Methods and Applications in Adaptive Control: Proceedings of an International Symposium Bochum, 1980

315 Pages·1980·4.29 MB·English

by  K. J. Åström (auth.), Prof. Dr.-Ing H. Unbehauen (eds.)

Lecture Notes ni
Control dna
noitamrofnI Sciences
Edited by .V.A Balakrishnan and M.Thoma
24
Methods and Applications
ni Adaptive Control
sgnideecorP of na lanoitanretnI muisopmyS
1980 Bochum,
Edited by .H Unbehauen
galreV-regnirpS
Berlin Heidelberg NewYork 1980
Series Editors
A.V. Balakrishnan • M. Thoma
Advisory Board
L. D. Davisson • A. G. .J MacFarlane • H. Kwakernaak
J. L. Massey • Ya. Z. Tsypkin • A. .J Viterbi
Editor
Prof. Dr.-Ing. H. Unbehauen
Lehrstuhl f(Jr Elektrische Steuerung und Regelung
Ruhr-Universit~t Bochum
Posffach 102148, 4630 Bochum 1
ISBN 3-540-10226-4 Springer-Verlag Berlin Heidelberg NewYork
ISBN 0-387-10226-4 Springer-Verlag NewYork Heidelberg Berlin
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PREFACE
Adaptive control was first proposed more than 25 years ago. For the
most part, however, it has been so far a province of experience and
art. Only in the last five years have sound theories of adaptive con-
trol been developed. For the realization of adaptive systems we now
have several theoretical approaches at our disposal. There are the
self-tuning regulator and the model reference approaches. Both have
already been used successfully in several applications. The major de-
velopments during the last two years include the resolution of the
long standing stability problem and the realization that the two ap-
proaches mentioned above are essentially equivalent. In addition, with
the advent of cheap realization possibilities using the recent major
advances in microprocessor technology it seems that today adaptive
control is about ready for industrial application.
In view of this development an International Symposium on Adaptive
Systems was held at the Department of Electrical Engineering of the
Ruhr-University Bochum during March th 20 and 21 st 1980 together with
GMR of the VDI/VDE. The aim of this symposium was the discussion of
the actual situation and the future development of adaptive systems.
About 180 specialists from 13 countries came together. All papers pre-
sented at this conference are published in this volume.
The papers of the symposium during the first day were concerned with
methods in adaptive control and during the second day with applica-
tions. The primary intention of the conference was therefore to bring
together researchers and practising engineers. Theorists on the one side
could learn from the relevant features of practical applications,
whereas on the other side practising engineers could learn what possi-
bilities are offeredby adaptive control theories, especially how to
apply specific theoretical methods.
Three of the 26 presented papers represent survey papers. The survey
paper of K.J. Astr~m gave a unified description of many types of self-
tuning regulators and their design principles. K.S. Narendra and
B.B. Peterson pointed out in their survey the recent developments in
adaptive control, especially the solution of stability problems in
adaptive systems. The survey paper of P.C. Parks et al. reviewed the
application of adaptive control in three areas: aircraft control sys-
tems, process control and electrical drives.
VI
Besides the presentation of the papers a round table panel discussion
on the future of adaptive control was held at the end of the symposi-
um. The main result of this discussion was that adaptive control is
now ready for practical application. However, during the next few
years most of the work probably has to be done in a close collabora-
tion between universities and industry, because there is still much to
be learned before adaptive control can be considered a routine indus-
trial technique.
There are many people whom I have to'thank for their assistance in
arranging this symposium. First I say a big "thank you" to the univer-
sity authorities and those industrial companies which gave us the nec-
essary financial support. Next I would like to thank my colleagues
Professor Parks and Professor Schaufelberger who served on the steer-
ing committee and who selected with me very carefully the papers sub-
mitted for this symposium. I also would like to thank the editor of
these lecture notes, Professor Thoma, for his willingness to publish
this volume. Finally it is a pleasure to acknowledge the contribution
of my assistants and secretaries, who prepared most of the administra-
tive details of this successful symposium.
Bochum, May 1980 H. Unbehauen
C O N T E N T S
METHODS IN ADAPTIVE CONTROL
K.J. Astr~m
Design Principles for Self-Tuning Regulators . . . . . . . . 1
B. ~ittenmark, K.J. Astr~m
Simple Self-Tuning Controllers . . . . . . . . . . . . . . . 21
D. Matko
Some Relations in Discrete Adaptive Control . . . . . . . . 31
M.A. Ei-Bagoury, M.M. Bayoumi
Multivariable Self Tuning Augmented Regulator ....... 14
Ph. de Larminat
Unconditional Stabilizers for Nonminimum Phase Systems 54
T. S~derstr~m
On Some Adaptive Controllers for Stochastic Systems with
Slow Output Sampling . . . . . . . . . . . . . . . . . . . . 64
R. Breddermann
Realization and Application of a Self-Tuning On-Off Con-
troller . . . . . . . . . . . . . . . . . . . . . . . . . . 74
K.S. Narendra
Recent Developments in Adaptive Control . . . . . . . . . . 84
K. Sobel, H. Kaufman, O. Yekutiel
Design of Multivariable Adaptive Control Systems without
the Need for Parameter Identification . . . . . . . . . . . 102
L. Dugard, I.D. Landau
Convergence Analysis of M.R.A.S. Schemes Used for Adaptive
State Estimation . . . . . . . . . . . . . . . . . . . . . . 112
H. Elliot
Non Model Reference Adaptive Model Matching . . . . . . . . 122
A. Kuzucu, A. Roch
Suboptimal Adaptive Feedback Control of Nonlinear Systems . 131
J.E. Marshall
Identification Strategies for Time-De].ay Systems ...... 141
J. Sternby
Adaptive Control of Extremum Systems . . . . . . . . . . . . 151
APPLICATIONS OF _ADAPTIVE CONTROL
P.C. Parks, W. Schaufelberger, Chr. Schmid, H. Unbehauen
Applications of Adaptive Control Systems . . . . . . . . . . 161
IV
J. van Amerongen
Model Reference Adaptive Control Applied to Steering of
Ships . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
P.P.J. van den Bosch, W. Jongkind
Model Reference Adaptive Satellite Attitude Control .... 209
E. Irving
Implicit Reference Model and Optimal Aim Strategy for
Electrical Generator Adaptive Control . . . . . . . . . . . 219
P. Bonanomi, G. G~th
Adapted Regulator for the Excitation of Large Turbogene-
rators . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
A.H. Glattfelder, W. Schaufelberger
Adaptive Control by Self-Selection - An Application to
Hydropower Control . . . . . . . . . . . . . . . . . . . . . 251
U. Claussen
Adaptive Time-Optimal Position Control with Microprocessor . 261
C.T. Cao
A Simple Adaptive Concept for the Control of an Industrial
Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
W.L. Green, D.J. Sanger, B.N. Suresh
Using the Self-Optimising Control of an Electro-Hydraulic
Servo System to Minimise the Power Loss . . . . . . . . . . 280
E.G. Kunze
Adaptive Control by a Sensitivity Method without Need for
On-Line Identification . . . . . . . . . . . . . . . . . . . 291
NGISED SELPICNIRP ROF GNINUT-FLES SROTALUGER
K.J. H~RTSA
tnemtrapeD of Automatic Control
dnuL Institute of ygolonhceT
,dnuL nedewS
TCARTSBA
A unified description of ynam types of self-tuners is given. Relations to design of
controllers for systems with nwonk parameters dna recursive estimation sdohtem are
.dezisahpme ehT distinction neewteb self-tuners desab no identification of explicit
dna implicit process sledom are discussed sa well sa the relations neewteb Self-
gninuT Regulators (STR), dna ledo1~ Adaptive Reference smetsyS .)SARM( nA overview
of practical problems dna operational issues is given. ehT particular smelborp of
integral action dna estimator are pudniwcovered in erom detail.
NOII. TCUDORTNI
Adaptive control sah neeb a challenge to control engineers for a long time. ynaM
adaptive control semehcs have neeb .desoporp In spite of this progress in the field
sah neeb comparatively slow. enO reason is that it is difficult to understand woh
adaptive work systems esuaceb they are inherently nonlinear. Another reason is that
it sah neeb costly dna fairly complicated to adaptive implement controllers. ehT
situation sah degnahc drastically with the advent of microprocessors which sekam
implementation of adaptive controllers feasible. Recently there sah also neeb pro-
gress in theory of adaptive control. eeS Ljung (1977), Egardt (1979), niwdooG et al
(1978), esroM (1979) dna ardneraN et al (1979),
Self-tuning regulators )RTS( dna ledom reference adaptive systems )SARH( are owt
popular .sehcaorppa nA overview of RTS is given in Section 2. It is nwohs that self-
tuning regulators nac eb derived in a simple yaw which sah a strong intuitive appeal.
It is then nwohs yb examples, woh ynam different types of self-tuners nac eb genera-
ted, Relations neewteb RTS dna SARM are also discussed in Section 2. Practical aspects
no self-tuners are discussed in Section .3 This includes different syaw to esu RTS
sa well sa sesuba of self-tuners. owT particular practical namely problems woh to
intrbduce integral action dna woh to avoid estimator pudniw are discussed in
snoitceS 4 dna .5 ehT parametrization problem is discussed in Section 6.
.2 GNINUT-FLES SROTALUGER
This section gives a brief description of self-tuning regulators. ehT discussion is
limited to control of single-input single-output described systems yb
q(A -l) y(t) = q(B -l) u(t) (2.1)
erehw u is eht input, y eht output dna q(A -l) dna q(B -1) polynomials in eht -kcab
draw shift-operator. roF further details ew refer to eht original srepap akreteP
(IgT0), dna m~rtsA dna kramnettiW )3791( dna eht recent review m~rtsA (1979a), erehw
ynam references era given. ehT principles era first .dessucsid A self-tuner desab
no classical control design is then detneserp sa na .elpmaxe ehT notion of explicit
dna implicit algorithms is also .dessucsid
pl Princi se
A block margaid of self-tuning regulator is nwohs in Fig.l.
I
ngiseD ':~ rotomitsE
r o t a l u~ g e R
k~ s s e c ° r P
Figure I. citamehcS margaid of a self-
tuning regulator
ehT self-tuner nac eb thought of sa being desopmoc of three parts, a retemarap esti-
,rotam a design calculation dna a regulator with adjustable .sretemarap ehT ngised
calculation setupmoc eht sretemarap of eht regulator from eht sretemarap hcihw -ed
scribe eht .ssecorp ehT retemarap estimator senimreted eht sretemarap hcihw -carahc
terize the ssecorp dna its tnemnorivne from stnemerusaem of eht ssecorp input dna
.tuptuo
ehT regulator structure nwohs in Fig.l is very flexible esuaceb it allows ynam
different snoitanibmoc of ngised dna estimation .sdohtem oS far, only a small rebmun
of eht possible snoitanibmoc evah neeb explored. Intuitively it smees elbanosaer to
esoohc a ngised ,dohtem hcihw gives desired ecnamrofrep nehw eht sretemarap of eht
ssecorp era ,nwonk dna na estimation dohtem hcihw will krow well for eht particular
disturbances. It turns out, ,revewoh that eht structure nwohs in Fig.l also sah -nu
detcepxe properties. ehT regulator nwohs in Fig.l is a c#~tt~xi~ ,uqc Lv~ence con-
trol in eht terminology of stochastic control theory esuaceb eht fact that the para-
retem estimates era ton exact is .dedragersid It is possible to introduce modifica-
tions hcihw also take eht uncertainties of eht retemarap estimates into tnuocca
~uoLyt~z~e( control) dna modifications which introduce extra pro6ing 6&~ngi~ nehw the
retemarap estimates are uncertain. ehT principles will eb illustrated yb a wef
simple .selpmaxe
A self-tunin~ servo
redisnoC a servoproblem. A classical formulation of the design problem is to find a
regulator which gives the desired transfer function from the dnammoc signal to the
output. Let the desired transfer function eb
= M ~ G (2.2)
P
A self-tuning servo which gives this transfer function is given yb
MHTIROGLA IE (B~i¢ ~XcL~pxe algorithm)
:ataD ehT polynomials ,P TI, dna lQ are given.
petS l: Estimate the parameters of the ledom
Ay(t) = Bu(t) (2.1)
yb least squares.
petS 2: Factor the estimated polynomial into +B dna -B erehw all zeros of +B are
well depmad dna all zeros of -B are unstable or poorly .depmad
petS :3 Solve the linear equation.
RA l + S-B = TP I. (2.3)
(Notice that there are ynam solutions dna that a choice sah to eb .)edam
petS 4: Calculate the control variable u from
uR = uT - yS (2.4)
c
erehw = R RIB+, dna T = QIT l •
ehT steps l, 2, 3, dna 4 are repeated at each sampling period, n
ehT algorithm is discussed in detail in Astr~m dna Wittenmark (1979). Similar al-
gorithms for regulation are discussed in Wellstead et al (1979). If the parameter
estimates the converge closed loop transfer function will eb
lQ -B
P
Notice that this is the best that can eb obtained because it is not possible to
cancel unstable or poorly damped process zeros.
The algorithm El is called na algorithm based no noZt~om~t6e of process parameters
or an algorithm with expZicx~t ~oL~Yacif~nedi because the parameters of the process
model (3.1) in the standard form are estimated. Using the terminology of model re-
ference adaptive systems the algorithm is also called indX~e~t, because the para-
meters of the regulator are updated indirectly via estimation of the process para-
meters (Step I) and the design calculations (Steps 2, 3, and 4). eeS Narendra, Lin
and Valavani (1979).
The algorithm El can eb simplified little in two special cases. If it is known that
the process has no unstable zeros apart from a known number of time-delays it follows
that B-(q -I) = q-k. Step 2 is then not necessary. The second step in the algorithm
is also avoided if all process zeros are considered sa unstable or poorly .depmad In
that case B" = B.
Implicit algorithms
It is possible to construct algorithms where the design calculations are avoided and
the parameters of the regulator are updated directly. ehT basic self-tuning regulator
in Astr~m and Wittenmark (1973) is a prototype for algorithms of this type. The
idea is to rewrite the process model in such a yaw that the design step is trivial.
yB a proper choice of model structure the regulator parameters are updated directly
and the design calculations are thus eliminated. Algorithms of this type are called
algorithms based on~mpZZci~tiden~fic~tZon of a process model. In the terminology
of model reference adaptive systems the corresponding algorithms are also called
d~eo~t methods because the parameters of the regulator are undated directly.
nA example of na explicit algorithm will won eb given. Consider a process described
by (3.1) with B- : q-k. Assume that it is desired to find a feedback such that the
transfer function from the reference value to the output is
-k
z
P(z -I )
This means that all process zeros have to eb cancelled. Assuming that the process
model is known the design equation (2.3) semoceb
TP 1 = RA 1 + q-k s
ecneH
PTIY = ARlY + q-ksy = q-kR1Bu + q-ksy = q-k(Ru + Sy) (2.5)