC 13 & Aut 14…
Input-Output approach Hybrid / Impulsive syst.
Models for aperiodic sampling
Sampling via Delay / 4
e(t) = y(t) - y(sk )
+ robust control techniques
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Input-Output approach Hybrid / Impulsive syst.
Input delay systems
Models for aperiodic sampling
Sampling via Delay / 4
Dullerud -Lall S&CL 99, Hu et al. TSMC 03,
Nešić -Teel TAC 04, Naghshtabrizi-Hespanha-Teel S&CL 08 …
+ stability techniques for HyS
discontinuous Lyapunov functions
Molchanov-Bauer TAC 99, Hetel-Daafouz-Iung TAC 06,
Fujioka TAC 09, Cloosterman et al. Aut 10,
Hetel-Kruszewski-Perruquetti-Richard TAC 11
Hybrid switched systems + convex embedding
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Input-Output approach Hybrid / Impulsive syst.
Models for aperiodic sampling
Sampling via Delay / 4
Input delay systems
Mikheev-Sobolev-Fridman AutRem.Ctrl 1988, Nešić -Teel-Kokotović CDC1998,Fridman-Seuret-Richard Aut 04, Fridman Aut 10, Seuret Aut 12, Karafyllis-Krstić TAC 12,Mazenc-Malisoff-Dinh Aut 13
+ stability techniques for TDS
x(tk) = x(t −[t − tk] ) = x(t − h(t) )
Lyapunov-Krasovskii functionals
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Thus… another statement of the packet loss problem
• maximum nb of successively lost packets � hmax
• piecewise-continuous delay with
delay
Sampling via Delay / 4
1 lost packet ↓
2 lost packets ↓ ↓
0 ≤ h(t) ≤ hmax
h(t) ≤ 1dtd
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
How fast should we sample?
Another question in networked systems: How to reduce the number of the sent packets?
Sampling via Delay / 5
versus
Reduce the packets nb so to:- better schedule other tasks- reduce the communication cost- save wireless sensor batteries
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
"A robust stability framework for time-varying sampling“ C. FITER, L. HETEL, W. PERRUQUETTI, J.P. RICHARDAutomatica , 45: 56-64, 2015.
Another question in networked systems: How to reduce the number of the sent packets?
Sampling via Delay / 5
Various ways of controlling the sampling instants:
� Event-triggering: dedicated sensor hardware (send yk when…)(Donkers-Heemels 2012; Lunze-Lehmann 2010; Postoyan-Anta-Nesic-Tabuada, 2011; Tabuada, 2007)
� Self-triggering: the previous without dedicated hardware (online estimation)(Anta-Tabuada, 2010, 2012; Mazo-Anta-Tabuada, 2010; Wang-Lemmon, 2009, 2010)
� Periodic event-triggering: the previous but estimation at periodical instants(Arzén 1999; Heemels-Donkers-Teel, 2013; Peng-Yang, 2013; Postoyan-Anta-Heemels-Tabuada-Nesic, 2013; Yue-Tian-Han, 2013)
� State-dependent sampling: partition of the state space into conic regions (off-line) (Fiter-Hetel-Perruquetti-Richard, 2012, 2015)
see cross-links and tools in
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Another question in networked systems: How to reduce the number of the sent packets?
State-dependent sampling (state x k )
"A state-dependent sampling for linear state feedback"C. FITER, L. HETEL, W. PERRUQUETTI, J.P. RICHARD
Automatica 48 (8), p.1860-1867, 2012
Sampling via Delay / 5
� Self-triggering
� Complexity is off-line
� LRF technique
Max next sampling computed off-line ( β-stab.) � often less than with periodic sampling
state-spaceangle θ
x2
x1
angle θ (rad) �Max
sam
plin
g τ
(sec
)� slow↑
↓
fast
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Another question in networked systems: How to reduce the number of the sent packets?
Hybrid systems modeling (Teel et al.)"Robust stab. of bilinear syst. under aper. sampled-data ctrl "H. OMRAN, L. HETEL, J.P. RICHARD, F. LAMNABHI-LAGARRIGUE
Automatica 50 (4), p.1288-1295, 2014
Sampling via Delay / 5
� constructive
� LMI
or Dissipativity–based (Fujioka)
"On stability of input-affine nonlinear syst. with sampled-data ctrl"H. OMRAN, L. HETEL, J.P. RICHARD, F. LAMNABHI-LAGARRIGUE
ECC2013 Zurich, 2013
� constructive
� SoS
+ the case of Bilinear/Nonlinear Systems
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
transmission time + access time + packet loss + sampling…
Measurement
channel
1 - Controller 2 - PlantActuating
channel
Network
... let’s sum up until now:
variable delay h1
variable delay h2
= 2 variable delays
can be estimated by Plant(time stamps + packet nb)
can be estimated by Controller (time stamps + packet nb)
known / unknown ?
Hyp: Clock Synchro NTP, GPS
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
• Motivations and examples
• Modelling
• Sampling and delay
• A crude example
• Control : to buff, or not to buff? A selection of results
• Conclusions
Overview
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
controller poles = -1 and -15observer poles = -2 and -20
A crude example
driveu position y
target
y ref
-
State Feedb. ( )with
Observer ( )
K
L
Net
internetwifi…
Theory (when neglecting the network effect)©
jea
n-pi
erre
.ric
hard
@ec
-lille
.fr
A crude example
LTI model with order 2state feedback gain ( )
and observer gain ( )computed by pole assignement
without paying attention to the net (here, Internet over 40km)
KL
yref
yremote
.yobserver^
yobserver^
Controller poles = -1 and -15Observer poles = -2 and -20
Experimental results (with network)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
A crude example
drivevoltage u measured angle x
+-
gap
ε = 0 – x
Interpretation on a simplified model
speed
target anglexc = 0
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
measured angle xutarget anglexc = 0
+-
ctrl.channel.� delay~h/2
meas.channel� delay~h/2transmitted angle x(t-h/2)
ε
transmitted controlε(t-h/2)
A crude example
remote feedback:
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
t
x
x0
0
?
?
t0
t1
t2 t3 t4 t6t5 t7 t8 t9 t10
Exercise…
A crude example
Exercise… for my students, don’t worry ;-)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr ?
A crude example
w.r.t.
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
… and mind the variable delays!
1 π/2
constant : ∀h ∈ [0,1] iff ∈ grey zone
variable : asymptot. stable iff ∈ yellow zone :
a
b
(T=1)
2
2
0
-2
-2
2
1
2
stable h(t)<1 - unstable h=cte<1
unstable h(t)<1 - stable h=cte<1
=1
A crude example
for
if
if
1 2 3 4 5 6 7 8 91
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Few words about Lyapunov method for TDS
� need of specific adaptations:1) functions of Lyapunov-Razumikhin (not here)
2) functionals of Lyapunov-Krasovskii
ODE :
(« usual » quadratic)
FDE :
cross terms
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Illustration of the LKF approach (Lyapunov-Krasovskii functionals)
(quad + integral)
Lyapunov for TDS
Remarks on the conservatism: 1) here, a « pessimistic » condition since it is i.o.d. - independent of the delay h…
2) linked with the majoration of the crossed terms, here :
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
More general…Lyapunov for TDS
x vector + variable delay
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Still more general…ongoing extensions for nonlinear TDS systems
Lyapunov for TDS
"Development of homogeneity concept for time-delay systems"D. EFIMOV, W. PERRUQUETTI, J.P. RICHARDSIAM J. Control & Opt., 2014 http://hal.inria.fr/hal-00956878
“Weighted homogeneity for TDS: Finite-time and independent of delay stability"D. EFIMOV, A. POLYAKOV, W. PERRUQUETTI, J.P. RICHARDIEEE TAC 2015, 60:1-6 https://hal.inria.fr/hal-01145321
"Implicit Lyapunov-Krasovskii Functionals for stability analysis and control design of TDS"A. POLYAKOV, D. EFIMOV, W. PERRUQUETTI, J.P. RICHARDIEEE TAC, to appear, 2015
HOMOGENEITY IMPLICIT LYAPUNOV FUNCTIONS[Korobov 1979, Polyakov 2012][Rothschild&Stein 1976]
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
A link with finite time
Few words on convergence types
;-)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
• Motivations and examples
• Modelling
• Sampling and delay
• A very basic example
• Control : to buff, or not to buff? A selection of results
• Conclusions
Overview©
jea
n-pi
erre
.ric
hard
@ec
-lille
.fr
to buff, or not buff?
1rst solution = act « as if » constant� [Niemeyer & Slotine 98][Huang & Lewis 03] � approximation
[Azorin et al. 03][Fattouh & Sename 03] etc.
control process
buffer
buffer
2nd solution = force thedelay tobe constant� therefore, maximize it : � thanks to a buffer � time-driven
� then, apply classical techniques:�predictor (Smith) [Lelevé & Fraisse 01]
�error eqn. obeying a retarded model [Estrada-Marquez-Moog 07]…
�
Network delay: variable, asymmetric �
4th solution = keep the variable delay…
� model & predict the delay [Witrant et al. 07] � event-driven
� complexify the Lyapunov technique[Seuret-Richard 08][Kruszewski et al.11,12] [Demirel et al.13][Zhang PhD12][Zhang et al.14]
3rd solution (intermediate)just one buffer
[Seuret PhD 06] [Jiang et.al 08]
1
2
3
4
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
4. Buffer-free control (event-driven)A. Seuret, J.P. Richard - IFAC Seoul 2008 (theory only)
A. Kruszewski, W.J. Jiang, E. Fridman, J.P. Richard, A. Toguyeni - IEEE T. CST 2011 (with experiments)
Set value
Observer
ControllerImplementation
card
Sensors
GPS/NTP
h1
h2
Master Slave
Zero-Holder
Zero-Holder
τ1
Net
wor
k
τ2
GPS/NTP
GainK
Gain L
buffer
4
buffer
knownthx to
time-stamps
UDP
• defines the target• receives Slave’s output• observes Slave’s state• computes & sends control
• receives & applies control• sends measured output
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Experimental set-up
MasterSlaveMiabot
SlavePC Bluetooth
(2m)
Internet
(40km)
Night-timevs
Day-time
Internet: Bluetooth:120 ms
60 ms
A switched system approach to exponential stabilization through communication network.A. KRUSZEWSKI, W.J. JIANG, E. FRIDMAN, J.P. RICHARD, A.TOGUYENI. IEEE TCST, 20 (4) 2012
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
One week of RTT…
Link max delay ↔ provable performance
0.5sec
0.05sec
The achievable exponential rate depends on hm ,which motivates some adaptation w.r.t. QoS...
e−αt
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
globaldelay
states
chatter+ obs.IC
α = 1 α = 3α = 0
� buffer and gains K, L adapted to the QoS (delay ranges)
Note the predictor effect(compensates the network delay)
α = 3
Experimental results with one buffer (time-driven)x 10ms
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
control
(without buffer)
(with buffer)
states
delays
switches
Experimental results without buffer (event-driven)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
force & position tracking (haptic rendering)PhD Bo Zhang (2012) + Zhang, Kruszewski, Richard, Int.J.Control 2014
Proxy
Network
MasterOperator EnvironmtSlave
Controller
( )mF t
( )sF t ( )sx t( )hF t ( )eF t
( )eF t
( )mx t
( )( )2eF t tτ−
( )hF t
( )1( )m tx t τ−
( )1ˆ ( )h tF t τ−
( )px t
• Proxy synchronized on Master• Slave synchronized on Proxy• Combines LKF with H
∞
• Reduction of the delay effect• Accurate haptic rendering
(environnement’s force)
5) Natural continuation: teleoperation (event driven)5©
jea
n-pi
erre
.ric
hard
@ec
-lille
.fr
« combines LKF with H∞
» means…
( ) ( )( )
e
h
F tw t
F t
=
( )( )( )
( ) ( )
s
m
s m
t
x t t
t t
θθ
θ θ
= −
&
&
= z(t)
5) Natural continuation: teleoperation (event driven)
perturb.forces
w(t)
positionerror
z(t)
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
• Motivations and examples
• Modelling
• Sampling and delay
• A very basic example
• Control : to buff, or not to buff? A selection of results
• Conclusions
Overview
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Conclusion-Summary
� Control with a network model [Witrant 05] predictor with variable delay
� General case (without network model) :
� with 2 buffers [Estrada 08] retarded error equation
� with 1 buffer [Seuret 06] state feedback + observ./predict.
� + adapt. to QoS [Jiang-Kruszewski-R-T 08] ‘ ‘
� with 0 buffer [S-R 08, Jiang-K-R-T 09] ‘ ‘
� Bilateral teleoperation with performance (alternative to passivity)
� with 0 buffer [Zhang-K-R 14] state feedback + obs + H∞
� Quite general problems formulated thx to delay/switched models
⇒ design in the presence of variable delays
© j
ean-
pier
re.r
icha
rd@
ec-li
lle.fr
Other healthy readings:"Deteministic and stochastic approaches to supervisory control design for NS with time-varying com. delays "B. DEMIREL, C. BRIAT, M. JOHANSSON - Nonlinear Anaysis: Hybrid Systems , 10, 94-110, 2013
"Master-Slave synchronization for two inverted pendulums with communication time-delay“H.J. ESTRADA-GARCIA, L.A. MARQUEZ-MARTINEZ, C.H. MOOG - Springer LNCIS vol.388, Chap. Part V, 403-414. 2009
"A switched system approach to exponential stabilization through communication network"A.KRUSZEWSKI, W.JIANG, E.FRIDMAN, J.P.RICHARD, A.TOGUYENI - IEEE TCST,20 (4) 887-900, 2012 http://hal.inria.fr/inria-00602327/fr/
"Control design for teleoperation over unreliable networks: A predictor-based approach"A. KRUSZEWSKI, B. ZHANG, J.P. RICHARD Springer , in Delay Systems: From Theory to Numerics and Appl., 2013
"Control of a remote system over network including delays and packet dropout"A. SEURET, J.P. RICHARD, IFAC'08 , 17th IFAC World Congress, Seoul, South Korea, July 2008
"A refined input delay approach to sampled-data control”E. FRIDMAN, Automatica , 48 (2), 2010
"SOS for sampled-data systems“A. SEURET, M. PEETS, IFAC’11, 18th IFAC World Congress, Milano, Italy, 2011
"A novel stability analysis of linear systems under asynchronous samplings”. A. SEURET, Automatica 48 (1), 177-182, 2011
"Discrete and intersample analysis of systems with aperiodic sampling"L. HETEL, A. KRUSZEWSKI, W. PERRUQUETTI, J.P. RICHARD, IEEE TAC 56 (7), p.1696 - 1701, 2011
"Remote Stabilization via Communication Networks with a Distributed Control Law" E. WITRANT, C. CANUDAS DE WIT, D. GEORGES, M. ALAMIR, IEEE TAC, 52, 1480-1485, 2007
"A novel control design for delayed teleoperation based on delay-scheduled Lyapunov-Krasovskii functionals“ B. ZHANG, A. KRUSZEWSKI, J.P. RICHARD - Int. J. Control , 87 (8), 1694-1706, 2014. http://hal.inria.fr/hal-00939507
“A Historical View of Network Traffic Models”M. WILSON, online course http://www.cse.wustl.edu/~jain/cse567-06/traffic_models2.htm