ON THE ANALYSIS AND COMPENSATION OF NETWORK
INDUCED COMMUNICATION DELAYS FOR
DISTRIBUTED CONTROL SYSTEMS
By
EMMANUEL VYERS
Bachelor of Science
Florida Institute of Technology
Melbourne, Florida
1995
Submitted to the Faculty of the
Graduate College of the
Oklahoma State University
in partial fulfillment of
the requirements for
the degree of
MASTER OF SCIENCE
December, 1997
OKLAHOMA STATE UNIVERSITY
ON THE ANALYSIS AND COMPENSATION OF NETWORK
INDUCED COMMUNICATION DELAYS FOR
DISTRIBUTED CONTROL SYSTEMS
Thesis Approved:
ToeaI1Of the Graduate College
II
PREFACE
The control of physical systems with a computer is becoming commonplace. In
addition, computer networking is now used to perform spatially distributed interrelated
functions . Sensors, controllers and actuators can then be interconnected via the network
to form a distributed control loop. However, due to the asynchronous nature of network
communications, time varying transport delays are introduced into the feedback control
loop. These network induced delays significantly degrade the performance of control
systems. This is illustrated and discussed in this paper. Further, different compensation
strategies proposed by control researchers are reported. Finally, a procedure has been
derived and exemplified to integrate time varying network induced delays within the
control design method trad itionally used with time invariant systems.
I sincerely thank my advisor, Dr. Gary Young, for his supervision of this project.
Through his support 1 was able to synthesize this review on the promising field of
networked distributed control systems.
I II
T ABLE OF CONTENTS
Chapter Page
2
3
4
5
INTRODUCTION
1.1
1.2
The Problem
Objective and Contribution of the Research
BACKGROUND ON NETWORKED CONTROL SYSTEMS
2.1
2.2
2.3
The Feedback Loop Situation. . . . . . . . . .
Characteristics and Impact of the Network Data Latency.
Dynamic Characterization of a Delayed Control Systems
REVIEW OF THE LITERATURE TOW ARD ANALYSIS AND
COMPENSATION . . .
3.1
3.2
3.3
The Pstep Observer .
Optimal Compensation with Stochastic Delay Assumption
Robust Analysis of Time Varying delays .
A NEW INTERPRETATION TO DESIGN
4.1
4.2
4.3
Proposition
Scope and Limitations
Example.
CONCLUSIONS
. 1
.2
.2
.4
.4
10
17
26
26
32
38
41
41
44
46
49
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . 51
APPENDIX . . . . . . . . . . . . . . . . . . . . . . 53
The Controller Area Network Communication Protocol
for Distributed Control systems. . . . . . . . . . . . . 53
iv
LIST OF FIGURES
Figure Page
1. Three Methods of Fanning a Closed Loop Over the Serial Bus . 5
2. Distributed Delays in a Control System . . . . . . . 6
3. The Variable Transport Delay in a Sampled Data System . 8
4. Data Loss on the Measurement Signal. . 9
5. Jitter on the Control Signal . . . . 10
6. Effect of Jitter in the Control Signal on the Output of the System . 15
7. Effect of Data Loss in the Measurement Signal on the Output of the System 15
8. Combined Effect of Jitter and Data Loss on the Output of the System 15
9. A Slower Controller on the Situation of Figure 8 16
10. Initial Situation of a Delay Differential Equation 19
11. Elimination of the Time Variations by Data Buffering 27
12. Schematic Representation of a Threestep Predictor/Controller 29
13 . Modeling Closed Loop TimeVarying delays as Disturbances . 42
14. Configuration of the Distributed Delay Disturbances. . . 45
15. Compensated System Response Under Jitter and Data Loss 48
v
CHAPTER I
INTRODUCTION
In control engineering, a number of systems implement distributed interrelated
functions incorporating more than one control device. The complexity of these functions
requires an exchange of data that is invariably cumbersome and expensive when realized
through hard wired signal lines. An efficient way to overcome these limitations is to
network the system components using a serial data bus. Substantial savings are then
achieved by reducing installation and maintenance costs while improving the system
reliability. Along with reduced wiring, increased flexibility and lower cost, the serial bus
system also enables the use of intelligent input/output devices. However, from the point
of view of the control system designer, trading a dedicated pointtopoint connection for a
multiplexed network results in the adverse effect of introducing transport delays. These
network induced communication delays represent a threat to the stability and dynamic
performances of feedback control systems. As the result, a prime interest is to examine
the possible compensation techniques. The core of this work is therefore composed of
three sections, respectively, chapters 2, 3 and 4. An overview of the necessary
background in relation to the characterization of the time varying network induced delays
is presented first. A survey of the different techniques that have been proposed by
researchers toward analysis and compensation of the network induced delays is given
next. Finally a new interpretation to design in the face of network induced transport
delays is introduced and discussed.
1.1 The Problem
Substantial advantages can be derived from networking a distributed control
system. However, due to the asynchronous nature of network communications, time
varying transport delays are introduced into the feedback loop. The compensation for
constant timedelays has been extensively treated and is straightforward (cf. section 2.3).
Comparatively, little work has been done to characterize and compensate the effects of
time varying delays. Indeed, the stability of time varying systems cannot be predicted
from the eigenvalues of the characteristic equation of the time invariant system. Further,
in discrete time, one of the problem in the compensation is that time variations typically
occur each sampling period. More precisely, the time varying nature of these delays affect
the control signal by introducing jitter at the input of the process and producing data loss
on the measurement data. This means that the traditional frequency domain analysis
which is suitable for linear timeinvariant systems may not be valid for analyzing the
dynamic performances and stability of a closed loop distributed control system subj ect to
time varying transport delays. Accordingly the sensitivity of feedback control systems to
the network induced time variations can vary substantially and is difficult to determine.
1.2 Objective and Contribution of the Research
The objective of this research is therefore to provide a perspective on the problem of
timevarying network induced transport delays for distributed control systems. This is
accomplished by reporting several compensation solutions from the literature. These
solutions represent a significant improvement over the uncompensated alternative but are
2
invariably complex to implement and analyze. Clearly it would be advantageous to still
be able to use the wide array of classical time invariant design methods despite the
presence of the network induced time variations. With this idea in mind an attempt has
been made to try to capture the detrimental effects of the network induced delays into
fictitious signals that once fed into the loop would account for the time variation effects
and enable time invariant analysis. The particular contribution of this work is based on
the development and discussion of such an interpretation. Specifically, jitter and data loss
caused by the network are respectively assimilated as fictitious disturbance and noise
signals. Qualitative reasoning on the controller's sensitivity to network induced delays
can then be made with conventional time invariant methods.
3
CHAPTER 2
BACKGROUND ON NETWORKED CONTROL SYSTEMS
To properly understand the distribution of the control function over the network,
many elements have to be considered. First a schematic representation of the feedback
loop along with an illustration of the control flow is given in order to present and qualify
the particular effects of the network induced transport delays. Then the characteristics of
the data latency and its impact on control systems are discussed qualitatively and
illustrated with an example. Finally, a short remainder on the compensation of both
constant and variable delays is given.
2.1. The Feedback Loop Situation
There are three methods of fonning a closed loop over a serial bus. The traditional
approach is for the feedback loop to be closed by a remote controller. Then, both the
measurement and the control signal travel back and forth on the bus in between the field
and the control room. With the advent of smart instrumentation, the control strategy can
also be moved away from the central controller and executed by the field instruments
either at the measurement site or at the actuator location. By allowing devices to
communicate directly with one another, extra passes through a central controller can be
eliminated, thus allowing a loop to be closed with minimum elapsed time, minimum
bandwidth, and minimum risk of error or other failures. Figure 1 illustrates these three
alternati ve as a), b) and c).
4
a)
b)
c)
: ... .. ..... _ .. . .... .. .... ..... ........ .. ..... .. ... ... .... ......... .... ... .... . ~
error
Set Point
Set Point
Control
Algorithm
... _ ... ..... ... ~
: error :
....0,. ~
: .. ..... . . . . . . . . ... ~
Control
Algorithm
Fig. 1. Three Methods of Forming a Closed Loop Over the Serial Bus.
Let us examine the case where the controller is remote. Then the network transport delay
will affect both the control signal and the feedback measurement as shown on Figure 2.
The system under consideration consists of a continuoustime pJant and a discretetime
controller that share the same data communication network with other subscribers.
5
: ..... .. ......... .. ... ... ~
Network
~~...f\ __ Controller
''r/ Gc(z)
I _
I
I
I
I
I
Uk: Timevarying
 : Delay t co
: Zk : Timevarying
L ___________________ ~  Delay ·t sc
U(t)
ZOH f~
he ld on
arrival
Yk
I+~             
Fig.2. Distributed delays in a control system.
Plant
Gp(s)
T
y(t)
Note that the controller structure in Figure 2 is just one example. Nevertheless, in the
later part of this report, this framework will be implicitly considered along with the
following assumptions unless specified otherwise,
• There is a zero probability of data loss.
• The plant noise is defined and bounded.
• The plant is completely reachable and observable.
• Sampling and Zero Order Hold are ideal processes.
• There is no delay in the process of sensor signal generation.
• The delay t1 p in the processing of the control signal is constant.
• )[etwork induced delays are bounded to one sampling period.
• The actuator operates as a continuoustime device.
6
The network induced delays are only one source of delay among others of significance,
namely,
• Delays in the dynamic of the system itself. typically caused by a system with mass
transportation or by inertia in the actuation where it is difficult to obtain a
measurement without delay.
• Delays inherent to sampling in digital control systems, due to periodic operation and
zero order hold (ZOH) in the control system. This delay can be approximated by T/2,
given the sampling period, T.
• The processing delay at the controller, is the time required by the computer to
produce the expected control signal.
• The network data latency, defined as the difference between the instant of arrival of
the message at the transmitter queue and the instant of reception of its last bit at the
destination terminal.
• The detection delay, this delay is due to a lack of synchronization, either between
cooperating periodic activities or a periodic and an event based activity. It is the time
between the instant the last bi t of the message has been received and the instant the
message is actually picked up.
While the first three listed sources of delays can generally be treated as constant
values, the network data latency and the detection delays stand out as truly timevarying
characteristics. These timevarying delays are the primary focus of this report. Since the
delay from the sensor to the controller is timevarying, the controller may use sensor data
7
generated at the current or earlier samples. At the same time, even if the controller
generates the commands at a constant rate, the interval between their successive arrivals
at the actuator terminal may not be constant. Figure 3 is an illustration of this situation.
On this diagram, the sensor sampling instant and the point where the controller picks up
the measurement are assumed to be synchronized and time shifted by an amount .1s called
the time skew. The control signal is generated .1p time later and transmitted to the
actuator for immediate actuation. As the transmission delay is symbolized by a dropping
dotted line, one can see that, variations will affect the controlflow and on occasion,
samples will be either recycled or rejected. The effects on the measurement data have
been characterized in the literature (Halevi and Ray 1988) (Ray and Halevi 1988) by two
particular phenomena, Vacant Sampling and Message Rejection.
Sensor ~ignal tT~i .... r generatIOn ....
'. ,
"' .
I • • I
Control input :~: ' Vaca~t Sampling I'
sampling time : 4 . , ~
: 65 top ; : '
I 1 ! 1 r
Transmiss ion
Delay
l·.. . ,r· . '. ,, '. '.
I
' X: : : I'
MeS54ge Rejfction
I • I I • ,
VS + MR = Meashlremeht Data Loss
,
Control signal :
generation
Actuator
I
I l· '. I..... i " . ,
, ' • .1
, , ,
I· ....
Uneven Sampling Intervals = Control Signal Jitter
Fig. 3. The Variable Transport Delay in a Sampled Data System
8
,
I·.. · ... I
I •. ~ ...
Vacant sampling, is the case where, no fresh sensor message arrives at the controller
during its fh sampling period. The old sensor data is used at the U+ 1 )5t sampling instant
for computing the control signal so that, Zj + I= Yj . Vacant sampling only occurs when an
on time delivery is followed by a late delivery. Message rejection, is the case where, two
sensor messages arrive at the controller during its j Ih sampling period. The fanner sensor
data is discarded and the latter arrival is used for the computation of the control signal so
that, Zj+ I=Yj+ I' Message rej ection only occurs when a late delivery is followed by an on
time delivery. The process of samples being recycled is named data loss and illustrated in
Figure 4.
y(k), precise ly
sampled measurements
····v z(k). input
LO the controller
Fig. 4. Data Loss on the Measurement Signal
The effects of the data latency on the control signal are diffe rent since the delayed
samples from the controller are fed into a continuous system. As a direct consequence of
9
the variable network delays, the plant then receives samples with a variable time interval.
This effect is designated as jitter at the input of the process and is illustrated in Figure 5.
Variable
transport delay
u(k). output
of the controller
Fig. 5. Jitter on the Control Signal
2.2. Characteristics and Impact of the Network Data Latency
U(l), input
10 the plant
Toward completely digital distributed control systems, peertopeer network
communications between smart transducers seems to be the most logical communication
scheme. The principal feature of a smart transducer is its ability to offload some of the
processing functions from the control system. Clearly, complete distribution of data
acquisition and control functions within the field devices is expected to be geographically
distributed. Therefore, intelligent field devices are no longer limited to the task of making
measurements and driving final control elements. One is then to expect that. the traffic
induced by a control system application is both periodic and aperiodic. The periodic
traffic is typically time critical and generated by feedback control loops. The aperiodic
traffic is composed of control and noncontrol information. The aperiodic control
information may be viewed as onetime messages to announce an alarm often in re lation
10
to an emergency. The aperiodic noncontrol infonnation is the result of the augmented
role that smart instruments play. This infonnation generally contributes to the
management of the whole system but does not have a realtime significance. The
characteristic of the data latency is undoubtedly an important factor in the design of a
compensation algorithm. The data latency is significantly affected by the intensity and
the distribution of the network traffic. Extensive simulations have been made where the
bus load was generated for random traffic with Poisson arrival and exponentially
distributed message length (Wang, Lu, Hedrick and Stone 1992), (Tindell, Bums and
Wellings 1994). These simulations and analytical results may give the control system
designer some idea about the relationship between data latency, bus load and priority
setting. The assumption of randomness of the bus traffic and message generation rate is
however questionable. Indeed, in this particular case, This cannot be all true since
periodic traffic is introduced by the multiple control loops operating with a fixed
sampling time on the network. Halevi and Ray (1988) mentioned that. the network traffic
can be approximately periodic. Further. for certain applications, such as token bus, the
delay sequences have been shown to be periodic. Specifically, Ray (1987) showed an
actual profile of queuing delays for the SAE linear token bus that exhibits a triangular
wave fonn pattern at steady state. Clearly, the characteristics of the bus load is dependent
on the number, the type of stations, and possible misynchronizations. I f the number of
stations is small, with a combination of periodic and sporadic transmitters, the resulting
bus load will conserve its periodic characteristic. The outcome is a traffic that is qualified
as quasiperiodic. Halevi and Ray ( 1988) therefore suggested that, as a first step in the
I I
analysis, one should consider periodic traffic and accommodate for quasiperiodic traffic
in a second instance. Ray and Halevi ( 1988) also indicated that the variations in the
network traffic pattern are usually slow relative to the dynamics of the control system.
Consequently, because the characteristic of the bus traffic is not randomly di stributed
(Ludvigson 1990), average performance calculations may not provide an adequate
method for evaluating bus performances for distributed control systems. Consequently
the characteristics of the network data latency are bounded to be time varying.
Nonetheless, very little information exists toward the identification of these
characteristics.
[n the context of a control loop, it is reasonable to assume that the transport delay is
by design bounded by one sampling period. Delays of more than one sampling period are
not of much practical significance, firstly because the network design should not allow
such overload even under the worst conditions. Secondly, any unbounded delay goes
against the concept of closed loop operation. Accordingly, neither vacant sampling nor
sample rejection can happen twice in succession. In other words, the occurrence of vacant
sampling implies that only sample rejection can happen next. Truly, the problem is time
varying but discrete in behavior. These observations enable us to define four possible
cases over a two sampling instant window. Case #1, the first sample is late the second
sample is on time (vacant sampling), Case #2, the data at both instants are on time. Case
#3, the first sample is on time the second sample is late (vacant sampling), Case #4, the
data at both instants are late. Cases 1, 2. 3 and 4 can be seen in their respective order by
taking the sensor sampling instants by pair starting from the left on Figure 3. Truly,
12
vacant sampling is the constraining element as the measurement delay is increased and
the controller has to recycle old data. As an illustration of the effects of the network
induced time varying delays, the feedback loop situation of Figure 2 has been simulated.
The nominal continuous time plant model is chosen to be,
1000
G(s)=s(
O.5s + 1)
(1)
and a proportional state feedback controller is designed using Akermann's formula in
order to generate a system response with a desired damping of 0.7 and a desired natural
frequency of 56 rad/s. The observer poles are chosen to be 3 times faster than the system
poles. Within the simulation algorithm, the sampling of the feedback loop has been set to
0.01 second, however, the dynamics of the plant is solved at a sampling rate 0[0.001. In
other words, the output of the plant is solved 10 times in between each controller
sampling instant to simulate continuous operation of the plant. The data loss on the
measurement signal is a sequence that repeats according to the data loss vector
[0 a 1 0 1 0], where 0 symbolizes an on time transmission and I, the loss of one sample.
The delay on the control signal is also a repeating sequence driven by the jitter vector,
[.1 .5 .2 .7 .1 .8], where the numbers represent a fraction of the sampling period T=O.Ol.
There i.5 no documentation available on the characteristic of the network data latency in
the context of distributed control systems. Therefore, these two sequences have been
arbitrarily chosen to generate a sufficient alternation and yield an average close to 0.4 T.
The following three figures display the output of the control system subj ected to
distributed delays in the condition of the simulation described above. The resulting
13
f
responses have been obtained by setting the initial states to zero and tuning the set point
in order to get a steady state of one. On Figure 6, The continuous line is the nominal step
response and the dashed line represents the step response when only the control signal is
subjected to jitter. Figure 7 shows the same response when only data loss is affecting the
system. Figure 8 exemplifies the compounded effect of both control jitter and data loss
on the response of the system.
14
f
1.2r~~~~~
1
0.8
y(t)0.6
0.4
0.2
0.1 0.2
t
Nominal Response
Jitter Affected Response
0.3 0.4 0.5
Fig. 6. Effect of Jitter in the Control Signal on the Output of the System
1.2
1 I
I
0.8 t'
I
}
y(tP·6
J
0.4
Nominal Response
.... ... ...... Data Loss Affected Response
0.2
00 0.1 0.2 t 0.3 0.4 0.5
Fig. 7. Effect of Data Loss in the Measurement Signal on the Output of the System
2.5
Nominal Response
2 r ..... Combined Effects of Jitter and Data Loss f " .... ........
I \
I \
1.5 , \
( .....
I \ I " " " ,/
I \ f \ ".
y(t) ~ "../ 1/ \
I \ I " \ /
0.5 /
\ I
\ I
\ I ./
'\ I '\ .'"
\ /
\..,/
00 0.1 0.2 t
0.3 0.4 0.5
Fig. 8. Combined Effect of Jitter and Data Loss on the Output of the System
15
Qualitatively speaking, it has been observed on the above example and also has been
indicated by Tomgren (1996) that. a sudden change in the measurement delay (vacant
sampling) introduces a disturbance in the system to which the controller will attempt to
provide compensation. The compensated control signal, however, introduced a new
disturbance in the system when the delay returns to its original value (sample rejection).
More to the point, the detrimental effects are directly proportional to the speed of the
controller. For instance, in Figure 9 only the natural frequency of the desired response has
been relaxed to 21 rad/s leading to a lower gain controller. The response is indeed slower
as the rise time is almost doubled, but. at the same time the sensitivity to variable delays
in the feedback loop is reduced.
1 2 .~~~~__.
o B
o , 6
y (t )
o 4
o 2
, , ,, ,
,
/
, ...
, ,
J' , ...

Slower Nominal Response
Combined Effects of Ji tter
and Data Loss are Less Sign ificant
°O~O~10~. 2~O~, 3~~O~, 4~~O , 5
Fig.9. A Slower Controller on the Situation of Figure 8.
in an attempt to quantify the effect of data loss and j itter, the square of the difference
between nominal and actual response has been summed up from 0 to 0.5 second. The
result is a performance index that is inversely proportional to the quality of the control
16
function. That performance index has been used to asses the effects of the loss of only
one sample on the whole step response. Four different trials have been run with that one
particular sample lost at the respective instant, .05, .07, .09, and .011 seconds. The
resulting normaLized performance index for these four trials yielded the values 1 .. 18 •. 13
and .004. This shows that the location were the data loss occur is of major significance.
Moreover, it has been observed that adding jitter to the same particular situations
typically increased the performance index approximately and consistently by a factor of
14.
From these results and more individual experimentation we make the following points.
• The compounding effects of jitter and data loss are much larger than the summation
of the respective individual effects.
• The controller speed is a determinant factor to the sensitivity toward time varying
delays.
• The location along the step response where a sample is lost is of major significance to
the resulting control performance.
• Although not illustrated here, it has been observed in this particular simulation that
the observer dynamics have relatively little effect on the response.
2.3 Dynamic characterization of a delayed control systems
A timedelay is a system which delays a signal but otherwise does not change it. In
the sdomain it is characterized by the transfer function, eot s
. The consequence is very
17
detrimental to a control system by the way of introducing phase lag into the system. The
gain of a time delay is constant and equal to one and the phase lag grows exponentially
with frequency. The resulting effect on control systems is to decrease the stability margin.
A stable system is therefore difficult to design particularly if a high feedback gain is
desired. Elements of the characterization of delayed control system are presented in this
section. As de1ined before, the delays introduced by the mUltiplexed data network are
variable. The majority of the reported work deals with constant delays, but modeling and
compensation of the time varying delays cannot readily be done in discretetime control
systems. One has therefore to characterize the specifics of the situation at hand, namely
the feedback control loop closed via the communication network, to construct a
compensation solution.
Time delays are difficult to handle in the continuoustime case as the transfer
function becomes nonrational. A formulation of the system by ordinary differential
equations is no longer possible. The dynamic characteri zation of the system has then to
be done by a system of delaydifferential equations. The delaydi fferential equations
(DOE) are a special class of differential equations called functional differential equations.
The application of ODE's to control system design is extensively explained by Oguztoreli
(1966). In a DOE, the derivative of an. unknown function. x, has a value at t that is related
to x as a function of some other function at 1. For example:
xU ) = A x (l  L ) L > 0
Or more generally:
x(t) = f (l ,x(.)) (2)
18
It is interesting to note that, since a DDE can describe a process with after effects
(previous history of the system), the initial data now includes an initial function ~ in place
of an initial condition. The solution is therefore: x(t)=x(t,to, ~) with I.e.= ~(to) and the
initial situation has to be seen according to Figure 10.
heredity assumed
faded out x(t)= ~(t)
4__+1 • 1 I
a =cst to
Fig. 10. Initial Situation of a DDE
For control systems, even with variable delays a suitable model equation could be viewed
as,
x(t) = f(/ ,u(t),d(I),X(.)) (3)
where: u(t) is the control signal
d(t) is the disturbance signal
x(.) is a function defined on [a,t]
In this case the change in the state x is affected by u(t), d(t), but is also dependent upon
how x is affected by some mechanism x(.). The solution can exhibit exponential growth
or decay but can also be oscillatory. ODE's also make the case for a possi bl e optimization
19
problem. namely, trying to maximize performances by choosing the best {<I> , u} pair. A
good example of the use of DOE's to the analysis of control systems can be found in a
work by Hirai and Satoh (1980). In that short paper a first order system is written by,
.r(f) +a x(t) + ~ x(t  L(.)) = 0 (4)
where L(.) is a variable delay which is a function of time t. L(t) is chosen to be a
particular arbitrary "saw tooth" delay wave form. Proof has been made that the time
varying system is unstable even if the time invariant system is stable.
Time delays can also be studied in continuoustime using analytical
approximations. We consider here three approximations studied by Wang, Lundstrom and
Skogestad (1994). The approximations correspond to the power series expansions of
respectively the numerator (zero), denominator (pole) and a combination of the two
referred to as, the Pade approximation.
Zero, eu :::::; 1 1 S
I
Pole, eu :::::;
1+ 't S
"[
1  s
Pade, et·\ :::::; =2 
't
1 + s
2
(5)
(6)
(7)
The relative accuracy of these approximations has been qualified by Wang, Lundstrom
and Skogestad (1994) and compared based on how well they predict the smallest delay
required to destabilize a certain closed loop system. The outcome is, zero is always
20
conservative while pole is overestimating the stability margin. Pade is clearly the best
approximation while still a bit optimistic. They also pointed out that theoretically it is
possible to get arbi trary high accuracy by dividing the delay in n parts (e ~\)" and use
T
  s
any approximation for each of the smaller delays e /I
A delayed control system is easier to handle in discretetime. The approach is called
state augmentation and has been described in Astrom and Wittenmark (1990) and
Franklin and Powell (1994). Let the system be described by,
x = Ax(t) + Bu(t  r)
The general solution is,
I
x(t) = eA(I IV) x(to) + fe ·IU  ')Bu(sr)ds
III
Ifwe let to =kT and t= kT + T, then,
k7'+ r
x(k + 1) = e A/ X( k) + f e "'(h l  ,) Bu(s  r )ds
kT
The next step consist in breaking the integral into two parts as follow,
k J'+T kT+ l'
(8)
(9)
(10)
x(k + 1) = eATx(k ) + f e A(k+h') Bds'u(k 1) + f eA(k+)  r' ) Bds'u(k ) (11)
k1'+T
In this form, the control signal u is constant in each part and sampling of the continuous
system gives,
x(k + 1) = <Dx(k) + r ou(k) + r )u(k  1) (1 2)
21
where,
tT
'r1h' = eAt, r 0 = Je A·<ds B ,
o
T 11 = eA(Tt) JeA1ds B
o
The state space model is therefore,
[ X(k + 1)] = [ <1> 11][ x(k) l [ro]
lI( k ) 0 0 u( k  1) J + I u( k )
(13)
(14)
Now if the delay is longer than T, one needs to separate the system delay into an integra!
number of sampling periods plus a fraction. such that.
T;=ITmT with, I~O and, O~m~1
Equation (12) than becomes,
x(k + 1) = cD(x(k) + rou(k 1 + 1) + rluCk I) (15)
Thus the state space model is therefore,
I x(k + 1) cD [I [0 0 x(k) 0
u(kl+l) 0 0 I 0 u(k I) 0
= + : u(k) (16)
li(k  1) 0 0 0 I u(k  2) 0
Il(k) 0 0 0 0 u(k  1) I
This state augmentation approach consists of incorporating the delay in the plant mode!
(namely A, B and C). Provided that the sampled system is reachable, the dynamics of the
22
augmented system can be controlled with linear state feedback. One can then synthesize
the controller gains that must accommodate for the loss of phase margin due to the delay.
The new model that incorporates these delays rapidly becomes cumbersome and
complete controllability and observability may be lost as additional states are added. It is
therefore more convenient to keep the induced delays outside the plant model. This
altemati ve approach has lead to the multistep prediction scheme presented in section 3.1.
Along the lines of state augmentation, a methodology for the characterization and
compensation of delays both in the input and output variable has been developed by
Halevi and Ray (1988). Halevi and Ray assumed the situation presented in section 3.2,
the sensor data is subject to a transport delay that generates, vacant sampling and sample
rejection. Accordingly, z, the delayed measurement data is, zi = Yi  f'Cil where y is the
sensor data and pO) a nonnegative integer bounded by 11. In addition, the control input
data is also subject to a timevarying delay. This implies that even if the controller
generates the command at a constant rate, the interval between their successive arrival at
the actuator is not constant. The model therefore uses the facts that the input to the
process is piecewise constant. In other words u(t) assumes at most (1+ I) different values
in the interval [kT,(k+I)T) where changes occur at the instants kT+tjk , with i=1,2,3, ... J.
Thus, the solution of the state equation can be reformulated accordingly,
r I
x(k + 1) = e'.f'lx( k) + J e,I(I" 'l Bu(s)ds =e Arx(k) + L B;k ti(k  i) (17)
o I ~O
where.
23
1,J._ 1
B," = J e A( f  <l Bds with t~1 = T, t/' = 0
I.'
For simplicity, the control law is chosen to be purely proportional such that.
(18)
(19)
Where rk is the reference signal, and Zk the delayed sensor data as defi ned previously.
The state vector of the augmented state system is then,
Ray and Halevi 's work (l988) presents a generalized formulation of the state augmented
model. A simplified version of this model is given here. in a sense that the control law is
proportional feedback. the reference signal is constant and equal to zero, the bound on the
variable delay is equal to one and the control signal can assume only three different
values per sampling periud (L =2). The compensated system then becomes,
X k+1 c:t>  B~ K(1  p(k ))  B~ Kp(k) B k
I
Bk
2 xk
Yk C 0 0 0 Yk\ = (20)
Uk  K(l p( k»)  Kp(k) 0 0 U k _I
Uk_ I 0 0 0 Uk _2
where,
B; = 1 exp(t ~  T). Elk = cxp ( ( ,~  T)  exp(tt  n, B; = exp(t lk  n  exp(  T)
24
This compensation algorithm has been simulated on a simple system by Ray and Halevi
(1988). Let us recall that the time skew Lls between measurement and controller
acquisition of the input data determines the distribution and proportion of vacant
sampling and sample rejection. In Ray 's work, a series of simulations were conducted for
different combinations of Lls and K to result in the definition of a stability region. Further,
the simulations showed that the stability analysis cannot be made solely on the basis of
average values of the time varying delays. Indeed, three different delay sequences of the
same average characteristic revealed different stability ranges.
25
CHAPTER 3
REVIEW OF THE LITERATURE TOWARD ANALYSIS AND
COMPENSATION
The first concept is the so called pstep delay compensation observer. The
compensation scheme eliminates the time variations by mean of buffering. The resulting
time invariant delay of several sampling periods as seen from the output of the buffer is
compensated for by a multistep prediction method. Encouraging simulation results later
prompted the development of a Loop Tranfer Recovery (L TR) synthesis method to
identify an observer gain that minimizes the H2 norm of the sensitivity error transfer
matrix. The second concept reported in section 3.2 from Ray ( 1994), is also along the
lines of the situation exposed in 1988. and consists of an output feedback contro l law in a
stochastic setting. In this case the delays are considered to be stochastic and knowledge of
the their probability repartition is assumed to be available. Finally, section 3.3 reports the
work of Lundstrom and Skogestad (1994) toward the construction of an uncertainty
model suitable for robust control analysis.
3.1 The Pstep Observer
With the idea that it is more convenient to keep the induced delays outside the plant
model, Luck and Ray ( l990) proposed to eliminate the time variations in the network
transport delay using buffering and estimation. In this concept, the idea is to monitor the
26
data when it is generated and to keep track of the delay associated with it. The time
variations are eliminated by buffering the data and always presenting samples that have
the same age at the controller. In this conditions the control function only has to
compensate for a fixed amount of delay. Note that, the delayed data is used regardless of
whether the current data is available. If more fresh data is available, it has to be kept in a
firstin firstout buffer for later processing. Referring to the control structure shown, in
Figure 1 I, the network delays 'tsc and 'tae are bounded by rand q units of sampling period
respectively. The data is kept in a first infirst out buffer to absorb the time variations
both at the controller and actuator sites. Accordingly, the model can now be treated with
two constant time delays rand q respectively in place of the variable network delays
previously 'tsc and 't nc '
rk
~. Controller
Gc(z)
I _ '___ .....J , ,,
I
I
I
I L ______ _
First in/out
buffer L...___ .J
Uk : Timevarying
  ....: t Dl!lay 't
: ca
Timevarying
 : Delay 't se
Network
First in lout Plant
buffer Gp(s)
Yk T
1+;  
Fig. 11. Elimination of the time variations by data buffering.
The control problem is therefore one of compensation of a constant delay of multiple
y(t)
sample interval. For that aim the algorithm proposed by Luck and Ray (1990) consists of
using an observer to estimate the delayed states and then predict the current state using
27
the state variable model of the plant recursively. The basic equations used in the multistep
delay compensation scheme are listed below, consider the plant,
(21)
The observer model is.
(22)
The pstep predictor is,
(23)
With the predictive control law.
(24)
Where,
Zk l r = prediction of xk based on the measurement history {y kr ' Yk  r  I , ... 1
Luck and Ray (1990), have implemented and verified the resulting closed loop equations.
(25)
where,
(26)
and,
if p "C. 2 }
ijO s, p <2
(27)
Schematic representation of a threestep predictor/controller is given in Figure 12.
28
1
:"Ob~~'n,'~~"" ........................... .. .
Yk•p :
Predictor Blocks
Control
)..;....+1 Law
Fig. 12. Schematic representation of a threestep predictor/controller
The number of predicted steps could be obtained as the sum of the specified bound,
namely p=r+q, if the joint statistics of rand q are known, p could be computed more
precisely. Extensive simulations of the compensation scheme can be found in Luck and
Ray (1994), the experimental results come from the a d.c. motor assembly interfaced to a
microcomputer. Data from the A/D converter is stored in a buffer to generate a constant
delay. A proportionalintegral (PI) controller is used with and without the delay
compensation algorithm. In that particular paper, the authors clearly showed that the
dynamics of the motor is considerably improved with the observer. Further. the predictive
properties of the observerbased control algorithm were able to cancel a limit cycle
problem happening at low reference input of the uncompensated system. The delay
compensator has also been investigated for a simulated fli ght control system within a
network environment. The design showed superior performance but also yielded a steady
state error. Indeed the observer based controller produces a small steady state error
29
1
because the integrator acts upon the estimate of the state and not on the true system
output. Some of the robustness issues of the delay compensator for structured
uncertainties have been covered. Nevertheless, the effect of the modeling uncertainty
upon the performance of the predictor controller have been studied using the gain matrix
that were originally designed for the nondelayed system. Toward robust compensation,
Shen and Ray (1993) proposed to synthesize the control system for delay compensation
by extending the concept of loop transfer recovery (L TR) to the multistep observer
described in Luck and Ray ( 1990). The uncertain communication delays are lumped at
the plant input in the form of an input mUltiplicative term. The idea is to tune the loop
transfer recovery matrix such that the error transfer matrix, the difference between the
actual and target sensitivity matrix. is minimized. Let us initially consider the L TR
concept for the regular one step observer. In a first stage, the target loop transfer matrix is
designed by selecting fullstate feedback gain for a given performance index. Next, the
loop transfer matrix and the sensi tivity matrix of the compensator are calculated by
incorporating an observer in the loop.
Consider the plant,
(28)
with the fullstate feedback law,
(29)
The plant transfer matrix is then,
G(z) = CcI>(z) 8, where ¢(z) = (z/  A)I (30)
The target loop transfer matrix is.
30
H(z) = Fc:D(z)B (31 )
The target sensitivity is.
S(z) = [J + H(z)r' (32)
The observer introduced in the loop to compensate the one step delay has the transfer
matrix,
GI (z) = F(=J  A + BF + LCr' L = F[J + ¢ (z)(BF + LC)r' ct>(z)L (33)
The loop transfer matrix with the compensating observer then becomes,
L, (z) = GI (z)G(z) = F[J + c:D(z)(BF + LC)r' cD(z) LCcD(z)B
= [I + E, (z)r l [H(z)  EI (z)]
where E1(z) is the Istep error matrix with.
E,(z) = F[zl A + LCr' B
The resulting Istep sensitivity matrix is,
Finally the relative sensitivity error is.
E, (z) = S(zrl [SI (z)  S(z)]
The same reasoning as been applied in Luck and Ray (1990) to the pstep delay
(34)
(35)
(36)
(37)
compensator. the loop transfer matrix is derived first. Then, the error of the sensitivity
matrix relative to that of the target loop is formulated. The approach used in the synthesis
of the pstep delay compensator is to minimize the loop recovery error where the gain of
the observer is set to a prescribed value. In other word s. the key is to identify an L that
minimizes the relative sensitivity error transfer matrix. The procedure is then as follows.
31
f
First. the target loop is designed assuming no delay with full state feedback. econd the
observer gain L is calculated by solving the steady state Riccati equations for a fictitious
measurement noise p, where p is a tunable scalar parameter. This parameter p is then
adjusted so that the maximum singular value of the compensated loop transfer matrix are
below those of the target loop transfer matrix to satisfy the requirement for stability
robustness. The minimum singular values of the compensated loop transfer matrix
represent the lower bounds of the performance. As expected, Ray observed that it is
impossible to fully recover the target loop characteristics by tuning the observer gain
when a predictive state estimator is used. In addition, for a fixed requirement on the
stability robustness, performance decreases as the compensated delay is increased.
3.2 Optimal Compensation with Stochastic Delay Assumption
In the design presented in section 3.1. the state estimate was consistently obtained
on past measurements regardless of whether the sensor data is delayed or not. It is similar
to having the measurement data always delayed by a specific number of samples.
However if the probability of delayed arri val of measurement data is small. then the cost
of introducing a constant delay may be excessive. As an alternative, Ray Liou and Shen
(1993) and Ray ( 1994) proposed an estimation algorithm that uses the most uptodate
sensor data at each sampling instant. Consequently output feedback control under
randomly varying distributed delays has been formulated as an alternative to the
deterministic approach used in the pstep observer. The control system under
consideration is as described in section 2.1 and illustrated on FigurlJ 2. The maj or
32
assumption is that the statistics 0 f the induced delays are white and independent, and
knowledge of the their probability repartition is assumed to be available. The approach
consists of a combined state estimation and state feedback. The state estimation and state
feedback control laws are synthesized separatel y on the principle of optimality and then
integrated together. The state estimation fil ter is formulated when the sensor data arrival
is either timely or delayed by one sampling period and the probability of vacant sampling
is made to be very small. Based on the concept of Linear Quadratic Gaussian, (LQG) the
estimation filter assumes that, the plant is subject to random disturbances, the sensor data
is contaminated with noise and the measurement delay is a random sequence from the set
{O,l }. The regulator follows the structure of the conventional linear quadratic regulator
(LQR) control law and is formulated by Ray (1994) in the presence of randomly varying
delays from the controller to the actuator and full state feedback. Accordingly. the control
architecture is reported from the referenced publications in two parts. The estimator is
presented first and accounts for the variable delays, plant noise and sensor noi se. The
regulator then assumes full state feedback and variable delays in the control signal but no
plant and measurement noise.
The state estimator illustrated here has been extracted from the work of Ray, Liou
and Shen (1994). It is a modification of the conventional minimum variance state
estimator to account for the effects of sensor to controller randomly varying delays. The
plant model is expressed as.
33
(38)
where,
Sk the plant state at instant k
Ph the random delay from the set (0, I:.
Wk the noise vector
Zk is the delayed sensor data (either on time zk=Yk or late Zk=Ykl)
If the measurement history Zj up to the fit instant is available, the conditional estimate is.
(39)
the state estimation error is.
~
ek ll = (Ski!  Sk ) for j k (40)
and the conditional error covariance is.
(41 )
Note that E{.} represents the expectation value with respect to the statistic of the plant
noise, sensor noise and the variable delay sequence. The problem of finding an optimal
estimate of the state is solved by minimizing the following cost functional at each sensor
sampling instant.
(42)
34
The objective is therefore to synthesize a sequence of filter gain matrices. {Kd for
k= 1 ,2,3 ... , that would minimize the cost functional for each k. This is accomplished by
considering the recursive structure.
~ ~
Sk = L/:'klk_1 + Kkzk
(43) ~ ~ SkI = <Dk .k  I~k  I k  I
where, the gain matrices Lk and Kk orthe above filter are derived in a sequel.
The linear quadratic regulator is compensated for control signal delays varyi ng but
bounded. Similarly to the methodology of state augmentation presented before from
Halevi and Ray (1988). the input to the plant is considered piecewise constant during a
sampling interval in the controller frame to take into account the effects of controller to
actuator delays. The augmented state vector is then composed of the plant states plus the
control input at di screte instant of time,
(44)
where,
~ E ~H/I is the plant states
Uk E ~H'J1 represent u(t) at discrete instants of time
Following the same methodology introduced in section 4.2.(Halevi and Ray 1988). the
augmented plant model is then.
(45)
where,
35
(k+I) 1'
b ~ = f <D[ (k + 1) T, A ]dA (46)
k1'+ I '
(k+ I )],
h; = f¢[(k + l)T. A]b(A)dA  b~
k1'
Note that relation (46) is a stochastic process because the time period tk limiting the
integration are random. The relationship for optimal control is derived recursi vely by
minimizing the following cost functional over a ti.nitetime horizon ofN sampling
intervals,
(47)
where,
(48)
and u; is the optimal state feedback law at the k'h sample.
For k=N, we assume that the terminal state is reached and there is no need for any
control. Therefore.
(49)
where PN = S, the tinal state penalty matrix, is given. Practically, the optimal control law
is given via a recursive relationship. Let the control law at the kth stage be
('iO)
for k<N and the resulting performance cost
(51 )
36
where
(52)
backward starting from Nl. The control law is computed offline to numerically obtain a
steadystate value of the gain matrix F on a finitetime horizon. The expected values are
numerically generated based on the known probability di stribution of the controlleractuator
delay.
The integration of the state estimator and the state feedback controller is now
executed. The estimate obtained with the predictive filter replaces the actual plant states
part ofthe augmented state vector in the formulation of the optimal control law. The
combined state estimation and state feedback contrallaw is then obtained by changing
the plant states in the augmented state vector of the full state feedback contro l law by
their estimated counterpart. The feedback control law is then,
(53)
for k<N and where Zk is the history of the delayed measurements used for generating the
control signal and Fk is the state feedback control gain given in equations (52).
The proposed compensation technique has been simulated by Ray (1 994) on the
unstable longitudinal motion dynamics of an advanced aircraft. It been found that even
though the delay compensated LQG algorithm only offers a SUboptimal solution when
variable delays are present. the state estimator together with the feedback regulator are
capable of compensating for randomly varying delays. The control perfo rmance generally
37
1
,
degraded with larger noise covariance but no evidence of instability was found. Finally
the delay compensated regulator was found to be sensitive to both structured and
unstructured plant uncertainties. As pointed out by Ray (1994), This is expected because
LQG has poor robustness properties and the injected delays further deteriorated the
robustness of the compensated regulator.
3.3 Robust Analysis of Tirne Varying Delays
All networked distributed control systems have to be digitally implemented.
Consequently, it is logical to design the compensation mechanism on the basis of the
discrete time sampled data system. This approach has been exemplified in the previous
sections by explicitly considering periodic operation and zero order hold. Nevertheless.
even though continuous time analysis is not really relevant to the case of networked
distributed control systems. it may bring additional elements of understanding to the
problem of variable delays. Furthermore. a continuous system can sti II be trans lated to a
discrete time implementation with sufficient oversampling. Robust design for instance.
is easier to study in continuous time. fn ~l synthesis and H'1J design, it is interesting tn
view uncertain or time varyi ng delays as model uncertainties. Therefore, in this section.
attention will be given to the translation of variable del ays into an uncertainty model.
In section 2.3 rational approximations have been introduced for time delays, they
were respectively called. zero, pole and Pade. These approximations can also be used to
represent a delay uncertainty of the type.
(5 4 )
38

i
Wang, Lundstrom and Skogestad (1 994) indicated that. to represent a complex
perturbation only :::ero can be used since pole and Pade would produce an infi ni te
uncertainty for frequencies above respective ly 1!r and 21T. Another alternative.
commonly used in robust design is to let the /1 uncertainty in the denominator of the Pade
approximation equal I and let the remaining /1 become complex. such that.
LS
e ti\, ~ 1   /). = 1+ w(s)/).
L
1 +  s
2
Then the uncertain plant can be written.
g,,(s) = g( s)(1 + w(s)t1(s»
(55)
(56)
To account for varying network delays using an uncertainty model. the uncertainty has to
be with respect to the average data latency. Accordingly the delay to be considered would
include a constant and an uncertain part, or.
 ] ::; /1 ::; 1 (5 7)
where, LA is the average latency
LV is the variation with respect to the average
Two alternatives to design have been proposed by Wang, Lundstromand Skogestad
(1994). The first consists of lea ving the average del ay in the nominal model and Itt the
uncertainty model account for the \'arying part. The second option leaves the nominal
model delay free and the time delay uncertainty is as (57). Comparable results have been
shown with both npproaches by Wang, Lundstrom and Skogestad (1 994), They however
39
pointed out that the delay free (nominal model without delay) design problem is easier to
handle.
40
CHAPTER 4
A NEW INTERPRET A TION TO DESIGN
4.1. Proposition
An interesting approach introduced by Torngren (1996) is motivated by the fact
that vacant sampling and sample rej ection seem to affect the control system just as
disturbances would. With this idea in mind, a feedback control system with variable
delays could be viewed as a timeinvariant system exposed to disturbances that are
introduced by the communication system. The control signal and the measurement data
are nevertheless affected differently. The control signal is only affected by the
communication delay, it is variable and causes periodically generated control samples to
arrive at the input of the process with a varying sampling period Gitter). The
measurement data on the other hand is affected by the communication delay and the
detection delay, the effects have been characterized before as vacant sampl ing and sample
rejection. One can see on the left hand side of Figure 13, the measurement data subject to
vacant sampling and message rejection assimilated as the disturbance signal Vt . On the
other side of the Figure 13, we assume the control signal to be already compensated for a
constant transport delay Cc' Once again the variabi lity of the transport delay can be
translated into a disturbance signal WT •
41
y, T~ry~
~... . .... .
VS = Vacant Sampling
SR = Sample Rejection
u(tT(k))
w,
I
T : T:
~...,:
I : I .
I
t :
...,:
I .
1c ind icates the amount of delay
compensation included ill the design
subsequent delays L ':F LC generate the
disturbances WI
Fig. 13. Modeling closed loop timevarying delays as disturbances
The characterization of \'k can be made as follows.
Consider the delayed output,
where,
y = output vector
z = delayed output
p (k)= variable sensor to controller delay belonging to the set {O, I l
Then the following situations may occur.
42
(58)
f
where,
P (kl ) = 1; p(k) = I ~ Zk=Zkl+6Ykl
P (kl) = 0; p(k) = I ~ Zk= Zk l
P (kl ) = I; p(k) = 0 ~ Zk=Zk_l +6Yk + 6 Ykl
6 Yk= (YkYkl)
6 Ykl = (YklYk2)
• In the first situation of expression (59) the system does not suffer any delay .
(59)
(60)
• In the second situation the whole system is simply phase lagged by one sampling
period: Zk is off the actual value by 6 Yk 6Ykl .
• In situation 3, a vacant sampling has occurred: Zk if off the actual value by  6Yk .
• Situation 4, illustrates a message rejection where Zk if off the actual value by 6Yk_I'
Along these lines it is suggested that from the above situation. the effects of the delay
variability on the measurement data can be expressed by,
(61 )
where Vk is a train of impulses with varying amplitude (ampl itude related to the rate of
change of y(k)). [t is these impulses that distort the control signal. Under the assumption
that the sampling period is usually much faster than the system. let 6 Yk ;::::6Ykl and vI.
43
f
could be viewed as a linear function of (YJ,;YJ,;I)' Moreover, it seems reasonable to see VJ,;
as a signal bounded by,
(62)
The characterization ofwJ,; is obtained differently. [t is assumed that the control
signal is already compensated for the average communication delay t e' The actual
communication delay is time varying and denoted t (k) . The disturbance model w, is then
a function of ['L(k) TJ and the control signal uCk). This disturbance model in continuoustime
is expressed as.
w.c t)=u( t t( k) }u( t cJ (63)
and is illustrated on the left hand side of Figure 13. The effect on the control system is the
result of the time integral wit) during a period.
4.2 Scope and Limitations
The disturbance signal interpretations may be used to evaluate and shape the design
of networked distributed control systems. For instance. if the time varying characteristics
of the data latency are known from the study of the network characteristics. the
disturbance model will be known. These disturbances may be concentrated at certain
frequencies and one might want to emphasize regul ation at those frequencies. The
disturbance signal interpretation illustrated above can be viewed entering the system in
the configuration of Figure 14.
44
r
Controller
Gc(s)
a,'
~ , ... ~ .... ~ . .
Plant
Gp(s)
Network
Induced
Disturbances
y
Fig. 14. Configuration of the Distributed Delay Disturbances
Provided that the characteristics ofv~ and w, are known or can be estimated, the control
configuration is now a familiar one. The frequency loop shaping approach then becomes
an alternative to design. Accordingly the detrimental effects of the network induced delay
can be integrated in the design tradeoff, high loop gain for tracking and small loop gain to
reduce the effects of the network delays. The main obstacle to that objective is that the
frequency characteristic of the network data latency typically include both high and low
frequencies. Furthermore, the frequency characteristic probably varies with the number of
active network stations and their respective synchronization changes. With these
limitations in mind, the example treated in section 2.2 is considered again for
improvement on the system' s response.
45

4.3 Example
Recall the plant transfer function of the example in section 2.2.
1000
G(s)=s(
O.5s+ 1)
(64)
with the combined effect of jitter on the control signal and data loss on the measurement.
it was not possible to achieve a stable system response that would satisfy the specified
requirements of 0.7 damping ratio and a 56 rad/s natural frequenc y. It is the intention of
this section to show that this situation can be improved with prior knowledge of the
characteristics of the induced network delays. For the benetit of shaping the loop gain to
better reject the disturbances caused by the variable transport delays, the jitter and data
loss sequences have been examined in the frequency domain. As a reminder, the control
signal jitter is driven by the vector [.1 .5 .2 .7 .1 .8] where each element represents the
transport delay as a fraction of the sampling period T=O.01. Similarly. measurement
samples are lost due to late arrival for each 'one' in the repeating vector [0 0 1 0 I 0].
These two vectors have the same frequency spectrum when repeated at the sampling
period of 0.0 1 second. Their common frequency spectrum exhibit three di stinct peaks,
respectively at 103, 207 and 314 rad/s. It is these relatively high frequencies that have to
be targeted and suppressed by rolling off the loop gain. For that matter. two poles have
been added to the compensation. The poles are located at 100 on the splane with the
intention to provide a 40dB per decade of gain loss after 100 rad/sec. The corresponding
transfer function is.
1
C.h:(s) = J
(O.Ol+s t
(65)
.+6

or equivalently in the zdomain.
0.2642z + 0.1353
Ge( z) = Z=2  0.7358 z+0.1353 (66)
in the context of the stepwise simulation it is easier to deal with the equivalent difference
equation,
y(k)=0 .2642 x(kI )+0.1353 x(k2)+0.7358 y(kl )0.1353 y(k2) (67)
Incorporation of this low pass transfer function into the simulation algorithm improved
the response of the system by reducing the effects of the jitter and data loss. With no
other changes to the conditions of the simulation, the system response is now stable as
shown on Figure 15. In this figure, the solid Line represents the same nominal response,
the dotdash line is the uncompensated system response, and the dashed line is the
compensated system response. The compensated response is an improvement over the
simple proportional state feedback that was unstable, nevertheless, the required damping
ratio of 0.7 is not achieved. One has to note that we are dealing with a border line
situation where both the sampling period, the plant dynamics, and the jitter and data loss
patterns are combined to generate a challenging control situation. Clearly, decreasing the
sampling period would have a much more beneficial effect. The point of this example is
to show that the detrimental effects of the network induced delays can be integrated in the
design process, reduced or possibly suppressed by frequency shaping the loop transfer
function.
47

y (t)
2.5 r~~~~~
2
1 . 5
I ,
, (
I ,
i ,
. I
I I a 5 ,, I
I ,
/;:
r,
"
, .....  ~, ....
I '
I
I
~'
. ~
, ~
    ',..
" 1T'/
a a~ ~~~~~ 0 1 a 2 a 3
Naill inal Response
U ncorn pensatecl Response
Compensated Response
a 4 a 5
Fig. 15. Compensated System Response Under Jitter and Data Loss
It is important to remember that this reasoning relies on the questionable assumption that
the frequency characteristic of the network data latency is known and constant.
Furthermore, the detrimental effects can only be attenuated provided that they are not
located in a frequency band that necessitates a high gain for other reasons, such as,
tracking requirements.
48

CHAPTERS
CONCLUSIONS
In many networked realtime distributed systems, the measurement and control
signals within the feedback loop are subject to timevarying network induced transport
delays. The timevarying nature of these delays has been shown to cause jitter on the
control signal and data loss on the measurement data. The detrimental effects of these two
phenomena have been simulated in the context of a networked feedback loop.
Interestingly, jitter and data loss proved to have a multiplicative detrimental effect upon
each other. Moreover, and as expected, the controller fastness is a determinant factor to
the sensitivity of the controller performance toward time variations. Last, for a single
sample loss, the instant of occurrence has a great significance on the effect of the
performance. This report therefore clearly provides the reader with a perspecti ve on the
problem of transport delays in the context of a distributed control loop and a report on the
current research status. In addition. it has been shown that successful qualitative
reasoning can be made by interpreting the time variations as disturbances introduced by
the communication system. Nevertheless, a major limiting factor in the design of any
compensation algorithm is the absence of information about the characteristics of the
network data latency. Consequently, further work is needed. first in the characterization
and identification of the network performances particularly when subject to quasiperiodic
traffic and secondly, in the integration of these characteristics into the
compensation design possibly using the disturbance interpretation provided here. To that
49

aim a short report on the Controller Area Network (CAN) of widespread LIse for
distributed control systems is given in the appendix.
50

BIBLIOGRAPHY
Astrom, KJ., and Wittenmark, B .. Computer Controlled Systems. Theory and Design
Prentice HaiL 1990
Bosh, "CAN Specification" Version 2.0 1991. Rohert Bosh GmbH, Postfacch 50. 07000
Stuttgart 1
Franklin. G.F., PowelL J.O .. and Workman. M.L., Digital Control Systems Addison
Wesley, 1994
Gergeleit, M., and Streich. Fl., "Implementing a Distributed HighResolution Realtime
Clock Using the CANBus"
Ha1evi, Y., and Ray, A .. "Integrated Communication and Control Systems: Part I
Analysis," ASME JOllrnal ojdynamic .\ystems. Measurement and Control Dec 1988 pp.
367373.
Hirai, K., and Satoh, Y., "Stability of a System with a Variable Time Delay" IEEE
Transaction on Automatic Control, Vol. AC25, No.3, June 1980, pp. 552554.
Liou, L. W., and Ray, A., "Integrated Communication and Control Systems: Part III
NonIdentical Sensor and Controller Sampling," ASME JOllrnal of dynamic systems,
Measurement and Control Sept. 1990.
Luck, R., and Ray, A., "An ObserverBased Compensator for Distributed Delays:'
Automalica. Vol. 26, No.5, pp. 903908, Sept. 1990.
Luck, R .. and Ray, A., "Experimental Verification of the Delay Compensation Algorithm
for Integrated Communication and Control Systems" InlernalionalJournal ajControl,
1994, Vol. 59, No.6, pp. 13571372
Ludvigson, M. T., "Thoughts on High Speed Data Bus Performance", National
Aerospace & Electronic Conference 1990 (NAECON) p. 163168
OguztorelL M. N., TimeLag C'onlro/ Systems Academic Press. 1966
Ray, A. "Performance Evaluation of Medium Access Control Protocols for Distributed
Digital Avionics" ASME Journal o/'Dynamic Systems. Measurement. and Control. Vol.
109 Dec.1987. pp 370375.
51

Ray, A., and Halevi. Y. "Integrated Communication and Control Systems: Part II Design
Considerations," ASME Jvurnal ofc(vnamic .~ys t ems. Meas urement and Control Dec 1988
pp. 374381.
Ray, A., Liou, L.W .. and Shen. 1. H .. ' State Estimation Using Randomly Delayed
Measurements". ASMEjoumal of Dynamic Systems. Measurement and Control. VoL
ll5.March 1993.
Ray, A., "Output Feedback Control Under Randomly Varying Distributed Delays",
Journal of Guidance. Control and Dynamics. VoL 17, No.4, JulyAugust 1994.
Shen, J.H., and Ray A .. "Discretetime LTR Synthesis of the Delayed Control System"
Proceedings o./the American Control Conference, 1992
Shen, J. H .. and Ray, A.. "Extended Discretetime LTR Synthesis of Delayed Control
Systems" Automalica, Vol. 29. No.2, 1993. pp. 431438.
Tindell, K., Burns, A., and Wellings. A. "Calculating Controller Area Network Message
Response Time" IF AC Distrihuted Computer Control Systems. Toledo, Spain, 1994.
Tomgren, M., "Modelling and Design of Distributed Realtime Control Systems: an
Automatic Control Perspective" DAMEKMechatronics, Departement (?lMachine design ,
The Royal Institute of Technology, Stockholm. Sweden. 1996.
Wang, Z., Lu, H., Hedrick. and G .. Stone, M .. "Message Delay Analysis for CAN Based
Networks" Oklahoma Slate University. 1992.
Wang, Z .. Lu. II.. and Stone. M .. "A Message Priority Assignment Algorithm for CAN
Based Networks" Oklahoma Stale University . 1992.
Wang, Z., Lundstrom, P .. and Skogestad. S., "Representation of Uncertain Time Delays
in the H O'J Framework" International Journal oj'Conrrol. Vol. 59. No.3. 1994 pp. 627
638.
Wittenmark, B., Nilsson. 1.. and Torgren. M., "Timing Problems in Realtime Control
Systems" Proceedings o('the American Control Conference. Seattle, Washington, June
1995.
Zeltwanger. FL. "An Inside Look at the Fundamentals of CAN" Control Engineering ,
January 1995, pp. 8187.
Zhan, Z., and Freudenberg. 1.S .. "On Discretetime Loop Transfer Recovery "
Proceedings olthe American Control Conference. 1991 pp.22142219

APPENDIX
The Controller Area Network Communication Protocol
for Distributed Control System
The Controller Area Network (CAN) protocol is a serial network originally
developed by Robert Bosh GmbH (Bosh 1991) to provide the car industry with a
communication bus for incar electronics. It has been chosen as the communication
protocol of interest for its realtime capabilities. Specifically, the priority at which the
message is transmitted is incorporated into the identifier of each message. Bus access
conflicts are then resolved by bitwise arbitration on the identifiers involved by each
station. This mechanism fulfills the requirement of rapid bus allocation and reliabili ty by
decentralized bus control. These arguments along with low cost make CAN the preferred
solution for many control system applications.
Principle of Operation
CAN uses a contentoriented addressing scheme where each message is labeled by
an identifier that is unique throughout the network. The identifier defi nes the type of data
transmitted but most importantly defines a static message priority. For rapid bus
allocation when several stations wish to send messages. the CAN protocol uses bitwise
arbitration. A node can start transmitting its identifier at any time when the bus is silent.
During arbitration every transmitter compares the level of the bit transmitted with the
53
level that is monitored on the bus. If any node transmits a '0' (dominant bit) then all nodes
read back a zero. A unit sending 'I' (recessive bit) but reading a '0'. will automatically
withdraw from the contention. As the result. the bus continually tracks the winner, the
identifier with the lowest binary number. All losers automatically become receivers of the
highest priority message and will reattempt transmission at the next idle period.
The Message Frame Formats
The CAN protocol supports two message frame formats. standard and extended.
The only di fference is the length of the ident ifier, in the standard format the length is 11
bits and in the extended format. 29 bits. The two formats can be seen in the appendix. A
standard CAN message frame consists of seven different bit fields. A message begins
with a start afframe field to indicate the beginning of a message frame . This is followed
by the Arbitralionfield which contains the identifier and the remote transmit request bit
(RTR). The RTR bit indicates whether it is a data frame or a request frame. Next, comes
the control field Containing two dominant bits reserved for future use, and a count of the
data bytes. the data length code. In the middle of the frame. the data fi eld carries a
maximum of 8 bytes of data and is followed by the CRCfield. As part of the error
checking mechanism, the CRC field includes a fifteenbit cyclic redundancy check code
and a recessive delimiter bit. Following. is the ACKnowledge field which is over written
by dominant bits upon successful reception by other nodes. The end of the message is
indicated by the End a/Frame .field consisting of seven recessive bits. At last, the
inlermissionjield is composed of three recessive bits enabling the CAN nodes to prepare
S4
for the next task. Also shown in the appendix is the error frame, interspace space and
overload frame. The error frame is a mean by which a station can flag an error and abort
transmission. The overload frame can only be initiated during the intermission field to
delay any subsequent message frame.
The Error Detection Mechanism
Error detection is implemented at the bit level as well as at the message level with
several mechanisms capable of distinguishing and correct sporadic and permanent errors.
Resulting from noise corruption or spikes in the communication medium. transient errors
are detected and corrected by abortion and retransmission of the message. Permanent
errors are likely to be caused by bad connections. defective transducers or long lasting
external disturbances. They are selfcontained by shutting down the station that is
blocking the bus. The Cyclic Redundancy Check (CRC) is computed on the basis of the
message content. All receivers perform similar calculations and flag any errors. [n
addition, Certain predefined bit values such as eRe and ACK delimiters. EOF bit field.
and intermission will also trigger an error flag if invalid. Likewise. If a transmitter has not
been acknowledged an error is 'flagged. Finally, all transmitters compares the bit level of
the bus with the level it transmitted and Hags an error if the two are not the same (ACK
bit and arbitration excepted). In order to maintain bit synchronization in between stations
a minimum number of bit transitions has to occur. Therefore, after five identical bit levels
have been transmitted. the transmitter will automatically inject a bit of opposite polarity.
Receivers of the message wi ll automnticnlly delete that extra bit. Inside the CAN node, a
55

register called the error count is dedicated to summing the number of receive and transmit
errors. In order for the error count to remain low, every good message decrements the
register. When the error count reaches 128 the node switches to the error passive mode. In
this mode the station can still transmit and receive but can no longer flag errors. when the
error count reaches 255 the node switches to bus off mode. In this mode, the device will
cease to be active on the bus
The CAN Controller
The communication controller has many functional blocks. Of particular interest
are, the CAN controller. the RAM and the CPU interface logic. The CAN controller
controls the data stream between the RAM and the bus line. The RAM provides storage
for 15 message objects and various control and status registers. The CPU interface logic
provides a flexible interfacing to many commonly used microcontrollers. Each message
object has 8 bytes of data. an identifier and control data segments. In addition each
message object can be con figured to either transmit or receive. To initiate a transmission.
the transmission request bit has to be written to the message object. In a same fashion a
message object can be confi gured to receive a message. In that case, Acceptance filtering
is performed by matching the identifier of the incoming message against the identifiers of
aU message objects. A message is accepted and the receive interrupt activated only if a
match is found. Note that. a message object can store only one message, any message that
has not been picked up will be overwritten.
S6
1
The Design Implementation of CAN
CAN is commonly modeled as a single channel queuing system. The bus is the
server and all the spatially distributed waiting messages form a single queue. One has to
note that, a message object can only contain one message. When another message with
the same identifier is queued then the content of the message object is overwritten and
destroyed. The queue therefore, can contain no more than one message with the same
identifier. The priority scheme as described by CAN only affects the order inside the
queue. In other words, depending upon its priority, a transmission request will enter the
queue at different levels.
Cooperating activities in a distributed control system can occur synchronously or
asynchronously. Synchronous operation enable the application to operate in a
deterministic timely fashion according to a strategy defined off line. This operating mode
is supported by static scheduling and ensures predictable bus loading. Hence, in this
approach, the time variations can be minimized or eliminated. As the result. synchronous
operation guaranties predictability of the data latency and constant detectio n delays.
Consequently, several attempts have been made to provide for synchronous operation on
the CAN communication medium. A simple approach consist of using a highpriority
signal at prescribed interval to reset the respective sensor and actuator clocks and to
maintain a loose synchronization between sensor, controller and actuator. One such
endeavor described within the DIRECT project (Gergeleit and Streich) consist of a
protocol that synchronizes accurate local clocks via the CANbus network. An accuracy
57
of about 20 microseconds is obtained using a reasonably small amount of bandwidth «
20 messages / second). The system designer can then benefit from the distributed realtime
clocks to schedule synchronous operations. Another concept, supported by the
CANinAutomation (CiA) forum. "CAN Open", is a protocol that allows synchronous
data transfer over the CAN bus. A very high priority synchronization telegram is sent on
a set time period to all devices. On reception, those devices that are configured to respond
to it send data onto the bus. Once again, this allows static scheduling and ensures
predictable bus loading. Moreover, it is very well suited to the type of periodic operations
often found in control systems, namely, sampling and actuation. For instance, after
receiving the measurement data synchronized to one synchronization telegram, the
controller can send its control signal back to the actuator on reception of the next
synchronization telegram. Equally important, sampling and actuation messages can be
configured to occur on a common multiple of the synchronization period. Synchronous
and predictable operation is a significant advantage. On the other hand it provides very
little room for sporadic transmissions which may occur occasionally but with a high
degree of urgency. Hence, all choices must be made conservati vely to cater for every
possible demand. Last, it does require more intelligence to be installed in every
communicating devices to support the synchronization mechanism. The synchronous
solution is therefore complex. inflexible, slightly inefficient and costly. The
unsynchronized alternative would inc.:lude sensors that send periodic information blindly
and oversampled actuators that operate on reception. In particular. it is believed that the
low cost of CAN makes it very suitable to that alternative. This unsynchronized choice is
58
time varying in behavior and will need to rely more on control engineering solutions for
compensation of the time variations. Accordingly, this approach calls for the modification
of the existing control systems or the development of a new control structure. Even
though the design of a modified control law to compensate for the time variations
represents an additional etTort. It will payoff with a highly enhanced bus utilization
together with an increased robustness to other possible disruptions or even malfunctions
of the network, truly expanding the tlexibi lity and reliability of the system.
The Expression of the Transport Oelay in CAN
According to the CAN arbitration protocol and the queuing model presented above,
the time a station must wait for the bus to become idle is called the waiting time. The
waiting time is the time needed for the current message utilizing the bus to finish plus the
time needed to transfer all higher priority messages waiting in the queue and arriving
during the \vaiting time. Typically, one station will have already gained control ofthe bus
when the transmission is requested. The longest time a station must wait for the bus to
become idle is the time needed to transmit the largest CAN frame (fu ll 8byte extended
message) and is called the blocking time. The time that the request must wait until the
current transmission releases the bus can vary from 0 to the blocking time. Secondly. The
request has to wait for all of the higher priority messages in the queue to go through first.
Recall that messages can enter the queue at any level depending on their respective
priority. Consequently, One has also Lo account for those messages that have been
generated with higher priority during the waiting time. Only then, a station can finally
59
seize the bus and transmit its message. The receiving station will acknowledge reception
after the last bit of that message has been transmitted. The transmission delay or data
latency. is then composed of the waiting time plus the time needed to transmit that
message, or OJ = Wj+Fj with 0, W, F being respectively the transmission delay, the
waiting time, and the length of the frame for the ilh priority message.
Rather than dealing with all possible transmission times. one solution is to consider
just the longest possible. or worstcase situation. Thus, the maximum delay analysis is
concerned with the worst case scenario. That is, the request happens when a message has
just seized the bus and all individual stations, with higher priority, are generating their
maximum rate of messages. Let Wi be the maximum waiting time for illl priority message.
Fk the length of the frame for the kIll priority message, Mk the maximum message
generation rate for the kill priority message. IFS the time required for an inter frame space
and B the bandwidth of the bus. Then, the maximum waiting time for the i Ih priority
message has been given by Wang, Lu. Hedrick and Stone ( 1992) as.
iI /  1 W
Wi = (F,na. + IF.)' 1) + I( FIc + IFS) + I( FIc + IFS) Mk i
k=O k=O
(68)
The three terms at the right of the equality are respectively from left to right, the blocking
time, the time necessary to transmit all higher priority messages. and the time required to
transmit higher priority messages coming during the waiting time. The above formulation
can be solved for the maximum waiting time. The maximum transmission delay for a
60
particular message is then obtain by adding the maximum waiting time to the time needed
to physically transmit the message in relation with ttie request. One has to note that the
maximum delay analysis is a deterministic value that would provides ab olute certitude
on the upper bound of the transport delay if we had considered the error recovery
mechanism, overload frames, and remote transmission requests. The reader should refer
to Tindell, Burns, and WeI lings (1994) for the proper analysis on the cost of error
handling and remote transmission requests. Since in normal mode of operation these
omissions represent a negligible overhead. the simplified maximum delay formulation is
satisfactory. Nevertheless information on the upper bound is only good for robustness
analysis. Commonly the actual performance is likely to be much better due to interference
averaging of all the communication transactions.
The maximum delay analysis is only useful to guaranty that certain hard deadline
will be meet no mater what. Nonetheless, it is the representation of a very low probability
situation. Thus. the characterization of a message delay can be obtained by assuming
random generation of messages those stati stics are characterized by the Poison
distribution. Similarly the message length is also assumed to be exponentially distributed.
With these two elements in mind, the same reasoning as for the maximum delay analysis
can be carried out, using expectation values in the place of deterministic upper bound
values. This delay analysis model has been developed by Wang, Lu. Hedrick and Stone
(1992). The total expected waiting time for the i1h priority message is given along the
same reasoning and threeterm formulation as in maximum delay analysi s.
61
1 1
F+IFS \ A2)"k 1 1 W.
W; = p + k =O F + L(Fk + IFS)Ak '
2 IlCIl A) k  O B
(69)
The same notation is reused with the addition of.
Ai the average message generation rate of the ith priority message,
IL the expected number of messages the bus can transmit per second.
p the traffic intensity of the network (A/ ~t).
The expected delay analysis results are likely to be closer to the actual experienced
delays than the maximum delay analysis. It is however more difficult to obtain an
accurate expression for the expectation values than it is to obtain the upper bound.
Further. It will be pointed out later in section 3.1 that average performance calculations
do not provide an adequate method for evaluating the bus performance because the bus
traffic is not randomly distributed.
The Priority Setting in CAN
In network scheduling terms, priority is a positive integer representing the urgency
or importance assigned to a message. In CAN the urgency is in inverse order to the
numeric value of the priority. In addition. priority is a static property of the sender of the
message and cannot be changed dynamically. In most realtime systems, there is a
robustness issue and a pertormance issue. To ensure robustness. for every message the
allowed maximum transport delay cannot be exceeded. For performance we want the
62
average data latency to be minimum. To guaranty that the maximum delay requirement of
every message is satisfied. the priority assignment is to be carefully organized. Many
techniques are available for static priority assignment such as, ratemonotonic
(priority=period I), deadline monotonic (priority=deadlineI), or according to the
importance of each type of message. These well known techniques can provide a
workable assignment but do not generate an optimum solution. In CAN the interest is not
only to satisfy all the time constraints but also to create an optimum assignment that will
minimize the average delay of all messages. This "conditional optimum" (or optimum
subject to a set of hard constraints) assignment is based on a systematic search and
sorting of a characterized set of messages and as been described by Wang, Lu and Stone
(1992). The rationale of this technique relies on, putting a task into the lowest priority
position and checking whether a feasible result is obtained. Feasible meaning that, no
hard deadline is violated. I f this fai Is the next higher priority position is considered, and
so on.
63
0'\
~
Bit Stuffing and Bell coding range:
Bil stuffing: the transmiter insert a
complementary bit aft er 5 conseclltive
bits of identical values, the receiver will
th en decode accordinglv
Message Frame
Bus Idlt!
+.
Arbitration Field Control Data Field
SOF
Stan Of Framt:
RTR
Rt:mote
Transmission
Request . Data 0
Request I
Reserved bits
Delimiter
Data Lenght
Code 4 bits
(0 to 8 binary)
BCH Coding
generatorpolynomial
XI5+X 14 +XIO+ X8+X 7 + X4+ X3 + I
the remainder of th is polinamial
division is the CRC sequence
End Of Frame
7 recess ive bits
ACK. EOF Int Bus Idle
Delimiter
Sbl
ACK Slot
Tran smitting station sends 2 recessive bits,
receivers report a valid reception by
superscribing the recessive bit during the
ACK slot
Message Frame 2.0 A Format (Standard Frame)
0\
V\
Message Frame
"
Bus Idle. .:
SOF J
:. Arbitration Fi e~__ ~ontrol ...:.. Data Field , eRe fi eld ...:.. ACI',..:.. EOF ~ In! :... Bus Idle
~...,....,..........    ..........    y ...
Base ID
SRR
Substitute
remote request
Extended ID
18 bit Identifier
RTR
IDE
Identi fier
Extension Bit
r I
rO
Sbl
Message Frame 2.0 B Format (extended frame)
Delimiter
Error Frame:
Data Frame lnterframe Space or
+•.~ 4~··~~O~verTloa~d Frame
Error Frame
Superposition of error flags
Error Flag
I Error delimiter
Lfrom6to121.bits.::.::.::~+_ 8 recessive bits
I
Each station sends recessive bits until it
detects a recessive bus , then it starts
transmiting 7 more recessive bits, 1+7=8
Overload Frame:
Data Frame Overload Frame
Superposition of overload flags
Overload Flag
Over load delimiter
from 6 to 12 bits +. 8 recessive bits
I i
[nterframe spa.ce or
; +OVerload frame
Each station sends recessive bits until it
detects a recessive bit , then it starts
transmiling 7 more recessive bits, 1+7=8
Interframe Space:
Frame Interframe space Frame
3 bits 8 bits
Intermission
Bus Idle Frame
Suspend Transmission (optional,
only for error passive station,
waiting period)
66
VITA
Emmanuel Vyers
Candidate for the Degree of
Master of Science
Thesis: ON THE ANAL YSIS AND COMPENSATION OF NETWORK
INDUCED COMMUNICATION DELAYS FOR DISTRIBUTED
CONTROL SYSTEMS
Major Field: Mechanical Engineering
Biographical:
Personal Data: Born in Denain, Nord, France, on September 15, ] 969, the son of
Roger and Raymonde Vyers.
Education: Graduated from High School. Les Eucaliptus, Nice, France in 1988;
received Bachelor of Science degree in Aerospace Engineering from Florida
Institute of Technology, in May 1995. Will complete the requirements for
the Master of Science degree with major in Mechanical Engineering at
Oklahoma State University in December 1997.