Finite word length effects related to recursive identification

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Finite word length effects related to recursive identification Citation for published version (APA): Zhu, Y. (1984). Finite word length effects related to recursive identification. Technische Universiteit Eindhoven. Document status and date: Published: 01/09/1984 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. Download date: 22. Mar. 2022

Transcript of Finite word length effects related to recursive identification

Page 1: Finite word length effects related to recursive identification

Finite word length effects related to recursive identification

Citation for published version (APA):Zhu, Y. (1984). Finite word length effects related to recursive identification. Technische Universiteit Eindhoven.

Document status and date:Published: 01/09/1984

Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:[email protected] details and we will investigate your claim.

Download date: 22. Mar. 2022

Page 2: Finite word length effects related to recursive identification

DEPARTMENT OF ELECTRICAL ENGINEERING

EINDHOVEN UNIVERSITY OF TECHNOLOGY

Group Measurement and Control

FINITE WORD LENGTH EFFECTS

RELATED TO RECURSIVE

IDENTIFICATION

by ZHU Yucai

Report on a 4th-year project

performed from February 1984 until September 1984

in charge of Prof.Dr.Ir. P. Eykhoff

under supervision of Dr.Ir. A.J.W. v.d. Boom

The department of Electrical Engineering of The Eindhoven University

of Technology is not responsible for the content of this report.

Page 3: Finite word length effects related to recursive identification

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Page 11: Finite word length effects related to recursive identification

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Page 12: Finite word length effects related to recursive identification

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Page 13: Finite word length effects related to recursive identification

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Page 14: Finite word length effects related to recursive identification

Hflm ( 8) 1 't Is nn IJM::J dewr kw rf:v). ~e,s ()._CcrrrJ/,-::1 "4 p ()m rJ. (l . To s,11)W ti,(; / w-e do [).._ >/,,'fl~ fVX4.Jnf (-e :

TJ.e, prous~ 1s N(l) _ I --~-( ___ _ -1>(~ J - / i a,J-1 -1 ai. '}- -2 - (1- J~f f/;G)( 1-;;-'je-it1)

as ;r,lme Inf~ U})_) t;S wfi 1fe ) tiM1 '([!uu_ { 3-);::; 1

-d rs;/= 3- _1 § [ t + 3 (a/+ a:)+ z o, 07 C1-i-')

3 2'lrt IJl~1 (-3-'fe'i~)(1-3p~·,~)(1-nef')(1- Jpe~'6')

t a_,J-' fOz~-.,__ ] d~ ( 1 - 3-pe1i~ )(1- J -r e-ie) T

7

07; 2 == (2-'t)[ t-f 2p + 4fz7rA,.}-e (3/J~-f) + jp4 {i+p) J (/ o)

3 (t-f/) (pt!-- 2p 1~ ... 2~ -fl)

Frrtm £ i. ( f O) w/2 j/rr J

(f) p1-=r o;/-1 l2) of-;> ov).1

(fJ<f)

Th/s r~sv...& is cl,us-e to tlLe fYXj>0f1m-Mllts

fJieAse n,rf'le dM dvs ~na.0s,'s Cff71:,,f)-e-r5 ~f; tlu 'lt!tUllrlojf err5r

c(J,,ljsed b.!:J sitn~ . A,t&w/113 tlu:s rm~ S'1 s / -tie f roce-sf. ,5 a1A/

a,.5. I' (JJ) w s

V(k)

----... N (6) D(J)

-/0-

Page 15: Finite word length effects related to recursive identification

f) Us1~19 JJ&u~{.e Pr-tc1s/1Jn

Frem i· ( g) we S£e, t1J, UV 2 w:ll decret'«;~ 22t ~mJ>.S /f

51.rr;uf~1 cevn red11Jl W 0f(fJr.

I)}~ ~MW j-r&lh ~ e/tfe'1/mlbnit th.M,. IJ.SI t1J ().. ~,,)ie prnc/sr (yh

estl'JllaiA;r ca. n work rnucl1 beife,r ~n a. sr'13~ prec/s1e1: (}}rf..,. Frirn1

ll pract1.uJ /Joint of v;ew, we ca11 crnt::; use dlft·vtit pre.ct'sr~7 1~ tfJ:.

est1·m~1 fart ttJ (Jlit:4unn-t tlP_ rf!U;11dtf{ -e,rror, b.eca.use t/LJ- t'nput an:/

~ d<x.tfX <Mt- ntJ{ fte·m >imµ~ b~ frnn (,l reJJ sysf3,,17

-2) To Maiaz Srunpt~ NtNmber N smolJ.

Frr;m W .etxf<-r/111errl.) we l.ea.rn du..i -ernrr 1 h cr&.s2> wh~n IV /ncreas-ts . If w€ kef IV 5mJ1 , we ~J h-ve- be:tt-er r.esu.lts..

Bvt!v wA.f/71 N 1 s ~ Sm Ji w .e. ()J r'/L ~ 5-e tfu irrfr r mRJ<An . Ac c ff1' 11~

Vi 1);_ vxper/m.utlt s N ~ Qt)O is gofJd 1'n no/s~<; Ct".,,st,

- 3 ) To RedrAre ti.L Sample Fr~11>11 C!j

Let u..s detJote d.£ prvcet;s as;

:£ JH ( 6 2

- c"· g) . c'::f er-pi· eJ'&«)(11 f<·e-Jfk)

n :Z:- ]){.(Sf~)

c=~i (s+c;,) 1-+0i

-ff-

Page 16: Finite word length effects related to recursive identification

ft,= e-(i,· T

{ fl, """w, T

d ull> us tlw d.evr-trA.S~ fu SJY111ple freitl.J/flcy , f/ wi'tl rlecrev. )f.,

and ()<-· vJt'fl i"ncree'tse. Th1'.3 1T7~11s ~ bfltii jJ1· /1/Tld (J<' moue to

tA.2. rJ,'rec~n of redt1.eti1J w r~nrluff -error. Bv<X accenf./,,3 to tA_;,

SMnp/;;73 TlieBlfAmJ ) lf T IS tgo bt'3 , t'. e' ---tilt jreq@rc:; (j

WO l~w I we al~o /t{).J/f., fu ftrJbfUTJ ef wsl113 /hfarma"tifln. v;..c

ciYu,rs-e th/5 m-dir~d works en~ frr proc~s-e5 cvht'ch have,

.Y ~"- c lv S ,· fYl 1

- f) Thll rr;u11r/.-off noise CCU{res -orrtrr S 1t7 hftl7 f0t rts .' >l1111A 'd«.n

a,,nd e-sV:m~ ( wh/ch po.rt is sujfftre.d mrJre 15 nFJ't ye{ dear)

-2) wh.e--n ct proce,~5. Aas. frJ{f..~ ve;r~ 11-e.ar to th, Ut111t c./rde,) 11ve

rn ~ h().ve_ a 11 un o. cc1tbfe, resJ-t (J"r fl'il.erf IAIA.l J71tA._!J ha.pp e,,n dc1Ae_ to

tf..J rrrwnd-o-ff no;'s-e. Th.£ 71-eArvr t;V pofe..{ to th 2'l'71't c/rc{-f-; tJ.i.

{ar9flr -W. €1fr~ w1'U be . T!tx mrJf-e fro{ ts vvAi vii oJt ntvi r d<2

;}Ji1i cirdt 1

tliJ/ rnerL r.J..a11~Ufll)j 1}u_ sitrcJi-~1 i's. vJfrcn tf.1 p1(e)

ar ~ clJJ ~ e- "(/; tlu. r eJJ ()IX is 1 ~ 1 -rli.J· ~ p (JM 1 e , -tlrs_ r MJ. 11 ri -1/ J J /: ;:_

will ca-VSf {Qr9er errflr

- 3 ) Wh01 ~ po{~s, are nFYt dtJs-e to -r;h_ ~111't v'rc{e ) SfM_j )

If W r (J._d /f10 Of th_ f U'{l!. ()Ir f.._ (eh r;_ titAn () · f 0 1 ~ 0Y ( {} ( {flt<!"! j

b~ r1U<11rl-ojf no15-e /s 71e9(€rf6(e.

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prect'sr&17 b) Pf.ef S.Ovmflt fflWJnber /V SmrJl

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Page 17: Finite word length effects related to recursive identification

WQSt fffecii11e fer recl.J.,{(,f~1!J fil errer b~ , ·t asks. mrJt<IZ m~ &ry

>p().ce ~ m~N.- ~ far c~. /1)-€-t~od b) m~ c)

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PA c kA 6 E SATER I Po.rt I : ])e scr1rt~ of tit.£_ SA I el« SysU,11 J )}

(1 9 g 3 , I nferncJ l<eport )

3. 812 de L {(,{ ~/f,j Toljoh/s Q.- J<a ne.ko , (I q 6 9)

rr Errirr An ~t~ysr'5i of ]),'~/t,j_ F,.lt-n-s Re (AL'zerl w1fh f-wdW71-.~o/11t

A ritA n1e,(;_( 11

PR.OCEEIJ1NfrS or THE IEEE) VOL S}' No. fO, 'PP t13J-- ii-7

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Page 18: Finite word length effects related to recursive identification

.o ~()

.SP=(}

..j."!_"'Q _'='-+~ -f-:>---­}-'-'"O ~ r N (q

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Page 19: Finite word length effects related to recursive identification

f,OfO 1,1>2.0

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Page 20: Finite word length effects related to recursive identification

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Page 21: Finite word length effects related to recursive identification

{O _, ! e

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X--------K N ~I VOO

8----£1 N =: Z!fl>V

g-' f b·SJ-2

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Page 22: Finite word length effects related to recursive identification

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. --~--c--:---'--i----1

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1 tog. eenhe1d is 100 mm.

Page 23: Finite word length effects related to recursive identification

-' t e fO I

to-'-- -c.~g..

G---8

G----f>

v. 13 °•'J /, QO /. 0 f

Ci-El'El/'Al! ZEl> S ilUA/l'E S }

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1s 100 rnrn

Page 24: Finite word length effects related to recursive identification

e

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'T!eetpap1er - wormerveer 1460 H Dee.str P"'' 15 nvr. 1 log. cr·nhe1d 1~ 100 rnm

Page 25: Finite word length effects related to recursive identification

10 Utt'.>tre?"'ri 1> 1 S IT'm l ~og eenherd h 100 mm

Page 26: Finite word length effects related to recursive identification

0 G 0=8!i" x f!d/S' } N""2$0

, o G fJ~s·

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