JANOS GERTLER, Department of Computer and Electrical Engineering,
George Mason University, Fairfax, Virginia, USA
GERTLER & KEVICZKY (General Editors): A Bridge Between Control
Science & Technology
(Ninth Triennial World Congress, in 6 volumes)
Analysis and Synthesis of Control Systems (1985, No. /)
Identification, Adaptive and Stochastic Control (1985, No. 2)
Large-scale Systems, Decision-making, Mathematics of Control (1985,
No. 3) Process Industries, Power Systems (1985, No. 4)
Manufacturing, Man-Machine Systems, Computers, Components, Traffic
Control,
Space Applications (1985, No. 5) Biomedical Applications, Water
Resources, Environment, Energy Systems, Development, Social
Effects, SWIIS, Education (1985, No. 6) BARKER & YOUNG:
Identification and System Parameter Estimation (1985) (1985, No.
7)
NORRIE & TURNER: Automation for Mineral Resource Development
(1986, No. 1) CHRETIEN: Automatic Control in Space (1986, No. 2) DA
CUNHA: Planning and Operation of Electric Energy Systems (1986, No.
3) V ALADARES TAVARES & EVARISTO DA SILVA: Systems Analysis
Applied to Water and Related
Land Resources (1986, No. 4) LARSEN & HANSEN: Computer Aided
Design in Control and Engineering Systems (1986, No. 5) PAUL:
Digital Computer Applications to Process Control (1986, No. 6) YANG
JIACHI: Control Science & Technology for Development (1986, No.
7) MANCINI, JOHANNSEN & MARTENSSON: Analysis, Design and
Evaluation of Man-Machine
Systems (1986, No. 8) GELLIE, FERRATE & BASANEZ: Robot Control
"Syroco '85" (1986, No. 9) JOHNSON: Modelling and Control of
Biotechnological Processes (1986, No. 10)
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EYKHOFF: Trends and Progress in System Identifica1ion
ISERMAN/\:: System Identification Tutorials (Autonwtira Speria/
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ROBERT MAXWELL Publisher
Proceedings of the 7th IFACIIFIPIIMACS Conference, Vienna, Austria,
17-20 September 1985
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First edition 1986
British Library Cataloguing in Publication Data Digital computer
applications to prorcss control Proceedings of the 7th
IFAC/IFIP/IMACS conference, Vienna, Austria, 17-20 September
1985.-(IFAC proceedings series; 1986, no. 6) l. Pro<.:css
control-Data processing I. Paul, M. II. International Federation of
Automatic Control Ill. Series 670.42'7 TS 156.8 ISBN
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These firoceedings were reproduced by means of the plwto-ojjset
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Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
7th IFAC/IFIP/IMACS CONFERENCE ON DIGITAL COMPUTER APPLICATIONS TO
PROCESS CONTROL
Organized by Austrian Centre for Productivity and Efficiency
(OPWZ)
Sponsored by IF AC Committee on Applications IF AC Committee on
Computers
Co-sponsored by IF AC Committee on Education IF AC Economic and
Management Systems Committee IFIP International Federation for
Information Processing IMACS International Association for
Mathematics and Computers in Simulation
International Programme Committee A. Weinmann, Austria (Chairman)
K. J. Astrom, Sweden D. R. Bristol, USA A. van Cauwenberghe,
Belgium A. A. Concheiro, Mexico G. Davoust, France G. Doolittle,
USA K. H. Fasol, FRG D. Fischer, Austria C. Foulard, France ].
Gertler, Hungary R. Isermann, FRG
National Organizing Committee P. Kopacek (Chairman) ]. Hahne!
(Secretary) W. Karner
P. Kopacek, Austria M. Mansour, Switzerland M. Paul, Austria I.
Plander, Czechoslovakia I. V. Prangishvili, USSR K. Reinisch, GDR
G. Schmidt, FRG V. Strejc, Czechoslovakia T. Takamatsu, Japan ]. D.
Van Wyk, South Africa E. Welfonder, FRG J. H. Westcott, UK
M. Paul A. Weinmann
PREFACE
The IFAC/ IFIP / IMACS Conference on "Digital Computer Applications
to Process Control" in Vienna resumes a series which began in
Stockholm in 1964 and was continued in Menton (1967 ), Helsinki
(1971 ) , Zurich ( 1974), the Hague (1977 ) and Diisseldorf (1980 )
. The aim of this conference is, as of the previous ones, to
present, discuss and summarize recent advances in the application
of digital computers to operation and supervision of industrial
processes. Emphasis is based on the realization of modern control
principles, including advanced monitoring and optimization.
Looking at previous Conferences one can observe that there are
greater efforts in the area of process identification and
modelling. Adaptive and distributed control have become an
essential part of modern control principles. Software, robotics and
data networks become more and more important. Reduction of air and
water pollution caused by industrial processes and at the same time
improvement of production quality require more and more
attention.
The papers of the Conference are divided into four groups:
code
survey papers tutorial papers application oriented papers papers of
general aspects
no. of contributions
6 3
3S 40
The six survey papers summarize the trends, developments and
state-of-the art of adaptive control, dis tributed control
systems, internal model control and process fault diagnosis. Three
tutorial papers give an introduction into state space control as
well as digital control and into digital simulation methods.
The 7S technical papers are assigned to 17 technical
sessions:
code
A8
session
APPLICATION
Chemical and Oil Industries I Water Turbines Chemical and Oil
Industries I I Energy and Power Systems I Energy and Power Systems
I I Robotics and Manufacturing Cement, Metallurgical Processes and
Traffic Heating and Climate Systems
GENERAL ASPECTS
Adaptive Systems I Adaptive Systems I I Control Aspects
Multivariable Systems Optimization and Reliability Modelling and
Identification I Modelling and Identification I I Real Time
Software and Languages Distributed Systems and Data Networks
Vil
s 3
5
40
Vlll Preface
The papers stem from specialists from 21 different countries. It is
hoped that their papers will be a good basis for the Conference and
that their achievements may promote further research and
development in the field of digital compu.ter control.
It is a pleasure to thank the members of the International Program
Committee for their contributions in selecting the papers and for
their suggestions as well as the members of the National Organizing
Committee for their efforts in organizing the Conference.
Furthermore many thanks to the Osterr. Produktivitats- und
Wirtschaftlichkeits-Zentrum for their support in preparation of the
Conference as well as the publisher Pergamon Press in preparing
this book.
Sept. 1985 The editor
THEORY AND APPLICATION OF ADAPTIVE CONTROL
H. U nbehauen
Ruhr University Bochum, Department o/ Electncal Engineering, PO
102118, D-1630 Bochwn 1, FRG
Abstrac t . Systems which automatically adjust their controller
parameters t o compensate for changes in the controlled process or
its environment are referred to as adaptive control systems. This
survey of adaptive control theory and its applications reviews the
progress during the years 1980 till 1984. Different basic
structures of adaptive control systems, including model reference
adaptive controi self-tuning regulators and parame ter scheduling
control are discussed . It is shown that carefully designed
adaptive con trol systems have been used successfully in a broad
variety of application areas.
Keywords. Adaptive control systems; design structures and
principles; recursive process identification; model reference
adaptive control; self-tuning controllers; applications.
INTRODUCTION
In adaptive control the controller settings are au tomatically adj
usted in order to achieve good pro cess operation over a wide
range of conditions. The controller adaption is necessary either
for poorly understood processes or to compensate for unantici
pated parameter changes of the process due to envi ronmental
conditions or unpredictable operating point changes. Thus adaptive
control provides poss:io bilities to control processes with
uncertainties, as e . g . nonlinearities and time-varying
parameters.
Although adaptive control strategies have been dis cussed broadly
during the last 30 years it is only in the last few years that
adaptive control has found real industrial applications. This
situation is based on the one hand on the progress in the de
velopment of powerful adaptive control algorithms which have
reached today a mature state . On the other hand, modern
microelectronics offers cheap hardware which allows an easy
realisation of adap tive control strategies, leading already to
commer cially viable solutions.
This paper is intended both to introduce the non specialist brief
ly to the field of adaptive control and to evaluate the actual
status of this field for the more specialised control engineer .
Therefore , the paper i s organized as follows. First a short
classification and description of adaptive control principles is
given . Then it is shown that most adaptive schemes have nearly the
same structure . The further sections are devoted to a review of
re cent developments of adaptive control schemes and of practical
applications. This review does not in any way claim to be complete
, but tries only to dis cuss the most interesting developments
published during the last four years. Thus this paper is directly
connected to the previous reports of the author (Unbehauen and
Schmid , 1180; Parks et al , 1981).
The realization of modern adaptive control schemes includes a lot
of on-line computational operations. Therefore , adaptive control
algorithms are usually implemented on digital process computers or
micro processors. Thus, as will be discussed later , most
approaches are based on a discrete system represen tation .
BASIC STRUCTURES OF ADAPTIVE CONTROL SYSTEMS
Three main basic control system structures are to day relevant to
the design of adaptive control sys tems ( e . g . Unbehauen, 1985)
- model reference adaptive control (MRAC) , - self-tuning
regulators ( STR) , - parameter scheduling control (PSC) .
All three schemes have in common a basic feedback control loop with
a process and a controller with adjustable parameters. All the
three adaptive stru tures are characterized by automatic adjustment
of the controller parameters to accomodate changes in the process
or its environment ( see Fig . 1).
The adaptive schemes of MRAC and STR are applied to that c lass of
problems where parameter changes .f. of the process are unknown and
cannot be directly obtained from process measurements . The
MRAC-tech nique uses the reference model to specify the de sired
output behaviour y of the process with respect to the reference
signal w. As the reference model is a part of the adaptive control
system, two con trol loops have to be defined . While the inner
loop represents the basic control system consisting of the process
and controller , the parameters of this controller are adjusted by
the outer loop so long until the model error e*=y-yM becomes small
. Thus the basic ( inner ) closed loop system will achieve the spec
ified model performanc e .
The second structure , the STR-technique, is also based on an inner
classical control loop, whereby the parameters of the controller of
this loop are adjusted by the outer loop, which is composed of an
identification block ( usually a recursive estimator) acting on a
decision block and further on a modif i cation block representing
the actual adaptation of the controller parameters. In the second
loop the effect of controller modification is fed back to the
decision process through the basic control loop and the
identification process. Thus an adaptive error forces the
adaptation process to achieve the chosen criterion ( adaptive set
point) .
In many control problems the process changes can be anticipated or
inferred from process measurements. It is then possible to adjust
the controller para meters in a predetermined manner as process
condi-
2 H. Unbehauen
controller parameters
£ action
_______ J ©
y
Fig . 1 . Basic schemes of adaptive control (a) MRAC ; (b ) STR ;
(c) PSC
tions vary . The decision process thus is reduced to a fixed
mapping of the process parameters to the controller parameters,
whereby the original deci sion proces s is already realized in the
design phase of the adaptive control system , e . g . by a "table
look-up" approach different sets of controller para meters are
stored for different operating points of the plant. This strategy
has been originally applied to the adaptation of controller gain
factors and thus has been referred to as "gain scheduling" . How
ever, in order to be more genera l , this approach should be
defined to as "parameter scheduling con trol" ( PSC). This type of
adaptive control struc ture is wide spread and in vogue today,
since it allows one to tune a wide range of controllers using a
manifold of popular on-line process identification methods . To
guarantee a faultness operation of sys tems with the PSC-structure
, a good knowledge of the actual process dynamics is required . The
PSC strategy represents an open-loop adaptation of the controller
paramete>S of the basic inner loop control system, because the
results of the adaptation of the controller parameters are not fed
back to the adap tation unit and thus cannot be corrected .
Principles of design
MRAC- and STC-schemes are both based on s imultaneous process
identification and control . The operation of both these adaptive
techniques can be classified in to two general groups :
- direct (or implicit) adaptive schemes and - indirect (or
explicit) adaptive scheme s .
In a n indirect adaptive control system the unknown
process parameters are explicitely estimated and the adaptive
controller is designed indirectly on the basis of the estimated
process parameters . Usually a discrete model is used for the
recursive estima tion of the process parameters . Therefore the
cal culation for the design of this controller has to be repeated
at each sampling interval , whereby the identification and
controller adaptation are two different procedures . Without
directly identifying the process parameters it is often possible to
iden tify the controller parameters directly . Such an adaptive
control is based on an implicit process model and i s , therefore,
referred to as a direct (or implicit) adaptive controller . This
usually leads to a significant simplification of the adap tation
algorithm .
According to the above definitions the MRAC shown in Fig . l a
represents a direct (or implicit) adap tive controller since its
parameters and its control law are directly updated from the
signals u and y . The STC shown i n Fig . l b i s thus , however,
defined as an indirect (or explicit) adaptive controller .
Although the STC was originally developed for the stochastic
minimum variance control problem (Astr6m and Wittenmark , 1 9 7 3 )
many different extensions have since been made . The self-tuning
principle had also been successfully applied to adaptive control
lers using optimal quadratic cost functions , pole placement
techniques and phase and amplitude mar gins . Thus the
STC-design-principle consists of a combination of or.e of the above
mentioned control ler types and a recursive parameter
identification scheme .
The design of MRAC-systems is usually based on the minimization of
the model error e* as shown in Fig . la . The design problem for
MRAC-systems is thus to determine the structure of the adjustment
mechanism such that the model error e* goes to zero as t-+oo . This
problem had been solved originally by the gra dient method .
However , this approach does not in ge neral guarantee stability .
Therefore, modified ad justment procedures have been proposed
using stabi lity theory . In these approaches the adjustment
mechanism has to be determined such that the over all system is
globally stable , i . e . all signals re main bounded at any time
. The problem of proving global stability in MRAC-systems had been
solved only a few years ago i ndependently by several authors ( e .
g . Goodwin et al , 197 8; Egardt, 1 9 7 9 ; Schmid, 1 9 7 9;
Narendra and Lin, 1 9 7 9 ; Morse , 1 980) .
The design principles mentioned here will be de scribed briefly in
the following . As adaptive con trol is based on simultaneous
process identification and control , the problems of on-line
parameter esti mation must be dealt with primarily . The process
identification and the adaptation mechanisms are usually both
realized by digital process computers . Therefore , the
corresponding systems are described in discrete-time form.
Recursive process identification
Most adaptive control algorithms are based on a linearized process
model , which, for a typical single input/single-output (SISO)
system is given by the linear difference equation
n n yM (k ) = - l avyM (k-v) + l
v=1 v=o b u (k-v) . v ( 1 )
For a realistic description of the process model it is necessary to
include an additional disturbance model as in Fig . 2 , where rs (
k ) is a stochastic noise signa l , which can be thought of to be
genera ted from a white noise signal E (with normal distri bution
and zero mean ) by the noise filter trans fer function
G ( z ) r G* ( z ) . r (2)
Theory and Application of Adaptive Control 3
E(Z)
Fig . 2 . Complete model structure of the process
It follows using z-transformation from Fig . 2 that
Y ( z ) = y ( z ) + G ( z ) E ( Z) . M r ( 3 )
By inserting , Eqs . ( 1 ) and ( 2 ) into Eq . ( 3 ) and mul
tiplying by A ( z- 1 ) we obtain
A ( z- 1 ) Y ( z ) -B ( z- 1 ) u ( z ) = G* ( z ) E ( Z) = V ( z )
' r ( 4)
where V ( z ) is defined as general model error and
- 1 - 1 -n A ( z ) + a 1 z + . . . + a z (5) n - 1 - 1 -n B ( z ) b
+ b1 z + . . . + b z ( 6 ) 0 n
Eq . ( 4) defines an ARMAX-model . Depending on the selection of G;
( z ) all usual model structures are described by this equation (
Unbehauen, 1 982 , 1 985 ) . E . g . the selection of G; ( z ) = l
leads to the least squares (LS ) technique, which will be used for
sim plicity but without loss of generality in the fol lowing
.
Introducing the data vector
(k ) = [ -y (k- 1 ) . . . -y ( k-n ) i u (k- 1 ) . . . u (k-n) ]
T,
and the parameter vector
- n1 n
under the assumption b0=0 (which usually is led for physical
systems ) the output signal tained directly from Eq . ( 4) as
( 7 )
( 8)
( 9 )
The parameter estimation problem is to find a n esti mation£ of
12. using the known data vector (k ) such that the loss function
for N measurements
I = I ( £) n+N I' 2 1 T ! .
2 l E (k ) = 2 £ (N ) £ (N ) = Mm k=n+ l
( 1 0)
becomes minimal. The solution of this minimization problem can be
obtained directly by inserting Eq. ( 9 ) into Eq . ( 1 0) by
collecting N pairs of measure
ments and batch-wise data processing . In adaptive systems the
recursive solution of this problem, how ever , is prefered .
The recursive estimation of the LS-model is given by the following
equations :
.E_ (k+ l )
'.l (k+l )
T - 1 ( k ) (k+ l ) [ ! + ( k+ l ) ( k ) (k+ l ) ]
!'._ ( k ) - '.l (k+ l )T ( k+l ) (k )
y (k+ l ) -T ( k+ l ) .E_ (k ) .
( 1 1 )
( 1 2 )
( 1 3 )
( 1 4)
For the application of this estimation algorithm a suitable choice
of the initial values .E_ (O ) and (O ) must be made. While the
choice of .E_ (O ) is not criti cal , P (O ) should be selected as
a diagonal matrix with large elements , e . g . 1 04 to 1 05 ,
which will cause rapid changes of .E_(k) at the beginning . During
the calculation the values of the diagonal elements are reduced so
that p (k ) changes only slowly . This may lead to convergence of
parameter s . on the other hand for slowly varying process
parameters and for large values of k the algorithm may become
sluggish . This can be circumvented e. g . by introducing a
weighting factor to the matrix P (k+ l ) which can be obtained by
multiplying the r ight hand side of Eq . ( 1 3 ) by the factor 1 /p
(Bauer , 1 977 ) . A very usual and effective procedure is to
choose a constant weight ing factor of 0, 95 :::__ p :::__ 0, 99 ,
whereby recent me asurements are weighted more than older ones .
One draw back of the introduction of the weighting fac tor may
consist in the phenomenon of " estimator windup" . If the process
is operating satisfactorily , the excitation of the process is
small , which means for the expectation
( 1 5 )
Thus according to Eq . ( 1 2 ) q ( k+ l ) =o and from the modified
(weighted) Eq. ( 1 3) follows that
P (k+ l ) = .!:._ P (k ) - p- ( 16 )
grows exponentially , which causes the estimator to become
unstable. If this happens in an adaptive system, momentary
instability of the c losed-loop system may occur . But the
excitation leads again to an improved estimation followed by
improved con trol .
From this brief discussion it follows, that for a practical
computer realization of identification algorithms in adaptive
control systems the user should have a lot of operational
experience for im provements or compromises .
DESIGN OF SELF-TUNING CONTROLLERS (STC)
The original S TC proposed b y Astri:im and Wittenmark ( 1 973 ) is
based on the stochastic "minimum variance" (MV ) -controller . The
design of the MV-controller is based on a process model as shown in
Fig . 2 with the transfer functions
G ( z ) r
1 -
( 1 7 c )
The obj ective of the MV-controller is to minimize the variance of
the output signal under the assump tion that the reference value
w=O :
I
Substituting Eqs . - 1
Y ( z ) = - 1 A ( z ) or
( 1 7a , b ) into Eq. ( 3 )
-d C (z - l ) Z U ( z ) + --- -1 - E ( Z) A ( z )
follows
- 1 -1 B ( z ) U ( z ) + C ( z ) ZdE ( Z) . --_-!- --_-1-
A ( z ) A ( z ) Using the identity
C ( z- 1 ) = F ( z- 1 ) -d K ( z- 1 ) --_-!- + z --_ -1 -
A ( z ) A ( z ) where
-1 F ( z )
- 1 K ( z )
( 1 8)
( 1 9 )
from Eq . ( 1 9 )
- 1 ) Y ( z ) F ( z )iz )
C ( z ) C ( z )
- 1 d ( z ) +F ( z ) zE ( z ) . ( 2 2 )
Applying Eq . ( 1 8) to the predictive form of Eq . ( 2 2 ) leads
to
4 H. Unbehauen
where y* (k+dlkl represents the optimal prediction of y (k+d ) and
y (k+d l k l a prediction error . As y can not be influenced by
the actuating signal u (k ) the minimum of Eq. ( 2 3 ) is obtained
for
- 1 - 1 - 1 y* (k+d l kl = - l { Y ( z) + F ( z ) B ( z ) U ( z )}
= o.
C (z- 1 ) C ( z-1 ) ( 24 )
Under this condition the control law of the MV-con troller
directly follwws as
U ( z ) K ( z -l) ( 2 5 )
where the unknown coefficients of the polynomials F ( z- 1 ) and K
( z- 1 ) are obtained from Eq . ( 2 0) after multiplication with A
( z- 1 ) and by comparing coeffi cients of equal powers in z- 1
.
The MV-controller discussed above can be easily ex panded to
become a self-tuning controller (STC ) . For example, the process
parameters could be esti mated on-line at every sampling interva l
, and can be used to calculate the parameters of the control ler .
This would lead to an explicit STC-scheme . How ever , it is also
possible to estimate directly the controller parameters such that
an implicit or di rect STC-scheme is obtained . This is very
advanta geous because the above mentioned comparison of co
efficients can be avoided .
Introducing
- 1 - 1 F ( z ) B ( z ) - 1 H ( z ) - 1 -m-d+l h0+h z + . . .
+hm+d-lz ( 26 )
where h0 law
using the vector
b 0 v b 0 the signal vector
v [y (k ) . . . y (k-n+l) : u (k- 1 ) . . . u ( k-m-d+l) ] T
I
and
( 2 8 )
( 2 9 )
( 3 0)
The adaptation law for the controller parameters is directly
obtained from the recursive estimation scheme similar to Eqs . ( 1
1 ) to ( 1 4 )
v (k+l) = v (k ) + S!_ (k+l) v (k+l) ( 3 1 )
using the prediction error
T v (k+l) = y (k+l) - v (k ) (k-d+l) - b0u (k-d+l) ( 32 )
wherein S!_ (k+l) and !:_ ( k ) are identical to Eqs . ( 1 2 ) and
( 1 3 ) , and (k ) i s replaced by (k ) .
In this design of the classical STC, current esti mates of the
parameter vector have been accepted ignoring their uncertainties .
This procedure is usually defined as "certainty-equivalent
principle" . Thus the overall algorithm can be considerably sim
plified . The classical STC described above has a number of
disadvantages, e . g . the controller pro duces relatively large
magnitudes of the control variable u. Furthermore this controller
is not di rectly applicable both to non-minimum phase systems , i
. e . the case when B ( z- 1 ) has a zero outside the unit circle ,
and to servo control problems .
There are many ways in which a STC can be designed based on the
MY-principle . A very general approach
to remove the above mentioned disadvantages of the classical STC is
to introduce , as in Fig . 3 the ex tended process output
signal
-1 -1 -d -1 -d Y h( z ) = P (z ) Y ( z ) +Q ( z ) z U ( z ) -R ( z
) z W ( z ) ( 33 )
where P ( z- 1 ) , Q ( z- 1 ) and R ( z-l) represent stable filter
transfer functions . Completely analogous to Eq . ( 27 ) a control
law with the same structure can be derived as
u (k ) = - (k) (k ) , hho
( 34 )
i n which the extended and m contain the infor mation about the
additional fi1'ter transfer func- tions and the reference signal w
.
Self -tuning algorithm
Fig . 3 . STC-scheme using filtered signals
Self-tuning controllers as described above, in gene ral can be
formulated by two laws :
a ) contro l law
u (k ) = -£!(k ) (k ) , ( 35 )
where E_ (k ) represents the estimated vector o f controller
parameters and the measurement vector (k ) contains all information
about the signals in the control loop .
b ) adaptation law
p ( k ) = p ( k-l) +P (k- 1 ) (k ) c (k ) =--s =-s --s -s s ( 36
)
where (k ) i s a regression vector obtained from sensed signals
within the control loop and Es (k ) is the prediction error . For
the recursive LS estimator both these variables and the matrix
!'..s (k ) can be obtained directly from Eqs . ( 1 1 ) to ( 1 4 )
.
During the last few years considerable progress has been made in
the theoretical treatment of ST-con trollers: especially many
efforts had been made to solve the stability and convergence
problems . It is possible to find sufficient conditions for
stabilit however , necessary and sufficient conditions are so far
not available for STC . Convergence of the para meter vector Es
means that the parameters converge to the values that would be
obtained if the actual process parameters would exactly be known .
As al ready discussed above there are several possibili ties to
improve convergence within the parameter estimation according to Eq
. ( 3 6) . Other theoretical problems are related to the robustness
of STC , i . e . the situation, wherein the assumed process model
structure is incorrect or the process changes its operational
conditions . The theoretical results of robustness analysis of STC
, available today , are still not satisfactory .
DESIGN OF MODEL-REFERENCE ADAPTIVE CON TROLLERS (MRAC )
As already mentioned above the key problem on MRAC-
Theory and Application of Adapt iYe Control 5
systems is that the model error e*=y-yM ( see Fig . la ) becomes
small o r even zero . Therefore a n adjustment mechanism has to be
determined to solve this prob lem. Many methods have been proposed
for the solu tion of this nontrivial problem . The first attempt
is due to Whitaker et al ( 1 958) , who used the gra dient method
for the continuous adaptation of the controller parameters
(MIT-rule) :
dl2_
dt = -an(£)' ( 37 )
where the performance index I (p ) is assumed t o be a function of
model error e* ( t ) ,
- e . g . the mean square
model error , which has to be minimized :
2 I
I ( l2_) = f [ e''(t , )2_) ] = e* ( t ,p ) ,; Min . ( 38 )
Inserting E q . ( 38 ) into E q . ( 37 ) and then integrat ing
this equation gives the adaptation law
t l2_ (t ) = )2_ ( 0) - 2a J e* ( T) ( T, l2_) dT
0 where the sensitivity vector
contains the partial derivations
( 39 )
( 40)
of the process output signal in accordance with the controller
parameters pi , and the bar on the inte gral signifi es the mean
value. The sensitivity func tions vi (t , )2_) can easily be
generated under the as sumption of slowly varying parameter s ,
from the filtered reference variable w ( t ) as
( 4 1 )
where G and G are the transfer functions o f the controler and5the
process respectively . From Eq. ( 4 1 ) it follows that the filter
network contains a model of the inner loop, which is defined as
sen- ' sitivity mode l . The principal block diagram of the
complete MRAC-scheme based on the gradient approach is shown in
Fig. 4 . Although the structure of this adaptive scheme is
relatively simple to understand ,
w
____ _, model
+
2ae*
Fig . 4 . MRAC-scheme based on the gradient approach
it has one great disadvantage because the overall stability is not
guaranteed depending heavily on the selection of the gain parameter
a. Therefore, modified adaptation laws had been derived using s
tabi lity theory . These rules provide very similar adaptation laws
as shown by Eq. ( 39 ) , however , the sensitivity functions are
replaced by other ex pressions . Such approaches provide for the
deter mination of the adj ustment mechanism in such a way that the
overal l system is globally stable. This means that the plant input
and output signals u (t )
and y ( t ) respectively remain bounded for all time and thus
either the model error e* or the state error vector * converges to
zero . This problem had been solved independently by several
authors during the last few years . Ljapunov ' s stability theory
and Popov ' s hyperstability method have been extensively applied
to MRAC-systems , both with state feedback and output feedback
.
The main idea in applying stability theory to MRAC systems is to
transform the highly non-linear adap tive system to the standard
form of a non-linear " error system" as shown in Fig . 5, where the
model
G (s/z)
Fig . 5. Non-l inear standard "error system"
error e* either in continuous or discrete form re presents the
output signal of a linear time inva riant system, described by the
transfer function G , while F contains all non-linear and
time-variant subsystems . This structure has the advantage that the
stability of the overall MRAC-system can be ob tained from the
individual properties of the linear and non-linear subsystems , e.
g . the linear subsystem must be strictly positive real ( s . p . r
. ) . Thus the output error
e* = cT e* ( 4 2 )
or the elements e o f the state error vector
-* [-* -* -*] T = el . . . e£ . . . en ( 43 )
can i n general be represented b y a nonlinear time varying
differential equation of the form
( 4 4a )
E ( k+ l ) = f 1 [ E ( k ) , R(k), k] , ( 44b)
where E can be replaced either by e* or*, and is either the
parameter vector or the corresponding parameter error vector of the
adaptive controller , for which the adaptation law
or
t (t ) = ( 0) - f !_2 [ E ( T) , T]dT ( 45a )
0
(k) = ( k- 1 ) - !_2 [ E ( £) , k] ( 45b )
must be developed , such that all signals are uni formly bounded
and
lim E ( t ) = 0 t-+oo
( 46 )
using a l l available data . The function !_2 in Eq. ( 45 ) can be
obtained either by estimation or from filtered process measurements
.
In order to obtain a causal control law
u ( t) = T - (t ) (t ) ( 47a)
T ( 47b) u (k) = -(k) R ( k ) ,
which i s linear in the parameters , it is usually necessary to
introduce filters for filtering the model error and eventually to
augment the model error by adding auxiliary signals . Thus E
becomes an "augmented" error signal. To ensure stability the vector
' which in general contains functions
6 H. Unbehauen
of the process input and output signals , must be ge nerated to
ensure boundedness of u and y and asymp totic convergence of E
.
Adaptive control laws such as Eqs . ( 45) and ( 47 ) can be derived
in a number of different ways , but are not discussed in detail
here for the sake of brevi ty . However , it should be mentioned
that the general adaptation law of Eq . ( 4 5 ) includes in the
expres sion !_2 a multiplicative connection between the er ror E
and some regression vector '-.0 which is in ge neral represented
by functions of u and y similary to !!2MR• see e . g . Unbehauen (
1 985) . Thus Eq. ( 3 9 ) i s also included i n this law.
The discussion of MRAC-systems shows by comparing Eqs . ( 45 ) and
( 4 7 ) with Eqs . ( 35) and ( 36) that the basic structures of STC
and MRAC are nearly the same, although the background of MRAC was
the servo con trol problem, whereas the STC originally had been
designed for the stochastic regulation problem. Both principles are
characterized by two feedback loops . However the design principles
of these two loops are different .
DEVELOPMENTS IN THEORY DURING 1980- 1984
It is beyound the scope of this paper to describe the development
in the theory of adaptive control during the earlier years in
detail . Only a few main topics can be treated briefly . For a long
time the problem of s tabi lity had not been solved satisfac
torily . Basic contributions to guarantee global sta bility have
been published by 1980 by different authors , e . g . Narendra et a
l . ( 1 980 a , b ) , Goodwin et a l . ( 1 980) ( see Table 1 ) .
Thus it is possible to design adaptive control systems with
guaranteed stability properties , Unbehauen ( 198 1 ) . Conditions
for the exponential convergence of the adaptation laws of
controller parameters have been derived by
Anderson and Johnson ( 1 982 ) . A necessary condition for
convergence of the estimated controller parame ters is that the
process input is persistently ex citing . Sin and Goodwin ( 1 982
) proved the global convergence of a modified rec ursive
LS-algorithm . In the case of stochastically disturbed systems the
application of the martingale theory provides rea sonable results
( Landau 1982c ) .
Robus tness of adaptive control systems means the preservation of
stability or boundness properties when ideal conditions are not met
( Ioannu and Koko tovic , 1984 ) . The usual assumptions that
there are no disturbances and that the plant order is not higher
than the model order are very unrealistic . Bounded disturbances
and unmodelled dynamics make the basic adaptive scheme unstable.
Several propo sals had been made to modify, therefore, the adap
tation laws . The aim is to prevent instability by counteracting
the parameter drift through eliminat ing the integral action of
the adaptation law . If an upper limit of the disturbances is
known, the stability of the system can be guaranteed by intro
ducing a "dead zone" into the adaptation law ( Peter son and
Narendra 1982 ) . Ioannu ( 1 983a) , Ioannu and Kokotovic ( 1 984 )
introduced the so-called a-modifi cation of the adaptation law in
order to obtain sta bility of the adaptive system under the
influence of limited disturbance magnitudes . Within this ap
proach the usual integral parameter adaptation law, e . g .
according to Eq. ( 45) ,
l2_ ( t ) = -!_2 (t ) ( 48a)
or
is replaced by
l2_ (t ) -0.!2_ ( t ) - !.2 ( t ) a > o ( 49a )
.!2_ (k ) a2 ( k- l ) - !.2 (k ) I a I < 1 ( 49b)
This modification should be applied only if the norm of the
parameter vector exceeds some a priori defined value II .Ell >
N0• In this case simple stabi lity is guaranteed for stochastic
disturbances and errors for unmodelled high-frequency modes of the
proces s . Thus the stability of adaptive control systems using
reduced-order models is obtained .
Another idea for robust adaptive control systems , proposed by
Narendra and Annaswamy ( 1 984 ) , is based in the sufficient
excitation of signals . Rohrs and Shortelle ( 1 984 ) introduce
spec ial filters which provide that high-frequency modes of the
process are included in damped form in the adaptation law .
The formal extension of single-input/single-output adaptive control
systems to multivariab le structures using parameterization issues
( see e .g . Elliot and Wolovich, 1 984 ) includes some
difficultiP.s in re spect of the dead-time, which can be separated
into an input and output portion . Hahn ( 1 98 3 ) introduced a
systematic approach for this sepaation .
Whereas most design procedures of adaptive control systems are
based on unknown but linear and time invariant systems only a few
papers deal with non linear and time-varying processes . Goodwin
and Teoh ( 1 98 3 ) investigated the convergence of a modified
LS-algorithm for time-varying systems , which had been successfully
applied to processes with jump parameters and drift parameter s .
Mosca and Zappa ( 1 982 ) presented an interesting extension of a
STC system for processes with variable dead-times , using parallel
operating estimation algorithms .
Many contributions have been published on different aspects of
adaptive control s tructures. Several papers are devoted to new
structures which repre sent combinations and modifications of
already known adaptation algorithms using appropriate detectors for
changeover switching. Other aspects such as
adaptive sampling (de la Sen , 1 984 ) , special design schemes
based on quadr•atic cost functions and pole p lacement have been
reported . Extensions of the adaptive control principle deal with
multi-loop cascaded structures (Gawthrop , 1 984 ) and with the
introduction of hybrid adaptive control structures ( see e. g .
Narendra et al . , 1 98 3 ) . In principle the hybrid structures
consist of a continuous control system combined with a discrete
parameter estimation scheme. However in practice these systems are
digi tally realized by different sampling rates for the control
and the adaptation law .
Numerous papers touch upon more general problems for STC- and
MRAC-sys tems. Especially the design of non-minimum phase adaptive
control system has been of great interest ( e . g . Noth, 1 982;
Hahn, 1983; Clarke, 1 984 ) , whereby the introduction of special
correction networks parallel to the process provided high
advantages for a stable design . Landau et a l . ( 1 983 ) show a
variety of possibilities to deal with this problem .
For a broad break-through of adaptive control sys tems in
industrial appliacations it is necessary to provide simple adaptive
control ler structures. Se veral proposals and already some
industrial solu tions are available today . Astr6m and Hagglund (
1 984 ) describe an interesting solution based on an adaptive
PID-controller . Introducing a known non linearity and then
applying the describing function method the critical gain and
frequency of the limit cycles can be obtained on-line. Thus the
Ziegler Nichols rules for on-line tuning of the controller
parameters can directly be applied .
Very little experience is available up to now with adaptive control
theory of large scale sys tems s truc tures and distributed
parameter sys tems. Ioannou and Kokotovic ( 1 983b) show that the
<J-modification of the adaptation law can be used also in the
case
Theory and Application of Adaptive Control
TABLE 1 Papers dealing with theoretical aspects of adaptive control
systems
Survey papers and books : Narendra & Monopoli ( 1 980) ,
Unbehauen ( 1 980) , Harris & Billings ( 1 98 1 ) , Goodwin
& Ramadge ( 1 98 1 ) , Alix et a l . ( 1982 ) , Isermann ( 1
982 ) , Landau ( 1 982b) , Astrom ( 1 983) , Elliot ( 1 983) ,
Landau ( 1 983) , Goodwin & Sin ( 1 984 ) , Voronov &
Rutkovsky ( 1 984 ) , Wittenmark & Astrom ( 1 984 ) .
7
Stabi lity : Astrom ( 1 980) , Gawthrop ( 1 980a ) , Goodwin et al
. ( 1980) , Fuchs ( 1 980) , Morse ( 1 980) , Narendra et al . ( 1
980a ) , Narendra & Lin ( 1 980b ) , Lozano & Landau ( 1 98
1 ) , Dugard et al . ( 1 982 ) , Kreiselmeier & Narendra ( 1
982 ) , Landau ( 1 982a) ,de Larminat ( 1982 ) , Kosut ( 1 983a , b
) , Kosut et a l . ( 1 983) , Samson ( 1 983) , Christi ( 1984)
Kung & Womack ( 1 984 ) .
Convergence : Goodwin et a l . ( 1 981 ) , Osorio-Cordero &
Mayne ( 1 98 1 ) , Johnstone & Anderson ( 1 982 ) , Anderson
& Johnson ( 1 982 ) , Dugard et a l . ( 1 982 ) , Landau ( 1
982c ) , Sin & Goodwin ( 1 982 ) , Sternby & Rootzen ( 1
982 ) , Good win et a l . ( 1 983) , Boyd & Sastry ( 1 984 ) ,
Goodwin et al. (1984 ) , Kumar ( 1 984 ) , Moore ( 1 984 ) .
Robus tness : Gawthrop & Lim ( 1 982 ) , Johnson & Goodwin
( 1 982 ) , Kreisselmeier & Narendra ( 1 982 ) , Lim ( 1 982 )
, Peterson & Narendra ( 1 982 ) , Shah & Monopoli ( 1 982)
, Bar-Kana & Kaufmann ( 1 983) , Ioannou ( 1 983a) , Ioannou
& Kokotovic ( 1 983a) , Praly ( 1 983a , b ) , Chen & Cook
( 1 984 ) , Christi ( 1 984 ) , Fuji et al , ( 1 984 ) , Ioanrou (
1984 ) , Ioannou & Kokotovic ( 1 984a , b ) , Kokotovic &
Riedly ( 1 984 ) , Kosut & Johnson ( 1 984), Krause ( 1 984 ) ,
Narendra & Annaswamy ( 1984 ) , Rohrs & Shortelle ( 1 984 )
.
Mu ltivariab le sys tems : Goodwin et a l . ( 1 980) , Koivo ( 1
980) , Lu & Yuan ( 1 980) , Bayoumi et a l . ( 1 98 1 ) ,
Kevicz ky & Kumar ( 1 98 1 ) , Koivo et a l . ( 1 98 1 ) ,
Prager & Wellstead ( 1 981 ) , Wonq & Bayoumi ( 1 981 ) ,
Elliot & Wolovich ( 1 982 ) , Favier & Hassani ( 1 982 ) ,
Hahn & Unbehauen ( 1 982 ) , Morris et a l . ( 1 982 ) ,
Okohawa & Yonezaewa (l'HJ2), Zinober et al . (l'Jl:l:!), Hahn (
l'Jl:l3) , Bar-Kana & Kaufmann ( 1 984 ) , Bezanson& Harris
( 1 984 ) , Dion & Lamare ( 1984 ) , Dugard et a l . (1984a , b
) , Djaferies et a l . ( 1 984 ) , Elliot et a l . ( 1 984 ) ,
Elliot & Wolo vich ( 1 984 ) , Grimble ( 1 984 ) , Lee &
Lee ( 1 983 ) , Tsiligiannis & Svoronos ( 1 984 ) .
Nonlinear and time-varying processes : Anbumani et a l . ( 1 98 1 )
, Lachmann & Goedecke ( 1 982 ) , Pajunen ( 1 982 , 1 983) ,
Anderson & Johnstone ( 1 983) , Goodwin & Teoh ( 1 983) ,
Mosca & Zappa ( 1 983) , Balestrino et a l . ( 1 984 ) , Kung
& Womak ( 1 984 ) , Urwin & Swanick ( 1 984 ) , Xianya
& Evans ( 1984 ) .
Contro l s tructures
A. A lgorithms (combinations and modifications) : Goodwin et a l .
( 1 980) , Lozano ( 1 982 ) , Sin & Goodwin ( 1 982 ) , Gupta
et a l . ( 1984 ) , Hagglund ( 1 984 ) , Holst & Paulsen ( 1
984 ) , Lam ( 1 984 ) , Milnert ( 1 984 ) , Moore & Bo el (
1984 ) , Radke & Isermann ( 1 984 ) , Silveira & Doraiswami
( 1 984 ) , Stankovic & Radenkovic ( 1 984 ) .
B. Samp ling prob lems : de la Sen ( 1 984a, b ) , Kanniah et al. (
1 984a , b ) , Kanniah & Malik ( 1 984 ) .
C. Variab le dead time : Kurz & Goedecke ( 1981) , Fuchs ( 1 98
2 ) , Vogel & Edgar ( 1 982a , b ) , Costin & Buchner ( 1
983) , Mosca & Zappa ( 1 983) , Chien et a l . ( 1 984 )
.
D. Structures based on quadratic performance i ndex : BOhm et a l .
( 1 984 ) , Grimble ( 1 984a , b ) ,Halme & Ahava ( 1 984 ) ,
Makila ( 1 984 ) .
E. Structures based on pole p lacement: Astrom & Wittenmark ( 1
980) , Tsay & Shieh ( 1 98 1 ) , Clarke ( 1 982 ) , Elliot ( 1
982 ) , Hesketh ( 1 982 ) , McDermott &Mellichamp ( 1 984 ) ,
Djaferi s et al . ( 1 984 ) .
F. Cascaded s tructures : Gawthrop ( 1 984 ) .
G. Hybrid s tructures : Gawthrop ( 1 98Cb) ,Christi ( 1 982 ) ,
Christi & Monopoli ( 1 982 ) , Elliot ( 1 982 ) , Narendra et
al . ( 1983) .
H. Se lf-tuning structure s : Astrom & Wittenmark ( 1 980) ,
Allidina & Hughes ( 1 980) , De Keyser & van Cauwen berghe
( 1 981 ) , Fjeld & Wilhelm ( 1 98 1 ) , Fortescue et a l . ( 1
98 1 ) , Grimble ( 1 98 1 ) , Radke & Isermann ( 1 984 ) ,
Warwick ( 1 981 ) , Wellstead & Sanoff ( 1 98 1 ) , Clarke ( 1
982 ) , De Keyser & van Cauwenberghe ( 1 982 ) , Gawthrop ( 1
982a , b ) , Grimble ( 1 982 ) , Noth ( 1 982 ) , Ortega ( 1 982 )
, Wellstead & Zanker ( 1 982 ) , Allidina & Hughes ( 1 983)
, Hoopes et a l . ( 1 983) , Toivonen ( 1 983a , b ) , Clarke ( 1
984 ) , Matko & Schumann ( 1 984 ) .
I. Mode l reference structures: Johnson ( 1 980) , Shah &
Fisher ( 1 980) , Landau & Lozano ( 1 98 1 ) , Lozano &
Lan dau ( 1 981 ) , Unbehauen ( 1 98 1 ) , Landau ( 1982 ) ,
Ambrosino et a l . ( 1 984 ) , Bar-Kana & Kaufmann ( 1 984 ) ,
Gupta et a l . ( 1 984 ) , Kennedy ( 1 984 ) .
K. Simp le contro l ler s tructures : Glattfelder et a l . ( 1 980)
, Wittenmark & Astrom ( 1 980) , Andreiev ( 1 981 ) , Clarke
& Gawthrop ( 1 981 ) , Astrom ( 1 982 ) , Banyasz &
Keviczky ( 1 982 ) , Gawthrop ( 1 982a) , Bristol ( 1 983) ,
Cameron & Seborg ( 1 983) , Dexter ( 1 983) , Hawk ( 1 983) ,
Hetthesy et a l . ( 1983) , Keviczky & Banyasz ( 1 983) ,
Unbehauen ( 1 983) , Astrom & Hagglund ( 1 984 ) , Halme &
Ahava ( 1 984 ) , Nishikawa et al. ( 1 984 ) .
L. Large scale sys tems s tructures : Costin & Buchner ( 1 983)
, Ioanmu ( 1 983) , Ioanmu & Kokotovic ( 1 983) .
f\1. Dis tributed parameter systems s tructure s :Balas ( 1 983) ,
Hulko et al. ( 1 983) .
of decentralized adaptive control . Especially in the field of
modern process control these problems of large scale adaptive
control structures have to be solved in the future.
APPLICATIONS DURING 1 980- 1 98 1
The following discussion on applications of adaptive control
systems does not c laim to be complete. How ever the discussion
wil l include the most represen tative papers published in
different fields of appli cation . The discussion is directed to
Table 2, in which the main applications fields are SlllilIIlarized
.
In the classical aerospace field interesting appli cations have
been made for the adaptive control of large scale structures in
space (Balas and Johnson, 1 980) . Because of the broad application
of robotic sys tems in production lines these systems demand high
positioning accuracy . This can be obtained by adaptive control in
robotic manipulators ( Koivo , 1 983; Neumann and Stone, 1983) .
Both STC- and MRAC systems are broadly applied .
Chemical indus try has become one of those fields, where adaptive
control schemes have been introduced most successfully and most
widely . Various types of chemical reactors have been equiped with
adaptive controllers. In distillation columns multivariable
8 H. U n bchauen
TABLE 2 Papers dealing with applications of adaptive control
systems
Survey papers and books : Belanger ( 1 980, 1 982 ) ' Narendra
& Monopoli ( 1 980) ' Parks et a l . ( 1 980) , Unbehauen &
Schmid ( 1 980) ' Harris & Billings ( 1 98 1 ) ' Unbehauen ( 1
98 1 ) ' de Keyser & van Cauwenberghe ( 1 982 ) ' Azab &
Nouh ( 1 98 3 ) ' Bristol ( 1 98 3 ) ' Clough ( 1 983 ) . Seborg et
al . ( 1 983 ) .
Air craft and space : Balas & Johnson ( 1 980) ' van den Bosch
& Jong kind ( 1 980) ' Kreiselmeier ( 1 980) ' Rynaski ( 1 980)
' Stein ( 1 980) ' Young ( 1 98 1 ) ' Balas ( 1 98 3 ) ' Bar-Kama
& Kaufmann ( 1 983 b ) ,Harvey ( 1 98 3 ) .
Robotics : Cao ( 1 980) ' Morris & Neuman ( 1 98 1 ) ' Hondered
( 1 98 3 ) ' Koivo ( 1 98 3 ) ' Neumann & Stone ( 1 98 3 ) '
Neumann & Tourassio ( 1 98 3 ) ' Tomizuka & Horowitz ( 1
983 ) ' Lee & Chung ( 1 984) ' Nicosia & Tome ( 1984) '
Vukobratovic et al . ( 1 984 ) .
Chemical industry
A . Extension: Englander ( 1 98 3 ) .
B. Reactors : Bergmann & Radke ( 1 980) ' Harris et al . ( 1
980) ' Clarke & Gawthrop ( 1 98 1 ) ' Hallager & Jorgen-
sen ( 1 98 1 , 1 983 ) ' Yang et al . ( 1 981 ) , Clurett et a l .
( 1 982 ) ' Hodgson & Clarke ( 1 982 ) ' Saxon & Glover ( 1
982 ) ' Kiparissides & Shah ( 1 983 ) ' Koutchoukali et a l . (
1 983a , b ) , McDermott et a l . ( 1 984 ) .
c. Dis ti l lation: Dahlquist ( 1 980) ' Morris et al . ( 1 98 1 )
' Chien et a l . ( 1 98 3 ) ' Gerry et al . ( 1 983 ) ' Wiemer et a
l . ( 1 983 ) ' Dahhou et . a l . ( 1 984 ) ' Martin-Sanchez &
Shah ( 1 984 ) ' Yang & Lee ( 1 984 ) .
D. Evaporation: Bucholt & Kummel ( 1 98 1 ) ' Martin-Sanchez et
a l . ( 1 98 1 ) ' Ellis ( 1 982 ) ' Song et al . ( 1 984 ) .
E. PH-neutra lisation: Bergmann & Lachmann ( 1 980) ' Jacobs et
a l . ( 1 980) ' Goodwin et al . ( 1 982 ) .
Paper indus try : d ' Hulster et al . ( 1 980) ' Fj eld &
Wilhelm ( 1 98 1 ) , de Keyser & van Cauwenberghe ( 1982 ) '
Sikora et a l . ( 1 984 ) .
Therma l processes : Haber et al . ( 1 980) ' Kurz et al . ( 1 980)
' Moden & Nybrant ( 1 980) ' Dahhou et al . ( 1 981, 1983 ) '
Dexter ( 1 981 ) ' Haber et a l . ( 1 98 1 ) ' Naj im et a l . ( 1
982 ) ' Radke ( 1 982 ) , Schumann ( 1 98 2 ) ' Lozano &
Bonilla ( 1 98 3 ) .
Cement industry and mineral processes : Westerlund et a l . ( 1
980) ' Westerlund ( 1 98 1 ) ' Rugot & Sauter ( 1982 ) .
Ste e l and meta l lurgical indus try : Desrochers ( 1 98 1 ) ' Yui
& Sato et al . ( 1 984 ) .
Power p lants and power sys tems : Bonami & Guth ( 1 980) '
Glattfelder & Schauf elberger ( 1 980) ' Irving et a l . (
1980a , b ) , Mehra et a l . ( 1 980) , Allidina e t al . ( 1 98 1
) ' Hamza et al . ( 1 982 ) ' Hahn et a l . ( 1 982 ' 1983 ) ' Amin
et al . ( 1 984 ) .
Electromechanical systems : Bonami & Guth ( 1 980) ' Green et a
l . ( 1 980) ' Morris & Neumann ( 1 98 1 ) ' Hahn et a l . ( 1
98 2 , 1 983 ) ' Balestrino et a l . ( 1 983 ) ' Brickwede ( 1 9 8
3 ) ' Hondered ( 1 983 ) , Hanus ( 1 983 ) ' Zohdy et a l . ( 1 983
) .
Position contro l : Claussen ( 1 980) ' Gutmann et a l . ( 1 980) '
Haque & Monopol i ( 1 980) .
Ship steering: van Amerongen ( 1980, 1 981 , 1 982 ) ' Cuong &
Parson ( 1 9 8 1 ) ' Fung & Grimble ( 1 98 1 ) ' Mort &
Linkens ( 1 98 1 ) ' van Amerongen et a l . ( 1 983 ) ' van
Amerongen & Hondered ( 1 983 ) .
Combusting engines and compressors : Wellstead & Zanker ( 1 98
1 ) ' Morris et a l . ( 1 983 ) ' Subbarao & Huntly ( 1983 ) '
Fuj ii et a l . ( 1 984 ) .
Misce l laneous areas : Behar & I nfante ( 1 98 3 ) ' Fjeld et
a l . ( 1 983 ) ' Makila & Syrj anen ( 1 983 ) ' Dochain &
Bastin ( 1 984 ) ' Kaufmann et a l . ( 1984 ) .
adaptive control systems provide a higher product quality and a
considerable reduction of thermal energy ( e . g . Wiemer et a l .
1 98 3 ) . Other applications of adaptive control system in
evaporation and pH value neutralization processes point out that
these techniques are now wel l beyond the theoretical stage in
chemical industries.
Interesting examples for practical applications of adaptive control
are reported from paper industry, e . g . for the moisture control
( Sikora et a l . 1 984 ) and from the broad field of thermal
processes, wherein adaptive systems have been installed success
fully in phosphate drying ( e . g . Dahhou et al . 1 98 1 , 1 982 )
, i n rotary dryers, glass furnaces (Haber 1980), heating plants
(Dexter 1 98 1 ) and air heating sys tems.
Only a few applications of adaptive control are in the fields of
cement industry and mine ral processes as well as steel indus try
and metal lurgical proces ses . An interesting example deals with
adaptive con trol of strip temperature for the continuous anneal
ing and processing line (Yui and Sato , 1 984 ) .
In power systems a few c learly defined singular problems as e . g
. compensation of reactive power ( Zohdy et al . 1 983 ) , control
of synchronous gene rator ( Hanus 1 983 ) and of turbogenerators
(Bonami and Guth , 1 980; Hahn et a l . 1 98 2 , 1 983 ) , power
net work control (Irving 1 980a , b) , power plant boi ler (Amin
et a l . 1 9 84) , nuclear (Mehra et al . 1980 ; Al lidina et a l
. 1 98 1 ) and hydro power control (Glatt felder and
Schaufelberger , 1 980) have been solved by adaptive control
schemes.
Applications of adaptive control systems have also been reported
from the field of e lectromechanical devices and position control
such as e . g . a radio telescope (Haque and Monopoli , 1 98 0) .
Various papers report on successful implementation of adaptive con
trol schemes for ship s teering and manoeuvring ( e . g . van
Amerongen 1 980, 1 98 1 , 1 982 ) . Also in combus tion engines and
compressors adaptive control systems seem to be very advantageous
for an economic opera tion .
Interesting applications of adaptive systems had been made in misce
llaneous areas such as sugar in dustry (Behar and Infante , 1 983
) , r iver regulation (Fjeld et a l . 1 98 3 ) , film thickness
control (Makila
Theory and Application of Adaptive Control 9 and Syrj anen, 1 983 )
, control of drug infusion rate (Kaufmann et al . , 1984 ) and
bacterial growth (Dochain and Bastin, 1 984 ) .
This very brief discussion shows the surprisingly broad area of
applications of adaptive control sys tems. Obviously more
heuristic ad hoc solutions are becoming rare , whereas most
applications are based today on well established approaches of
modern adap tive control theory. In special cases, however , the
theoretical standard approaches have to be slight ly modified to
overcome special demands of the prob lem .
It should also be mentioned that adaptive control schemes can not
yet be applied routinely by an in experienced engineer . A lot of
design specifications including as much as possible
11a-priori11-knowledge about the process must still be regarded .
In addi tion, various practical aspects for implementation of
adaptive control schemes, including e . g . robust ness, signal
conditioning , parameter tracking , esti mator wind-up , reset
action, start-up etc . have to be considered by the user ( see e .
g . Wittenmark and Astrom, 1 984 ; Goh and Bunn, 1 984 ) .
CONCLUSIONS
Adaptive control theory has reached today a high degree of maturity
. A lot of powerful design me thods are available now for the
experienced control engineer , including also computer-aided design
packages for adaptive controllers (Schmid 1985 ) . The numerous
applications of adaptive control systems in a broad area of
technical fields, discussed in the previous section , indicate that
adaptive control can be successfully used in many situations. How
ever, the inexperienced user still cannot apply a daptive control
schemes, routinely, because adaptive control structures offer
usually a great number of inherent degrees of freedom . In order to
make adap tive control still more accessible to many control
engineers, it will be necessary to reduce the de grees of freedom
by providing appropriate elements to simplify the tuning of
adaptive controllers. For achieving this, further efforts both in
practice and theory have to be undertaken.
Acknowledgment. This work was partially supported by research grant
Un 25/2 1 from the DFG ( German re search foundation ) . This
support is gratefully acknowledged .
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