Signal Processing for Control

431 Pages·1986·7.501 MB·English

by  Prof. J. L. Douce (auth.), Keith Godfrey, Peter Jones (eds.)

Lecture Notes ni
Control and
noitamrofnI Sciences
detidE yb amohT.M dna .A renyW
79
IIIIII IIIIII IIIII
Signal Processing rof Control
Edited yb
.K Godfrey, R Jones
IIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIII
galreV-regnirpS
nilreB Heidelberg New kroY oykoT
Series Editor
M. Thoma. A. Wyner
Advisory Board
D. L. Davisson • AG.. .J MacFarlane • H. Kwakernaak
.J L. Massey Ya • Z. Tsypkin - A. .J Viterbi
Editors
Keith Godfrey
Peter Jones
Department of Engineering
University of Warwick
Coventry, CV4 7AL
ISBN Springer-Verlag 3-540-16511-8 Berlin Heidelberg New Tokyo York
ISBN Springer-Verlag 0-387-16511-8 New Heidelberg York Berlin Tokyo
This work is subject to copyright. All rights are reserved, whether the whole or part of the material
is concerned, specifically thoseo f translation,r eprinting, re-use of illustrations, broadcasting,
reproduction by photocopying machine or similar means, and storage in data banks. Under
§ 54 of the German Copyright Lawwh ere copies are made for other than private use, a fee is
payable to "Verwertungsgesellschaft Wort", Munich.
© Springer-Verlag Berlin, Heidelberg 1986
Printed in Germany
Otfsetprinting: Mercedes-Druck, Berlin
Binding: B. Helm, Bedin
2161/3020-543210
FOREWORD
The last decade has seen major advances in the theory and practice of control
engineering. New algorithms such as self-tuning regulators have been
accompanied by detailed convergence analysis; graphical work-stations allow a
designer to explore a wide range of synthesis methods; microprocessors have
enabled the practical realization of advanced control concepts. This growth of
techniques has meant that only a few universities with large departments could
train research students over the whole spectrum of control. Students in smaller
departments could specialize in their research topics yet fail to appreciate
developments in related areas.
The U.K. Science and Engineering Research Council (SERC) has for many years
sponsored a set of six Vacation Schools designed to bring together research
students working in control and instrumentation and to broaden their perspective
of the field. The schools are all one week long and held st six-monthly
intervals over a three-year cycle. Recently the scheme has been modified
slightly to provide three 'basic' courses and three 'advanced' courses, the idea
being that a student whose research topic is within a certain area would attend
the advanced course relating to his topic and the basic courses outside his
topic. Attendance at the schools is restricted to some 50 to 60 and industrial
participants are allowed to take up spare places to encourage interaction between
the students and practising engineers.
The introductory schools in the cycle are Deterministic Control I (state-space
methods, classical control, elements of multivariable frequency-response design
methods), Computer Control (sampled data theory, computer control technology and
software, elements of instrumentation) and Signal Processing for Control. The
advanced schools are Deterministic Control II (optimization, numerical methods,
robustness and multivariable design procedures), Instrumentation (basic
technology, sensor development and application studies) and Stochastic Control
(stochastic systems, adaptive control, identification and pattern recognition).
Each school has lectures, examples classes and experimental sessions. Case
studies showing %he application of the ideas in practice are presented, often by
industrial engineers.
This volume consists of the lecture notes for the school on Signal Processing
for Control. This school, held every three years at the University of Warwick,
has proved to be popular with the students as it successfully combines the
educational role of introducing many important ideas with the motivation provided
by the wide range of interesting application examples. Whilst no multi-author
book can ever be completely comprehensive and consistent, the editors are to be
congratulated in providing an excellent introduction and overview of an
increasingly important and practical discipline.
D.W. Clarke
Oxford University
(Chairman, Control and Instrumentation Subcommittee, SERC)
ECAFERP
esehT lecture notes are morf a Vacation loohcS held at the University of kciwraW
(Coventry, )dnalgnE from yadnuS 15th to Friday 20th rebmetpeS 1985. ehT School,
derosnops yb eht U.K. Science dna Engineering hcraeseR Council ,)CRES( demia to
provide na introduction to the theory dna application of signal processing in the
context of control smetsys design.
erehT were 24 participants, 23 of mohw were research students in the areao f
control engineering (the majority no dednuf-eRES studentships), the remaining 01
being industry-based engineers involved in control engineering dna related topics.
emoS prior egdelwonk of classical control theory saw ,demussa involving familiarity
withcalculus, differential equations, Fourier series, Fourier dna Laplace trans-
forms, z-transforms, frequency niamod sdohtem of linear smetsys analysis, dna basic
matrix techniques.
ehT loohcS saw desab no a yratnemelpmoc set of lectures, case studies dna
practical sessions covering the following topics:
(i) analytical dna lanoitatupmoc techniques for characterising modnar signals
dna their effect no cimanyd ;smetsys
(ii) system identification dna retemarap estimation;
(iii) digital filtering dna state estimation;
(iv) state/parameter estimation in feedback control.
MULUCIRRUC FO EHT LOOHCS
ehT loohcS consisteodf three Revision Lectures IR( to R3), eleven further
Lectures 1L( to Lll) dna four esaC Studies 1C( to C4). ehT Revision Lectures erew
presented no the yadnuS afternoona t the start of eht loohcS dna contained material
hcihw tsom participants would evah deretnuocne at undergraduate level; ecnadnetta
at these saw optional. ehT "main-stream" Lectures 1L( to Lli) from presented were
yadnoM through to Friday. the covered topics These listed in (i) to (iv) ,evoba
building from the material in 1R to 3R through to erom decnavda techniques. ehT
four esaC Study lectures designed were to illustrate the practical application of
the erom theoretical material in 1L to LIt. Outlines of 1R to ,3R Ll to 11L dna
IC to 4C are given later in this Preface.
Facilities for interactive cimanyd data analysis were provided via the EMIRP 055
retupmoc metsys installed at the University of kciwraW sa a part of the CRES
V
Interactive gnitupmoC Facility. nI addition, the X-XIRTAM analysis dna design
egakcap saw available no a EMITSYS 0878 retupmoc at the University. Students
erew able to perform a series of experiments involving the analysis of modnar
data dna the modelling of cimanyd smetsys desab no accessible data files nesohc
to illustrate representative applications dna .smelborp
A erawdrah demonstration of data analysis techniques in both the time niamod
dna frequency niamod saw given no a Hewlett drakcaP B0245 Digital Signal Analyzer.
ehT d~nonstration saw devised dna nur yb Professor .A.W nworB of the tnemtrapeD of
Electrical Engineering, hsanoM University, Australia, ohw saw no sabbatical leave
in the tnemtrapeD of Engineering at the University of kciwraW at the time of the
School.
nO eht yadsendeW afternoon of the School, participants went nnoa industrial
visit to the sacuL hcraeseR Centre at Shirley (near )mahgnimriB to hear present-
ations of relevant research dna tnempoleved projects in the area of evitomotua
smetsys control dna to tour the engine test dna other experimental facilities.
ehT Vacation loohcS Dinner saw dedecerp yb given a address keynote yb Professor
samohT Kailath of the Electrical Engineering tnemtrapeD of Stanford University,
California. Professor Kailath entitled his "Signal address Processing dna Control"
dna dealt with numerical noitatupmoc aspects of signal processing (in particular,
erauqs root algorithms) together with implementation considerations invoIving
parallel processing dna VLSI. Traditionally, keynote sesserdda at Vacation sloohcS
of this type are intended sa na up-to-date overview of emos aspects of the topic
of the .loohcS sA such, lecture notes are not sought dna enon are available for
Professor Kailath's talk.
LAIRETAM DEREVOC NI EHT SETON
.A Revision Lectures IR to 3R
In RI, EangiG An~z/.ye'~ I, basic analytical dna computational techniques that
are available for the characterisation of cimanyd signals dna data are reviewed.
esehT are Fourier series dna the Fourier transform, the Discrete Fourier transform
(including the Fast Fourier mrofsnarT algorithm), the transform, Laplace delpmas
data dna the z-tra~sform dna a brief overview of modnar signal analysis dna
estimation errors.
sdohteM for characterising smetsys cimanyd era discussed in ,2R 8yetis eisyEanA
I. include These differential equation representation, response impulse dna con-
volution in the time ,niamod frequency response dna sdohtem of determining frequency
,sesnopser dna the (Laplace) transfer function. delpmaS data smetsys are also
,derevoc with material no difference equations, pulse transfer functions, zero order
hold elements, convolution mus dna the estimation of unit pulse using response cross-
correlation.
VI
enO of the primary aims of ,3R =Yr~cM jmev~YnhceT is to standardise notation dna
terminology of basic matrix concepts for tneuqesbus lectures at the School. ehT esu
of vector-matrix concepts in studying smetsys cimanyd is discussed, in particular
the transfer function matrix dna the state transition matrix. Vector-matrix diff-
erence equations for delpmas data smetsys are described dna the notes conclude with
discussions of quadratic forms dna diagonalisation, Taylor series, amixam dna aminim
dna multiple linear regression.
.B Lectures 1L to LII
In ,1L Re~ P~ob=~i¢y ,yro.~lT the main concepts of probability theory
applied to the characterisation of scalar dna vector modnar variables dna modnar
signals are outlined. dBiostchr ete dna continuous modnar variables are deredisnoc
and, sa well sa single variable probability distributions dna density functions,
joint dna conditional distributions are defined dna illustrated with .selpmaxe sesU
of the characteristic function are described dna aspects of vector modnar variables
are discussed, including marginal densities, vector stnemom dna lamron modnar
vectors. ehT notes conclude with a brief discussion of stochastic processes,
including aspects of stationarity.
Basic concepts in lacitamehtam statistics dna emos of their applications in the
analysis of signals dna cimanyd smetsys are described dna illustrated in ,2L ~rave~eR
6~Y~a~ ~he~I/. Bias, variance, consistency dna efficiency of na estimate are
defined dna sdohtem of hypothesis testing dna establishing confidence intervals are
described, with illustrative .selpmaxe ehT oaR-remarC dnuob dna mumixam likelihood
estimation are discussed dna the notes conclude with a discussion of optimal esti-
itam no techniques.
ehT sisahpme in ,3L smetsyS Ana~s~ ~IZ is no the esu of autocorrelation dna
crosscorrelation in the time niamod dna the corresponding Fourier-transformed
quantities, the rewop spectral yt~i~ned dna cross-spectral density function in the
frequency domain. ehT respons~of linear smetsys to stationary modnar excitation
is considered, in particular sdohtem for determining output rewop murtceps for a
metsys with a specified (Laplace) transfer function excited yb na input signal with
a specified rewop spectrum. gnidnopserroC quantities for discrete-time smetsys are
al os described.
nA important melborp in experiment planning is that of deciding in ecnavda woh
hcum data tsum eb collected "ot achieve a given accuracy. ehT considerations that
affect the question are Jdessucsid in ,4L Sig~I Ar~Zys~ If, for a rebmun of data
analysis procedures dna it is :nwohs woh a quantitative analysis leads to useful
guidelines for the design of experimental procedures involving modnar data. ehT
relationships neewteb record characteristics dna _-elbaborp error~, are described both
for time niamod dna frequency niamod analyses.
Vll
nI ,5L nggweO and /rnpZ~nent~£on of D~ita~ giZ¢~sj both finite-impulse-response
)RIF( filters (also nwonk sa gnivom average )AM( filters) dna infinite-impulse-
esnopser (IIR) filters (also sa nwonk average autoregressive-moving )AMRA( filters)
era considered. Impulse-invariant design of fIR filters is described. It is nwohs
woh aliasing nac affect the frequency esnopser of designs such dna a dohtem of
avoiding this inaccuracy yb esu of bilinear transformation is discussed. ehT design
of RIF fi]ters yb Fourier series dna gniwodniw is described dna desimitpo-retupmoc
RIF filters are discussed. smelborP of quantisation dna rounding, which are of hcus
practical ecnatropmi in digital filteringj are also considered.
Statistical techniques for the estimation of sretemarap of cimanyd smetsys morf
input-output data are described in 6L retenm~P .noitamitsE In the section no -non
recursive estimation, sisahpme is placed no doohilekil-mumixam estimation dna a
melborp in linear regression, that of estimating the pulse response ecneuqes of a
,metsys is considered in emos detail. Recursive least serauqs is discussed, in
particular, woh to avoid direct matrix inversion. ehT notes conclude with a brief
discussion of nonlinear regression.
ehT emeht of recursive sdohtem is continued in 7L Rec~slve sdohteM in Id~ifi-
action. Recursive forms of standard off-line techniques are described, in particular
least serauqs dna instrumental variables. Stochastic approximation dna the stoch-
astic notweN algorithm are discussed dna this is followed yb sections no the ledom
reference hcaorppa dna naiseyaB sdohtem dna the namlaK filter. ehT smelborp with
the various sehcaorppa nehw the metsys is time-varying are described dna the con-
ecnegrev dna stability of the different algorithms era considered.
ycneuqerF niamod analysis of cimanyd smetsys is dere~Ji=snoc in ,SL ~a~tcep~ -ZanA
ys~ dna .snoY~aoi~ppA In the first part of the notes, several selpmaxe of auto-
correlation functions dna corresponding (continuous) rewop spectra of smrofevaw are
given dna spectral relationships in closed loop smetsys era considered. ehT smelborp
of digital spectral analysis are then reviewed. emoS of the statistical properties
of spectral estimates are discussed dna the notes conclude with a brief description
of cepstral analysis.
In the first part of ,9L Obsez~s, ~o~c~ £sC~ion dna j,oitc£~e~P the -neuL
berger observer is described in emos detail, with asymptotic dna order reduced
observers being discussed. ehT closed loop properties of a metsys in hcihw a stable
asymptotic observer i s applied to na otherwise stable control metsys design are
considered. ]T~e regrebneuL observer arose with regard to state e~t~mation for
deterministic, continuous-time ;~metsys 'the sisahpme of ehE notes won switches to
discrete time ,smetsys in which yna noise that affects the system is directly taken
into account. sections Successive of the notes deal with the namlaK filter, pre-
diction dna .gnihtooms
VIII
ehT smelborp introduced yb nonlinearities era considered in LIO, noi~cudo~/nI to
Nonlinear smetsyS Ana~sis dna Identif~ation. Static nonlinearities era dessucsid
in the first part of the notes. Nonlinear smetsys with scimanyd era then ,deredisnoc
in particular theVolterra series representation. ehT inherent complexity of eht
analysis sah del to eht tnen~Foleved of noitamixorppa sdohtem desab no linearisation
seuqinhcet dna these era described. Identification algorithms for nonlinear ,smetsys
deredisnoc next, nac eb categorised sa functional series ,sdohtem algorithms for
block oriented smetsys dna retemarap estimation techniques. emoS of eht ideas
detneserp era illustrated yb a practical application in hcihw the relationship
neewteb input emulov flow rate dna level of liquid in a metsys of detcennocretni
tanks is identified. ehT notes edulcnoc yb considering control of nonlinear delpmas
data .smetsys
ehT final lecture, Ll1, nA Introduction to Dis cr ete-t em~ eS 7~rinut-°j~ Control,
sedivorp a tutorial introduction to self-tuning control in its traditional discrete-
time setting. ehT notes start yb gniredisnoc a slightly modified version of eht
self-tuning regulator of m)lrtsX dna ,kramnettiW eht modifications including control
gnithgiew dna set-point following. A dethgiew ledom reference controller is then
deredisnoc dna finally a pole tnemecalp self-tuning controller is discussed. All
three sehcaorppa era deweiv within a nommoc ,krowemarf yleman that of gnitalume
unrealisable srotasnepmoc using a self-tuning emulator.
.C esaC Studies 1C to 4C
In CI, ~xpl~ring Zz~igoZ~B Signals, emos applications of smetsys seuqinhcet to
enic iedreamoib described; in the selpmaxe described, signal gnissecorp dna gnilledom
era confined to lanoisnemid-eno time series. In the first part of eht notes, eht
gnilledom of signals is considered. This is illustrated yb eht application of Fast
Fourier ,smrofsnarT Fast hslaW ,smrofsnarT autoregressive modelling, esahp lock
loops dna raster gninnacs to electrical signals from eht gastrointestinal tract dna
yb the analysis dna tneuqesbus modelling of eht blood erusserp reflex control ~etsys
(part of the cardiovascular .)metsys In the dnoces part, eht modelling of smetsys
sa( distinct from signals) is illustrated yb owt ,selpmaxe eht first the noitanimreted
of lung scinahcem dna eht dnoces eht identification of elcsum relaxant drug .scimanyd
ehT latter is part of studies demia at achieving on-line identification dna control
in eht operating theatre.
gnireenignE surfaces evah in their erutcafunam a large proportion of modnar
events, dna eht study of surfaces, either for gnidnatsrednu of tribology or sa a
snaem of gnirutcafunam control, provides a very interesting application of modnar
ssecorp theory dna spectral estimation. A egnar of applications such is illustrated
in ,2C ~.ochas~ic sdohteM and Engine~i~ Burfaces. After a review of sdohtem of
gnilledom surfaces, tneuqesbus sections deal with profile statistics, ssenhguor
XJ
sretemarap dna profile filtering. Surface classification techniques are then
described dna these include the epahs of autocorrelation functions, the first t~
neve stnemom of the rewop spectral density dna the weks dna kurtosis of the ampli-
tude probability density function. ehT notes conclude with a erom detailed dis-
cussion of spectral analysis of surfaces.
secneirepxE gained in six applications of identification are described in ,3C
~a~Y~oa~P ~reZborP in Iden~ifieatlon. ehT sessecorp from a ranged steelworks blast
furnace to a sag turbine engine, from na oii refinery distillation nmuloc to a
namuh being. It is nwohs that ~ile useful estimates of the scimanyd of smetsys
in industry nac semitemos eb obtained from simple step responses, noise is often
at hcus a level that signals with impulse-like autocorrelation functions are ,dedeen
but that direction-dependent cimanyd sesnopser nac then eb a .melborp If lamron
operating records are used, smelborp nac arise if feedback is present dna this yam
not eb very obvious in emos instances. roF delpmas records, the spacing of selpmas
yam naem that emos sretemarap of a ledom are estimated with low accuracy. Finally,
nehw trying to esti~ate the sretemarap of na demussa nonlinearity, it is essential
that the dataav ailable adequately naps the nonlinear characteristic.
ehT final esaC Study, ,4C L(~ n~YseD of Ship gniteerG Oontrol ,eme~s~ is con-
denrec with the control of course of a ship in the face of disturbances from naeco
currents adensa waves. Modelling of the ship, wind, evaw dna steering gear dna then
the denibmoc ledom of ship dna disturbance are described. ehT cost function is
formulated dna the existence of the solution to the GQL (Linear, Quadratic, )naissuaG
melborp is investigated. ehT namlaK filter dna controller design are then described
dna then simulation results are presented. It saw found that eno of the niam pro-
smelb saw to design a namlaK filter estimate which would the ship motions; with the
disturbance ledom changing significantly in different aes conditions, a fixed gain
namlaK filter yam ton give na etauqeda estimation accuracy.
STNEMEGDELWONKCA
eW would like to take this opportunity to thank the contributors to these lecture
notes for their cooperation which greatly desae our editing task. In particular, ew
express our thanks to Professor John ecuoD dna Dr. Mike ,sehguH our colleagues at
kciwraW for their help dna tnomegaruocne throughout the planning, preparation dna
editing of these notes.
eW also thank sM Terri ssoM for reh excel(lent typing of the manuscript dna Mrs.
Alison sugeN for reh invaluable secretarial support.
University of kciwraW Keith yerfdoG
rebmeceD 5891 Peter senoJ
×
LIST OF CONTRIBUTORS
Dr. S.A. Billings Department of Control Engineering,
University of Sheffield, Ma ppin Street,
Sheffield I$ 3JD.
Dr. D.G. Chetwynd Department of Engineering, University of
Warwick, Coventry CV4 7AL.
Professor J.L. Douce Department of Engineering, University of
Warwick, Coventry CV4 7AL.
Dr. P.J. Gawthrop Department of Control, Electrical and
Systems Engineering, University of Sussex,
Falmer, Brighton 1NB 9RH.
Dr. K.R. Godfrey Department of Engineering, University of
Warwick, Coventry 7AL. CV4
Professor N.J. Grimble Industrial Control Unit, Department of
Electronic and Electrical Engineering,
University of Strathclyde, 204 George
Street, Glasgow IG ~XW.
.rD M.T.G. Hughes Department of Engineering, University of
Warwick, Coventry CV4 7AL.
Dr. R.P. Jones Department of Engineering, University of
Warwick, Coventry 7AL. CV4
Dr. H.R. Katebl Industrial Control Unit, Department of
Electronic and Electrical Engineering,
University of Strathclyde, 204 George
Street, Glasgow IG IXW.
Professor D.A. Linkens Department of Control Engineering,
University of Sheffield, Mappin Street,
Sheffield I$ 3JD.