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tkchn;cal report sac
HAVA1 rOSTGHADUATE
UCWOBSY. CAJUFOaMU
NPS62-78-003
NAVAL POSTGRADUATE SCHOOL
Monterey, California
A
BRIEF
SURVEY
OF ADAPTIVE
CONTROL
SYSTEMS
Donald A.
Stentz
March
1978
Final
Rep
ort
for Peric
d May
1977 -
March
1978
Approved for public release ; distribution unlimited
Prepared for:
search and Engineering Department
FEDDOCS /a l Torpedo Station
D 208.14/2:NPS-62-78-003 fport, Washington 98345
NAVAL POSTGRADUATE SCHOOL
Monterey, California 93940
Rear Admiral T. F. Dedman Jack R. Borsting
Superintendent Provost
The work reported herein was supported by funds provided
by the Naval Torpedo Station, Keyport, Washington.
Reproduction of all or part of this report is authorized
This report was prepared by: /\
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4. TITLE (and Subtitle)
A BRIEF SURVEY OF ADAPTIVE CONTROL
SYSTEMS
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"inal for Period
May 1977 - March 1978
6. PERFORMING ORG. REPORT NUMBER
7. AUTHORfsJ
8. CONTRACT OR GRANT NUMBERfaJ
Donald A. Stentz
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Naval Postgraduate School
Monterey, California 93940
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March 1978
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18. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverse aide If necessary and Identity by block number)
Adaptive control systems
Adaptive arrays
Adaptive filters
Index of performance
20. ABSTRACT (Continue on reverse aide It necessary and Identify by block number)
This document summarizes the principles of adaptive control
systems and suggests a number of possible uses of this new
technology on acoustic tracking ranges. A bibliography of
recent literature is included.
DD 1 JAN 73 1473 EDITION OF 1 NOV 65 IS OBSOLETE
S/N 0102-014- 6601 |
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TABLE OF CONTENTS
INTRODUCTION 4
ADAPTIVE CONTROL SYSTEMS DEFINED 5
INDEX OF PERFORMANCE 6
POSSIBLE USES IN ACOUSTIC TRACKING RANGES 9
BENEFITS OF ADAPTIVE SYSTEMS 11
ESSENTIAL PROCESSES OF ADAPTIVE CONTROL 12
ADAPTIVE CONTROL LOOP WITH TWO INPUTS 13
BLOCK DIAGRAM OF TWO SENSOR ADAPTIVE CONTROL SYSTEM ... 14
RECENT RESEARCH ACCOMPLISHMENTS 16
CONCLUSIONS 18
REFERENCE LIST 19
APPENDIX A. REFERENCES 20
INITIAL DISTRIBUTION LIST 30
INTRODUCTION
Historically, targets tracked on acoustic tracking ranges
have been accomplished in an artificially quiet environment.
All except essential ship movement is stopped, the desired
tracking signal is made as strong as possible, arrays are tuned
for the desired sound in both frequency and direction, and all
transmissions and receptions are kept synchronized.
When it is desired to determine how the target or weapon
reacts when operating in a noisy or interfering environment, the
above described methods are not satisfactory. For example: If
a torpedo is being tested for its tracking and detection ability
when being countermeasured intentionally or is being operated in
an environment of heavy shipping, the test range should be able
to track the torpedo in that environment accurately. If a track-
ing system could be designed that would ignore all CM, spectral
ship noise, and even broadband background noise, much more infor-
mation about the torpedo characteristics could be obtained.
Recent developments, including high density solid state circuitry,
may make this a very real possibility. This new technology is
called "adaptive control" and by making use of it could result
in accurate and highly sensitive adaptive range tracking systems.
The following paragraphs indicate the progress made since
about 1966. Parameters used to obtain control in the adaptive
process are defined, and the three processes generally used to
improve the control characteristics over a reasonable period of
time are described.
ADAPTIVE CONTROL SYSTEMS DEFINED
Some systems can be operated in an optimal manner because
the controller parameter /s can be preprogrammed to adapt to the
system's environment. In order to achieve optimum control, the
control parameters are automatically set relative to instanta-
neous environmental conditions encountered at each point in time.
Obviously, the changing environment may be so complicated or
unknown that a reasonable model is difficult to estimate and
evaluate. When no compromise between the design objectives is
possible that will result in an acceptable fixed-parameter sys-
tem, and where preprogrammed adjustments cannot be made due to
a lack of information regarding the system performance with time,
the use of an adaptive control system may be indicated [1].
Eveleigh [1] points out that adaptive control provides a
possible solution to control problems of the following general
form:
"The system to be controlled is normally exposed to a
time-varying environment either in the form of changing
system parameters, input signals and disturbances with
time-varying statistical characteristics, or changing
performance objectives."
Thus an adaptive system is one which measures its performance
relative to some performance characteristic called an Index of
Performance , or IP, and modifies its parameters to achieve
optimum operation.
INDEX OF PERFORMANCE
When designing an adaptive system, it is necessary to
establish uniquely the optimum solutions. Eveleigh suggests
that the concept of an index of performance, or IP, be utilized
and goes on to define some of the more generally accepted IP's.
a. Phase margin (9 ) - the angle between the negative real
axis and the straight line connecting the origin and the point
of intersection of the Nyquist plot and the unit circle.
b. Gain margin (G ) - 1/G , where G is the open-loop trans-
a — mo o r r
fer function magnitude at the frequency when phase lag is 180° .
G is a direct measure of the ratio by which loop gain may
increase before instability occurs. Other factors remain con-
stant of course.
c. Control-loop bandwidth (BW) - this bandwidth may have
to be constrained by making use of filters.
d. Peak frequency (M ) - the maximum magnitude of the closed-
loop system transfer function.
e. Percent overshoot - ratio of peak response minus final
value to final value.
f. Rise time (T ) - time axis projection of a line tangent
to the response curve at its steepest point.
g. Delay time (T^) - time it takes the output to rise to
half its final value.
h. Settling time (T ) - time necessary for the output to
settle and remain within ± five percent of the final value.
i. Steady-state error (E ) - for a unit step input this IP
is a common constraint and is zero for a type-n system, n >_ 1;
and it is (1/K + 1) when K is the open loop gain for a type-zero
system.
j . Mean- square error - perhaps the most used IP is the mean-
square error. It is defined as:
T
ms
lim
T->-o°
i
1/21 e 2 (t)dt
This IP is generally identified as the (LMS) algorithm. e(t) is
the closed-loop control system error.
Each of the above IP's listed have advantages and disadvan-
tages depending on the particular system being adapted and to
what extent optimization is to be obtained. Other IP's that
will not be defined and should be considered when designing an
adaptive system are mentioned below. A complete discussion of
these IP's may be found in reference [1].
a. Integral Squared-Error Criterion, ISE
Integral of Time Multiplied by Squared-Error, ITSE
Integral of Squared-Time Multiplied by Squared-Error,
b
c
ISTSE
d
e
ITAE
f
g
Integral of Absolute Value of Error, IAE
Integral of Time Multiplied by Absolute Value of Error,
Integral of Exponentially Weighted Squared-Error, IExSE
Integral of Modified Exponentially Weighted Squared-
Error, IMExSE
A Eveleigh points out, "It is apparent that an 'optimum
system" is a very subjective term ... in one application fast
initial response or rise time for a step input may be all impor-
tant ... in other cases rapid response may be equally undesir-
able . . . the optimum system is highly dependent upon applica-
tion." When n > 1 parameters are available as choice variables,
a unique solution is only possible when an IP exhibiting an
extreme value at the desired optimum point is used.
If no useful fixed-parameter controller provides acceptable
response of the system's operational envelope, then some means
must be found for adjusting controller parameters that are
sensitive to short-term conditions. If an IP can be selected
which dictates the system's instantaneous or short-term average
performance quality, and if a control-loop can be designed to
optimize the IP automatically by adjusting its parameters, then
the new configuration is called an adaptive control loop. This
adaptive system is actually an effort to extend the basic optimum-
control concept to time-varying systems. It is easily seen then
that the optimum parameter value is not generally determined by
a single set of measurements, but rather it is approached
gradually by a succession of identification, decision, and modi-
fication procedures. This suggests that there is a "learning
curve" associated with each system as a function of time. The
usefulness of a particular system may depend heavily upon the
shape of this learning curve; it could, for instance, preclude
real time processing.
POSSIBLE USES IN ACOUSTIC TRACKING RANGES
The literature concerning adaptive systems cites many
examples for use in missiles, radar antennas, and communications
systems. These examples include control of flight pattern,
turning a "deaf ear" to noise and interference, tracking, and
processing signals in the presence of noise. Very little will
be found concerning how this relatively new technology can be
used on an acoustic tracking range whether one similar to Dabob
Bay or on an at sea range designed for fleet exercises. How-
ever, it seems logical that most of the literature concerning
the above mentioned uses is directly applicable to the under-
water acoustic tracking range. Due to the slowness of sound
velocity in water, the speed of some targets, and ranges desired,
some adjustments would have to be made. It does seem likely that
the basic principles, the IP's, and advantages would apply even
though the parameters may vary widely. It is also quite likely
that the water environment as a propagation medium, sources of
interference, ambient noise level, and other constraints may
prove to be a more difficult medium in which to work when
compared to the radio frequency case most often described. It
would also seem likely that the use of adaptive systems in this
more complicated environment may actually make it unnecessary
to model the environment over a long time period, but only for
the short time required for a single adaptation to be performed.
This is related to the learning curve mentioned earlier. A
measurement (sample) is taken, and on the basis of that value
9
or when compared with an earlier sample or the desired signal,
a decision is made and the adaptive system parameter/ s varied
to produce a new point on the optimization or learning curve.
We, so to speak, gradually sneak up on the optimum operating
point as we learn what is happening from one sample to the
next. This is important because it may ultimately relieve
some of the hard to achieve requirements of the preprogrammed
approach to optimization.
10
BENEFITS OF ADAPTIVE SYSTEMS
What then are the benefits of using adaptive control on the
acoustic tracking range? The most obvious one is to improve the
signal-to-noise ratio of the output of the tracking receiver by
making the adaptive system ignore noise, multipath, or other
interference coming from directions and sources other than that
of the desired target. This is to say improve the S/N ratio by
decreasing noise and interference. For Dabob Bay, this technique
is appealing because by attempting to obtain improvement through
stronger signal sources may result in multipath interference,
reverberation, and detection of unwanted distant target signals.
All this may ultimately leave the S/N ratio unchanged or even
reduced. By holding signal power down and effectively decreasing
noise power, a beneficial effect can be obtained without the
above interference problems arising. It is possible that some
improvement could be achieved by adapting the bandwidth of the
tracking receiver to the desired signal spectrum while the beam
portion is being adapted as well.
11
ESSENTIAL PROCESSES OF ADAPTIVE CONTROL
Figure 1 shows a block diagram of a system and its adaptive
controller. Since the diagram does not identify the system
itself, no mention is made of the type of IP used. It could be
any of the IP's defined or listed earlier. Of great importance
is the sequence of events during a single adaptive event. These
are: identification, decision, and modification. Essentially,
the controller design depends upon the choice of IP, controller
topology, the adjustable parameters of the system, and the
characteristics of the means of response. It may be a replica
of the desired signal. The output response should eventually
match the desired response depending upon the time characteristics
of the system's learning curve.
Input, desired
response or
replica
i Error
/~S, O-MS)
Modification
controller
parameter
"^t settings
7K
Environmental effects causing
significant change in transfer
function of system
Control Systems to be
input
Parameters adjusted
to assure optimum
performance
■^
optimized
jJl
Decision
logic
7TT-
vj IP Measurement
Identification
Output
respons
(Should
eventuall
match desr
response
a c cor dingo
learning
curve. )
FIGURE 1. CONTROL SYSTEM WITH AN ADAPTIVE CONTROLLER
12
ADAPTIVE CONTROL LOOP WITH TWO SENSOR INPUTS
From such a block diagram as shown in Figure 1, it is
difficult to imagine how it would be used in a given system.
Figure 2 shows how the operations could be used to adapt an
underwater array composed of two hydrophones so that the array
and associated adaptive system would optimize the output. B.
and B~ represent beam-steering signals that command the main
beam to "look" or steer in a desired direction, 8 . At the
s
same instant that the beam is steered in the direction desired,
an in terf erring noise occurs in the direction, 9 . Ordinarily,
a side lobe (not shown) would pick up the noise and introduce
it into the processor along with the desired signal, thus
reducing the S/N ratio. The adaptive process will cause the side
lobe in the direction of the noise source to reduce to a null,
thus blocking the noise and resulting in a S/N improvement.
Again, the three essential processes are indicated: identifica-
tion, decision, and modification. For each new sensor added to
the array, an additional adaptive control loop must be added.
It is thus easily seen why solid state circuitry and digital
electronics are used rather than the more involved analog
technology. If it is assumed that B, , the input beam steering
command for hydrophone 1, is a fixed parameter, this signal
weights E-, in such a manner that in conjunction with the signal
from the second hydrophone, E~, amplifier, hard limiter, corre-
lator mixer and integrator, with added weighting given by B 2
will modify the E ? W~ value and ultimately optimize the
13
Desired
Signal
Wavefront
Hydrophone
1
Input bean
steering
command
signal
Interfering
Noise Signal
Wavefront
formed at
§ by adaptive
controller chang-
ing weighting
values
Hydrophone 2
Preamp
Hard
Limiter
Correlation
Mixer
l f OUTPUT
(W^ + W^)
IDENTIFICATION
g Output of hard
limiter freq,
(phase) and
time dependent
only
FIGURE 2. TWO SENSOR ADAPTIVE CONTROL SYSTEM
14
uncorrelated noise or interference signals arriving from the
direction 9 . The same pattern is used if there are signals
arriving from more than two hydrophones . Each control loop would
eventually be added in the summer just prior to the output. The
output would then consist of the sum of the weighted signal
from each sensor in the array. The performance factor of
ultimate interest in an adaptive array is the improvement in the
output SNR as compared to a conventional array subjected to the
same interference conditions [2].
15
RECENT RESEARCH ACCOMPLISHMENTS
Gabriel [2] defines an adaptive array as a system consisting
of an array of sensor elements and a real time adaptive receiver
processor. When given a beam-steering command, it samples the
current environment and automatically proceeds to adjust the
element control weights to optimize (determine by the choice
of IP) the output SNR in accordance with a selected algorithm.
He says that array systems of this type are sometimes referred
to as "smart" arrays. This term is appropriate since the adap-
tive system uses far more of the available information in the
array aperture than does a conventional array.
Widrow [3], [6] describes an adaptive noise canceller con-
figured as a notch filter and realized by an adaptive noise
canceller. Advantages of this method are that it offers easy
control of bandwidth, an infinite null, and the capability of
adaptively tracking the exact frequency of the interference.
This appears to be of value for tracking ranges as it sometimes
becomes necessary to track "keep track of" the unwanted source
of the interference in addition to reducing its effect on the
desired signal. For example: If a countermeasure is attached
to a vehicle, and a null is formed in the direction of the CM,
then it would not be possible to track signals from the CM vehicle
tracking the null would provide the necessary information about
the activities of the CM vehicle while the CM is nulled in the
array aperture. Widrow points out various applications for
using this principle of adaptive noise cancelling among which
16
he includes noise in speech signals, antenna side lobe inter-
ference, and periodic or broadband interference for which there
is no external reference source. Adaptive noise cancelling is
a method of optimal filtering that can be applied whenever a
suitable reference input is available. Widrow and his coworkers
established the least mean square (LMS) algorithm based on the
method of steepest decent. Griffiths [5].
The sensitivity of an array of sensors to interfering noise
sources can be applied whenever a suitable processing scheme
of the outputs of the individual array elements can be found
[4]. The particular combination of array and processing performs
as a filter in both space and frequency. Using the LMS criterion,
Widrow shows the sharpening of the null in the direction of the
noise source as each sample is taken and the learning curve is
forced toward the optimum condition. Tracking a particular tar-
get from among multiple targets seems quite possible when using
adaptive technology. The tracking array positively listens for
the desired target and determines through time of arrival by
taking into consideration the environmental condition and the
last or predicted position of the target.
17
CONCLUSIONS
This report has described the adaptive control system by
defining the most commonly used Index of Performances, IP's, and
discussing the three essential processes, identification,
decision, and modification, that are involved in all such sys-
tems. A block diagram of a system composed of two sensors is
included. A number of possible applications of adaptive systems
that could find use on an acoustic tracking range are discussed.
One of the purposes of this report was to acquaint the reader
with the research being carried on in the field of adaptive
control systems. To help provide a measure of this activity,
several reference lists are included.
It seems quite possible that many of the possible approaches
of adaptive processing may be applicable to the acoustic track-
ing range. These would include tracking improvement, keeping
track of noise and interference sources, reduction of signal
strength thereby reducing multipath and reverberation problems,
communications, and various other signal processing applications
associated with the range operation.
18
REFERENCES
1. Eveleigh, Adaptive Control and Optimization Techniques ,
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2. Gabriel, "Adaptive Arrays - An Introduction," Proc. IEEE,
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Noise Cancelling," Principles and Applications, Proc. IEEE,
Vol 63, No 12, Dec 1975, pp 1692-1716.
19
APPENDIX A
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29
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