Chapter #2 EEE State Space Analysis and Controller Design
|
|
|
- Ginger Bryan
- 5 years ago
- Views:
Transcription
1 Chpte EEE8- Chpte # EEE8- Stte Spce Al d Cotolle Deg Itodcto to tte pce Obevblt/Cotollblt Modle ede: D D Go - d.go@cl.c.k /4
2 Chpte EEE8-. Itodcto Ae tht we hve th ode te: f, ', '',.... Ve dffclt to td t eve f t le te we t olve th ode polol eqto. Theoetcll we c e geoetc d/o ltcl ethod bt th c be ppled ol oe pecfc ce. Copte c be ed to tckle th poble d the e bette wth t ode ODE we bek the th ode ODE to te of t ode ODE. Alo b g tce we c e powefl tool fo le lgeb. The gol of th chpte to todce ew ppoch the odellg of dcl te, the ethod clled tte pce l d t f oe vetle th the well-kow Tfe Fcto. Moe pecfcll, the clcl cotol te deg techqe (ch oot loc d feqec epoe ethod) e geell pplcble to: ) Sgle Ipt Sgle Otpt (SISO) te b) Ste tht e le d te vt (hve pete tht do ot chge wth te) The tte pce ppoch geelzed te do ethod fo odellg, lg d degg cotol te d ptcll well ted to dgtl pleetto. The tte pce ppoch c del wth: ) Mlt Ipt Mlt Otpt te b) No-le d te vt te c) Altetve cotolle deg ppoche Modle ede: D D Go - d.go@cl.c.k /4
3 Chpte EEE8- Eple: Ae the ple -pg te: F(t) k (t) Fcto, Ug Newto echc we get: d d F k F k choog, we hve: k F F k O k F A The vble d defe the tte vecto, whch t defe the tte ( coplete /decpto) of the te. owg the cet tte d the fte pt we c pedct the fte tte,.e. the fte behvo of the te. I the foeetoed ce, kowg the vle/decto of the foce F, the cet dplceet d peed of the object we c fll defe t fte dplceet d peed. Modle ede: D D Go - d.go@cl.c.k /4
4 Chpte EEE8- I oe geel ce whe we hve tte d pt we hve: d d... b b... b,,,,,,,... b b... b,,,,,,, d,,,..., b, b,... b, Th c be wtte vecto fo : A whee:,..., b, b,,......,, A,, , b, b,,......, Now, ode to oto the te we eed eo to ee vo vble lke the dplceet d veloct of the. et e tht we c b eo fo both vble (the peed d the dplceet), the we defe the otpt of the te to be: C et e tht we c b ol oe eo, tht ee the dplceet, the the otpt : C et e tht we c b ol oe eo, tht ee the veloct, the C the otpt : Modle ede: D D Go - d.go@cl.c.k 4/4
5 Chpte EEE8- et e tht we hve ol oe eo tht ee le cobto C of the dplceet d veloct: Hece, the ot geel ce: c, c, c, c, c, c, c, c, c, c, c, c, C p c c p, cp, c p p, cp, c p, Fll let e tht ( the tfcl ce) tht the pt c dectl flece the otpt, the we hve: C D, Fo oe t D. So the te decbed b A C D : A C D p O vecto fo: A C D Modle ede: D D Go - d.go@cl.c.k 5/4
6 Chpte EEE8- Whee: I geel:, p ( t) A t ( t) ( t) ( t) ( t) C( t) ( t) D( t) ( t) Whee tte vecto,.e. pt vecto,.e. p otpt vecto,.e. p A tte t,.e. A pt t,.e. C p otpt t,.e. C p D p feed fowd t (ll zeo),.e. D p If the te e Te Ivt (TI): ( t) A( t) ( t) ( t) C( t) D( t) D d/ C + A The tte of te coplete of the te t ptcl pot te. If the cet tte of the te d the fte pt gl e kow the t poble to defe the fte tte d otpt of the te. Modle ede: D D Go - d.go@cl.c.k 6/4
7 Chpte EEE8- The tte of te be defed the et of vble (tte vble) whch t oe tl te t o, togethe wth the pt vble, copletel detee the behvo of the te fo te t t o. The tte vble e the llet be of vble tht c decbe the dc te of te d t ot ece cott tht the e eble. The e whch tte vble chge wth te c be thoght of tjecto deol pce clled tte pce. Two deol tte pce oete efeed to the phe ple whe oe tte the devtve of the othe. The choce of the tte pce vble fee log oe le e followed: The t be lel depedet. The t pecf copletel the dc behvo of the te. Fll the t ot be pt of the te. Eple.: Fd the tte pce odel of the followg te: t t t t 4t 4 4 4, A C 4 Modle ede: D D Go - d.go@cl.c.k 7/4
8 Chpte EEE8- Eple.: Fd the tte pce odel of the followg te: t t t t t 6 t 5 5 t t t t t t t t Hece: t t 5 t t t t t t 5 t Eple of tte pce odel (NOT ASSESSED MATEIA) Eple. Ae the followg ple electoechcl tht cot of electoget d v(t) f The foce of the getc feld dectl elted to the cet the etwok. The foce tht eeted o the object f ka, whee k A Modle ede: D D Go - d.go@cl.c.k 8/4
9 Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k 9/4 potve cott. To plf the l we e tht the dplceet ve ll d tht ll e the cet h le eltohp wth the foce: k f A Ug cct theo: v d Ug Newto d lw: k k k f A Now, we c defe, d. Th: v v k k k k A A Hece the tte pce odel : A v k k A Now let e tht we hve ol oe eo tht wll et the dplceet : Th the tte pce odel : v k k A
10 Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k /4 Eple.4 Aothe eple how the et fge. The hft of the eptel ected DC oto coected to the lod J thogh ge bo. d v d v J T T T T J T T T T, T T T T J J d d v v I defe, : v J J v J J v J v(t) EMF T,θ N N θ o J T,θ T o,θ o
11 Chpte EEE8- Eple.5: It c be poved tht odel of the Idcto Mche : d D D D d Q Q Q D d D Q D Q D d Q Q D Q D Q D D Q Q D D D Q Q Q O: Modle ede: D D Go - d.go@cl.c.k /4
12 Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k /4 Q D q d Q D q d Q D Q q d Q D q D q d Q D d Q q d Q D Q D q d Q D D d d d d d d d d
13 Chpte EEE8- Stte pce The te tte c be wtte vecto fo :,, T,,,, T,,,,, T, => A tdd othogol b (ce the e le depedet) fo - deol vecto pce clled tte pce. Eple of tte pce e the tte ple (=) d tte D pce (=), Modle ede: D D Go - d.go@cl.c.k /4
14 Chpte EEE8- elto of tte pce d TF If we hve TI tte pce () te, how c we fd t TF? T ( t) A( t) ( t) X ( ) () AX ( ) U ( ) I A X ( ) U ( ) () X ( ) I A U ( ) I A () Ad fo the d eqto of the te: Y( ) CX ( ) DU ( ) => Y( ) C I A U ( ) I A () DU ( ) Y( ) C I A D U( ) C I A () defto TF: CI A D d CI A () IC. the epoe to the Alo: ( ) ( ) () IT X I A U I A X ( t) I A U ( ) I A () If = => X ( t) I A X () Modle ede: D D Go - d.go@cl.c.k 4/4
15 Chpte EEE8- So G C I A D the TF. Fo le lgeb: G, j I A Cj D I A, whee the th col of the t d C j the j th ow of C. Hece I A the CE of the TF!!! So: G ( ) G ( ) G q( ) G( ) G( ) Gq ( ) G () Gp( ) Gp( ) Gpq( ) Y U Y Y Y, G, G,... U U U G G Eple.6: Fd the TF of the followg te:. d 5 I A.5.5 G.5.5 Modle ede: D D Go - d.go@cl.c.k 5/4
16 Chpte EEE8- Eple.7: Fd the TF of the followg te:. d 5 I A.5.5 G,.5.5 I A.5.5 G,.5.5 O: G C I A D G G Modle ede: D D Go - d.go@cl.c.k 6/4
17 Chpte EEE8- Eple.8: Fd the TF of the followg te:. d 5 I A G, I A.5.5 G,.5.5 I A.5.5 / G,.5.5 / I A.5.5 G,.5.5 O: Modle ede: D D Go - d.go@cl.c.k 7/4
18 Chpte EEE8- G C I A D G G G Obevblt Ae tht we hve the followg te:. Notce tht the odel copled d ce C t poble to ee how behve (o poble f A w ot dgol o C w I ). Th ple tht we cot oto, fo eple t c dvege to ft wth cttophc elt fo o te. Ae tht we hve othe te: Modle ede: D D Go - d.go@cl.c.k 8/4
19 Chpte EEE8- Clel thee two odel e dffeet. I tht ce t c be poved tht the te hve the e tfe fcto thee pole-zeo ccelto: I A C D 6 G I A I A C D G I A 6 6 whch ectl the e the TF of the ft te, wht wog? Thee pole zeo ccellto t the ecod odel Cotollblt Ae tht we hve the followg te: I th ce we c ee how both tte behve bt we cot chge w o tht we c flece de to the fo of. If A w ot dgol we wold be ble to cotol thogh. Sll we hve pole-zeo ccellto : Modle ede: D D Go - d.go@cl.c.k 9/4
20 Chpte EEE8- I A C D G I A 6 6 Hece the ft ce b popel defg we c cotol both tte bt we cot ee the ecod tte, whle the ecod ce we c ee both tte bt we cot cotol the ecod tte. The ft te clled obevble d the ecod cotollble. The lo of the cotollblt d/o obevblt de to pole/zeo ccellto. Thee te e cceptble d the olto to tht poble to e-odel the te. The te tht e both cotollble d obevble e clled l elto. We eed to develop tet to detee the cotollblt d obevblt popete of the te. Dffclt tk f the te ole. I o ce we pl hve to fd the k (the be of e Idepedet (I) ow o col) of two tce. Fo obevblt: MO C CA CA CA. If the k of th t le th T the the te obevble. Fo cotollblt: MC A A A the the te cotollble.. If the k of th t le th Modle ede: D D Go - d.go@cl.c.k /4
21 Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k /4
22 Chpte EEE8- Eple.9: Detee the Obevblt of the followg te: CA 6 M O 6 Ad obvol thee ol oe I col/ow Eple.: Detee the Obevblt of the followg te: CA 6 M O 6 Ad obvol thee e I col/ow Eple.: Detee the Obevblt of the followg te: 4 A 4 M C Ad obvol thee ol oe I col/ow Eple.: Detee the Obevblt of the followg te: 4 A 4 M C Ad obvol thee e I col/ow. Modle ede: D D Go - d.go@cl.c.k /4
23 Chpte EEE8- Ttol Eece II. Deve tte pce epeetto of the pg te g tht the te h otpt: the dplceet d the veloct.. epet Qeto g tht the dplceet the ol te otpt.. Fd the tte pce odel of the followg te: 6 5 ( t) 4 4. A tte pce odel gve b A 4 5,.7.9, C 5, D () Wht the ode of the te? (b) How pt/ otpt do we hve th te? (c) Wht e the deo of the t D? 5. Fd the tte pce odel of: () 4 4'' ' 4.' 5 Modle ede: D D Go - d.go@cl.c.k /4
24 Chpte EEE8- Modle ede: D D Go - d.go@cl.c.k 4/4 (b) 4 4 I ech ce fd: The ode of the te? How pt/ otpt do we hve th te? 6. Fd the tfe fcto of te wth:,,, 4 D C A. 7. Fd the tfe fcto of te wth:,,, 4 D C A. 8. Fd the tfe fcto of te wth:,,, 4 D C A. 9. Wht the chctetc eqto Q.6-8? Wht the te ode? I tht te tble? Wh? Ae thee te obevble/cotollble?
Chapter Linear Regression
Chpte 6.3 Le Regesso Afte edg ths chpte, ou should be ble to. defe egesso,. use sevel mmzg of esdul cte to choose the ght cteo, 3. deve the costts of le egesso model bsed o lest sques method cteo,. use
2.Decision Theory of Dependence
.Deciio Theoy of Depedece Theoy :I et of vecto if thee i uet which i liely depedet the whole et i liely depedet too. Coolly :If the et i liely idepedet y oepty uet of it i liely idepedet. Theoy : Give
ECONOMETRIC ANALYSIS ON EFFICIENCY OF ESTIMATOR ABSTRACT
ECOOMETRIC LYSIS O EFFICIECY OF ESTIMTOR M. Khohev, Lectue, Gffth Uvet, School of ccoutg d Fce, utl F. K, tt Pofeo, Mchuett Ittute of Techolog, Deptet of Mechcl Egeeg, US; cuetl t Shf Uvet, I. Houl P.
2. Elementary Linear Algebra Problems
. Eleety e lge Pole. BS: B e lge Suoute (Pog pge wth PCK) Su of veto opoet:. Coputto y f- poe: () () () (3) N 3 4 5 3 6 4 7 8 Full y tee Depth te tep log()n Veto updte the f- poe wth N : ) ( ) ( ) ( )
10.2 Series. , we get. which is called an infinite series ( or just a series) and is denoted, for short, by the symbol. i i n
0. Sere I th ecto, we wll troduce ere tht wll be dcug for the ret of th chpter. Wht ere? If we dd ll term of equece, we get whch clled fte ere ( or jut ere) d deoted, for hort, by the ymbol or Doe t mke
Maximum likelihood estimate of phylogeny. BIOL 495S/ CS 490B/ MATH 490B/ STAT 490B Introduction to Bioinformatics April 24, 2002
Mmm lkelhood eme of phylogey BIO 9S/ S 90B/ MH 90B/ S 90B Iodco o Bofomc pl 00 Ovevew of he pobblc ppoch o phylogey o k ee ccodg o he lkelhood d ee whee d e e of eqece d ee by ee wh leve fo he eqece. he
Chapter 17. Least Square Regression
The Islmc Uvest of Gz Fcult of Egeeg Cvl Egeeg Deptmet Numecl Alss ECIV 336 Chpte 7 Lest que Regesso Assocte Pof. Mze Abultef Cvl Egeeg Deptmet, The Islmc Uvest of Gz Pt 5 - CURVE FITTING Descbes techques
= y and Normed Linear Spaces
304-50 LINER SYSTEMS Lectue 8: Solutos to = ad Nomed Lea Spaces 73 Fdg N To fd N, we eed to chaacteze all solutos to = 0 Recall that ow opeatos peseve N, so that = 0 = 0 We ca solve = 0 ecusvel backwads
Chapter 2: Descriptive Statistics
Chapte : Decptve Stattc Peequte: Chapte. Revew of Uvaate Stattc The cetal teecy of a oe o le yetc tbuto of a et of teval, o hghe, cale coe, ofte uaze by the athetc ea, whch efe a We ca ue the ea to ceate
A Dynamical Quasi-Boolean System
ULETNUL Uestăţ Petol Gze Ploeşt Vol LX No / - 9 Se Mtetă - otă - Fză l Qs-oole Sste Gel Mose Petole-Gs Uest o Ploest ots etet est 39 Ploest 68 o el: ose@-loesto stt Ths e oes the esto o ol theoetl oet:
Describes techniques to fit curves (curve fitting) to discrete data to obtain intermediate estimates.
CURVE FITTING Descbes techques to ft cuves (cuve fttg) to dscete dt to obt temedte estmtes. Thee e two geel ppoches fo cuve fttg: Regesso: Dt ehbt sgfct degee of sctte. The stteg s to deve sgle cuve tht
Journal of Engineering and Natural Sciences Mühendislik ve Fen Bilimleri Dergisi SOME PROPERTIES CONCERNING THE HYPERSURFACES OF A WEYL SPACE
Jou of Eee d Ntu Scece Mühed e Fe Be De S 5/4 SOME PROPERTIES CONCERNING THE HYPERSURFACES OF A EYL SPACE N KOFOĞLU M S Güze St Üete, Fe-Edeyt Füte, Mtet Böüü, Beştş-İSTANBUL Geş/Receed:..4 Ku/Accepted:
Chapter #3 EEE Subsea Control and Communication Systems
EEE 87 Chter #3 EEE 87 Sube Cotrol d Commuictio Sytem Cloed loo ytem Stedy tte error PID cotrol Other cotroller Chter 3 /3 EEE 87 Itroductio The geerl form for CL ytem: C R ', where ' c ' H or Oe Loo (OL)
3. REVIEW OF PROPERTIES OF EIGENVALUES AND EIGENVECTORS
. REVIEW OF PROPERTIES OF EIGENVLUES ND EIGENVECTORS. EIGENVLUES ND EIGENVECTORS We hll ow revew ome bc fct from mtr theory. Let be mtr. clr clled egevlue of f there et ozero vector uch tht Emle: Let 9
Linear Open Loop Systems
Colordo School of Me CHEN43 Trfer Fucto Ler Ope Loop Sytem Ler Ope Loop Sytem... Trfer Fucto for Smple Proce... Exmple Trfer Fucto Mercury Thermometer... 2 Derblty of Devto Vrble... 3 Trfer Fucto for Proce
CURVE FITTING LEAST SQUARES METHOD
Nuercl Alss for Egeers Ger Jord Uverst CURVE FITTING Although, the for of fucto represetg phscl sste s kow, the fucto tself ot be kow. Therefore, t s frequetl desred to ft curve to set of dt pots the ssued
«A first lesson on Mathematical Induction»
Bcgou ifotio: «A fist lesso o Mtheticl Iuctio» Mtheticl iuctio is topic i H level Mthetics It is useful i Mtheticl copetitios t ll levels It hs bee coo sight tht stuets c out the poof b theticl iuctio,
AN ALGEBRAIC APPROACH TO M-BAND WAVELETS CONSTRUCTION
AN ALGEBRAIC APPROACH TO -BAN WAELETS CONSTRUCTION Toy L Qy S Pewe Ho Ntol Lotoy o e Peeto Pe Uety Be 8 P. R. C Att T e eet le o to ott - otool welet e. A yte of ott eto ote fo - otool flte te olto e o
Numerical Methods for Eng [ENGR 391] [Lyes KADEM 2007] Direct Method; Newton s Divided Difference; Lagrangian Interpolation; Spline Interpolation.
![Numerical Methods for Eng [ENGR 391] [Lyes KADEM 2007] Direct Method; Newton s Divided Difference; Lagrangian Interpolation; Spline Interpolation.](/thumbs/72/67225597.jpg "Numerical Methods for Eng [ENGR 391] [Lyes KADEM 2007] Direct Method; Newton s Divided Difference; Lagrangian Interpolation; Spline Interpolation.")
Nuecl Methods o Eg [ENGR 39 [Les KADEM 7 CHAPTER V Itepolto d Regesso Topcs Itepolto Regesso Dect Method; Newto s Dvded Deece; Lgg Itepolto; ple Itepolto Le d o-le Wht s tepolto? A ucto s ote gve ol t
ˆ SSE SSE q SST R SST R q R R q R R q
Bll Evas Spg 06 Sggested Aswes, Poblem Set 5 ECON 3033. a) The R meases the facto of the vaato Y eplaed by the model. I ths case, R =SSM/SST. Yo ae gve that SSM = 3.059 bt ot SST. Howeve, ote that SST=SSM+SSE
Difference Sets of Null Density Subsets of
dvces Pue Mthetcs 95-99 http://ddoog/436/p37 Pulshed Ole M (http://wwwscrpog/oul/p) Dffeece Sets of Null Dest Susets of Dwoud hd Dsted M Hosse Deptet of Mthetcs Uvest of Gul Rsht I El: hd@gulc h@googlelco
Consumer theory. A. The preference ordering B. The feasible set C. The consumption decision. A. The preference ordering. Consumption bundle
Thomas Soesso Mcoecoomcs Lecte Cosme theoy A. The efeece odeg B. The feasble set C. The cosmto decso A. The efeece odeg Cosmto bdle x ( 2 x, x,... x ) x Assmtos: Comleteess 2 Tastvty 3 Reflexvty 4 No-satato
Fredholm Type Integral Equations with Aleph-Function. and General Polynomials
Iteto Mthetc Fou Vo. 8 3 o. 989-999 HIKI Ltd.-h.co Fedho Te Iteg uto th eh-fucto d Gee Poo u J K.J. o Ittute o Mgeet tude & eech Mu Id u5@g.co Kt e K.J. o Ittute o Mgeet tude & eech Mu Id dehuh_3@hoo.co
Chapter I Vector Analysis
. Chpte I Vecto nlss . Vecto lgeb j It s well-nown tht n vecto cn be wtten s Vectos obe the followng lgebc ules: scl s ) ( j v v cos ) ( e Commuttv ) ( ssoctve C C ) ( ) ( v j ) ( ) ( ) ( ) ( (v) he lw
ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY)
ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) Floet Smdche, Ph D Aocte Pofeo Ch of Deptmet of Mth & Scece Uvety of New Mexco 2 College Rod Gllup, NM 873, USA E-ml: md@um.edu
Moments of Generalized Order Statistics from a General Class of Distributions
ISSN 684-843 Jol of Sttt Vole 5 28. 36-43 Moet of Geelzed Ode Sttt fo Geel l of Dtto Att Mhd Fz d Hee Ath Ode ttt eod le d eel othe odel of odeed do le e ewed el e of geelzed ode ttt go K 995. I th e exlt
Answer: First, I ll show how to find the terms analytically then I ll show how to use the TI to find them.
. CHAPTER 0 SEQUENCE, SERIES, d INDUCTION Secto 0. Seqece A lst of mers specfc order. E / Fd the frst terms : of the gve seqece: Aswer: Frst, I ll show how to fd the terms ltcll the I ll show how to se
Sensorless A.C. Drive with Vector Controlled Synchronous Motor
Seole A.C. Dve wth Vecto Cotolle Sychoo Moto Ořej Fše VŠB-echcal Uvety of Otava, Faclty of Electcal Egeeg a Ifomatc, Deatmet of Powe Electoc a Electcal Dve, 17.ltoa 15, 78 33 Otava-Poba, Czech eblc oej.fe@vb.cz
On the Trivariate Polynomial Interpolation
WSEAS RANSACIONS o MAHEMAICS Sle Sf O the vte Polol Itepolto SULEYMAN SAFAK Dvso of Mthetcs Fclt of Eee Do Elül Uvest 56 ıtepe c İ URKEY. sle.sf@de.ed.t Abstct: hs ppe s coceed wth the fole fo copt the
Multiple Choice Test. Chapter Adequacy of Models for Regression
Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to
ROOT-LOCUS ANALYSIS. Lecture 11: Root Locus Plot. Consider a general feedback control system with a variable gain K. Y ( s ) ( ) K
ROOT-LOCUS ANALYSIS Coder a geeral feedback cotrol yte wth a varable ga. R( Y( G( + H( Root-Locu a plot of the loc of the pole of the cloed-loop trafer fucto whe oe of the yte paraeter ( vared. Root locu
Torque generation with Electrical Machines. Industrial Electrical Engineering and Automation Lund University, Sweden
Toqe geneton wth Electcl Mchne Indtl Electcl Engneeng nd Atoton nd Unvet, Sweden Toqe genetng phenoen Indtl Electcl Engneeng nd Atoton Condcto n gnetc feld Ion hpe n gnetc feld 3 Electottc 4 Pezotcton
ME 501A Seminar in Engineering Analysis Page 1
Fobeius ethod pplied to Bessel s Equtio Octobe, 7 Fobeius ethod pplied to Bessel s Equtio L Cetto Mechicl Egieeig 5B Sei i Egieeig lsis Octobe, 7 Outlie Review idte Review lst lectue Powe seies solutios/fobeius
COMP 465: Data Mining More on PageRank
COMP 465: Dt Mnng Moe on PgeRnk Sldes Adpted Fo: www.ds.og (Mnng Mssve Dtsets) Powe Iteton: Set = 1/ 1: = 2: = Goto 1 Exple: d 1/3 1/3 5/12 9/24 6/15 = 1/3 3/6 1/3 11/24 6/15 1/3 1/6 3/12 1/6 3/15 Iteton
The formulae in this booklet have been arranged according to the unit in which they are first
Fomule Booklet Fomule Booklet The fomule ths ooklet hve ee ge og to the ut whh the e fst toue. Thus te sttg ut m e eque to use the fomule tht wee toue peeg ut e.g. tes sttg C mght e epete to use fomule
are positive, and the pair A, B is controllable. The uncertainty in is introduced to model control failures.
Lectue 4 8. MRAC Desg fo Affe--Cotol MIMO Systes I ths secto, we cosde MRAC desg fo a class of ult-ut-ult-outut (MIMO) olea systes, whose lat dyacs ae lealy aaetezed, the ucetates satsfy the so-called
Nonlocal Boundary Value Problem for Nonlinear Impulsive q k Symmetric Integrodifference Equation
OSR ol o Mec OSR-M e-ssn: 78-578 -SSN: 9-765X Vole e Ve M - A 7 PP 95- wwwojolog Nolocl Bo Vle Poble o Nole lve - Sec egoeece Eo Log Ceg Ceg Ho * Yeg He ee o Mec Yb Uve Yj PR C Abc: A oe ole lve egoeece
X-Ray Notes, Part III
oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel
OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
VECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.
Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Fedad P. ee E. Russell Johsto, J. Systems of Patcles Lectue Notes: J. Walt Ole Texas Tech Uesty 003 The Mcaw-Hll Compaes, Ic. ll ghts eseed. Seeth
Integral Solutions of Non-Homogeneous Biquadratic Equation With Four Unknowns
Ieol Jol o Compol Eee Reech Vol Ie Iel Solo o No-Homoeeo qdc Eqo Wh Fo Uo M..Gopl G.Smh S.Vdhlhm. oeo o Mhemc SIGCTch. Lece o Mhemc SIGCTch. oeo o Mhemc SIGCTch c The o-homoeeo qdc eqo h o o epeeed he
8. SIMPLE LINEAR REGRESSION. Stupid is forever, ignorance can be fixed.
CIVL 33 Appomto d Ucett J.W. Hule, R.W. Mee 8. IMPLE LINEAR REGREION tupd s foeve, goce c be fed. Do Wood uppose we e gve set of obsevtos (, ) tht we beleve to be elted s f(): Lookg t the plot t ppes tht
Professor Wei Zhu. 1. Sampling from the Normal Population
AMS570 Pofesso We Zhu. Samplg fom the Nomal Populato *Example: We wsh to estmate the dstbuto of heghts of adult US male. It s beleved that the heght of adult US male follows a omal dstbuto N(, ) Def. Smple
Chapter Newton-Raphson Method of Solving Simultaneous Nonlinear Equations
Chapter 7 Newto-Rapho Method o Solg Smltaeo Nolear Eqato Ater readg th chapter o hold be able to: dere the Newto-Rapho method ormla or mltaeo olear eqato deelop the algorthm o the Newto-Rapho method or
XII. Addition of many identical spins
XII. Addto of may detcal sps XII.. ymmetc goup ymmetc goup s the goup of all possble pemutatos of obects. I total! elemets cludg detty opeato. Each pemutato s a poduct of a ceta fte umbe of pawse taspostos.
χ be any function of X and Y then
We have show that whe we ae gve Y g(), the [ ] [ g() ] g() f () Y o all g ()() f d fo dscete case Ths ca be eteded to clude fuctos of ay ube of ado vaables. Fo eaple, suppose ad Y ae.v. wth jot desty fucto,
Lecture 9-3/8/10-14 Spatial Description and Transformation
Letue 9-8- tl Deton nd nfomton Homewo No. Due 9. Fme ngement onl. Do not lulte...8..7.8 Otonl et edt hot oof tht = - Homewo No. egned due 9 tud eton.-.. olve oblem:.....7.8. ee lde 6 7. e Mtlb on. f oble.
Electric Potential. and Equipotentials
Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil
A Deterministic Model for Channel Capacity with Utility
CAPTER 6 A Detestc Model fo Chel Cct wth tlt 6. todcto Chel cct s tl oeto ssocted wth elble cocto d defed s the hghest te t whch foto c be set ove the chel wth btl sll obblt of eo. Chel codg theoes d the
14.2 Line Integrals. determines a partition P of the curve by points Pi ( xi, y
4. Le Itegrls I ths secto we defe tegrl tht s smlr to sgle tegrl except tht sted of tegrtg over tervl [ ] we tegrte over curve. Such tegrls re clled le tegrls lthough curve tegrls would e etter termology.
Chapter #2 EEE Subsea Control and Communication Systems
EEE 87 Chpter # EEE 87 Sube Cotrol d Commuictio Sytem Trfer fuctio Pole loctio d -ple Time domi chrcteritic Extr pole d zero Chpter /8 EEE 87 Trfer fuctio Lplce Trform Ued oly o LTI ytem Differetil expreio
E-Companion: Mathematical Proofs
E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth
( ) ( ) ( ( )) ( ) ( ) ( ) ( ) ( ) = ( ) ( ) + ( ) ( ) = ( ( )) ( ) + ( ( )) ( ) Review. Second Derivatives for f : y R. Let A be an m n matrix.
Revew + v, + y = v, + v, + y, + y, Cato! v, + y, + v, + y geeral Let A be a atr Let f,g : Ω R ( ) ( ) R y R Ω R h( ) f ( ) g ( ) ( ) ( ) ( ( )) ( ) dh = f dg + g df A, y y A Ay = = r= c= =, : Ω R he Proof
( m is the length of columns of A ) spanned by the columns of A : . Select those columns of B that contain a pivot; say those are Bi
Assgmet /MATH 47/Wte Due: Thusday Jauay The poblems to solve ae umbeed [] to [] below Fst some explaatoy otes Fdg a bass of the colum-space of a max ad povg that the colum ak (dmeso of the colum space)
6.6 The Marquardt Algorithm
6.6 The Mqudt Algothm lmttons of the gdent nd Tylo expnson methods ecstng the Tylo expnson n tems of ch-sque devtves ecstng the gdent sech nto n tetve mtx fomlsm Mqudt's lgothm utomtclly combnes the gdent
Lecture 38 (Trapped Particles) Physics Spring 2018 Douglas Fields
Lecture 38 (Trpped Prticles) Physics 6-01 Sprig 018 Dougls Fields Free Prticle Solutio Schrödiger s Wve Equtio i 1D If motio is restricted to oe-dimesio, the del opertor just becomes the prtil derivtive
Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden
Poton nd Speed Control Lund Unverty, Seden Generc Structure R poer Reference Sh tte Voltge Current Control ytem M Speed Poton Ccde Control * θ Poton * Speed * control control - - he ytem contn to ntegrton.
Introduction to Modern Control Theory
Itroductio to Moder Cotrol Theory MM : Itroductio to Stte-Spce Method MM : Cotrol Deig for Full Stte Feedck MM 3: Etitor Deig MM 4: Itroductio of the Referece Iput MM 5: Itegrl Cotrol d Rout Trckig //4
I. Exponential Function
MATH & STAT Ch. Eoetil Fuctios JCCSS I. Eoetil Fuctio A. Defiitio f () =, whee ( > 0 ) d is the bse d the ideedet vible is the eoet. [ = 1 4 4 4L 4 ] ties (Resf () = is owe fuctio i which the bse is the
Lecture 10: Condensed matter systems
Lectue 0: Codesed matte systems Itoducg matte ts codesed state.! Ams: " Idstgushable patcles ad the quatum atue of matte: # Cosequeces # Revew of deal gas etopy # Femos ad Bosos " Quatum statstcs. # Occupato
Physics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
RECAPITULATION & CONDITIONAL PROBABILITY. Number of favourable events n E Total number of elementary events n S
Fomulae Fo u Pobablty By OP Gupta [Ida Awad We, +91-9650 350 480] Impotat Tems, Deftos & Fomulae 01 Bascs Of Pobablty: Let S ad E be the sample space ad a evet a expemet espectvely Numbe of favouable evets
Chapter Unary Matrix Operations
Chpter 04.04 Ury trx Opertos After redg ths chpter, you should be ble to:. kow wht ury opertos mes,. fd the trspose of squre mtrx d t s reltoshp to symmetrc mtrces,. fd the trce of mtrx, d 4. fd the ermt
Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]
![Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]](/thumbs/83/87614710.jpg "Area and the Definite Integral. Area under Curve. The Partition. y f (x) We want to find the area under f (x) on [ a, b ]")
Are d the Defte Itegrl 1 Are uder Curve We wt to fd the re uder f (x) o [, ] y f (x) x The Prtto We eg y prttog the tervl [, ] to smller su-tervls x 0 x 1 x x - x -1 x 1 The Bsc Ide We the crete rectgles
SOLVING SYSTEMS OF EQUATIONS, DIRECT METHODS
ELM Numecl Alyss D Muhem Mecmek SOLVING SYSTEMS OF EQUATIONS DIRECT METHODS ELM Numecl Alyss Some of the cotets e dopted fom Luee V. Fusett Appled Numecl Alyss usg MATLAB. Petce Hll Ic. 999 ELM Numecl
Phys 2310 Fri. Oct. 23, 2017 Today s Topics. Begin Chapter 6: More on Geometric Optics Reading for Next Time
Py F. Oct., 7 Today Topc Beg Capte 6: Moe o Geometc Optc eadg fo Next Tme Homewok t Week HW # Homewok t week due Mo., Oct. : Capte 4: #47, 57, 59, 6, 6, 6, 6, 67, 7 Supplemetal: Tck ee ad e Sytem Pcple
Example: Two Stochastic Process u~u[0,1]
![Example: Two Stochastic Process u~u[0,1]](/thumbs/86/93797001.jpg "Example: Two Stochastic Process u~u[0,1]")
Co o Slo o Coco S Sh EE I Gholo h@h. ll Sochc Slo Dc Slo l h PLL c Mo o coco w h o c o Ic o Co B P o Go E A o o Po o Th h h o q o ol o oc o lco q ccc lco l Bc El: Uo Dbo Ucol Sl Ab bo col l G col G col
Lecture 2: The Simple Regression Model
Lectre Notes o Advaced coometrcs Lectre : The Smple Regresso Model Takash Yamao Fall Semester 5 I ths lectre we revew the smple bvarate lear regresso model. We focs o statstcal assmptos to obta based estmators.
(a) Counter-Clockwise (b) Clockwise ()N (c) No rotation (d) Not enough information
m m m00 kg dult, m0 kg bby. he seesw stts fom est. Which diection will it ottes? ( Counte-Clockwise (b Clockwise ( (c o ottion ti (d ot enough infomtion Effect of Constnt et oque.3 A constnt non-zeo toque
CS473-Algorithms I. Lecture 12b. Dynamic Tables. CS 473 Lecture X 1
CS473-Algorthm I Lecture b Dyamc Table CS 473 Lecture X Why Dyamc Table? I ome applcato: We do't kow how may object wll be tored a table. We may allocate pace for a table But, later we may fd out that
Summary: Binomial Expansion...! r. where
Summy: Biomil Epsio 009 M Teo www.techmejcmth-sg.wes.com ) Re-cp of Additiol Mthemtics Biomil Theoem... whee )!!(! () The fomul is ville i MF so studets do ot eed to memoise it. () The fomul pplies oly
University of Pavia, Pavia, Italy. North Andover MA 01845, USA
Iteatoal Joual of Optmzato: heoy, Method ad Applcato 27-5565(Pt) 27-6839(Ole) wwwgph/otma 29 Global Ifomato Publhe (HK) Co, Ltd 29, Vol, No 2, 55-59 η -Peudoleaty ad Effcecy Gogo Gog, Noma G Rueda 2 *
SYSTEMS OF NON-LINEAR EQUATIONS. Introduction Graphical Methods Close Methods Open Methods Polynomial Roots System of Multivariable Equations
SYSTEMS OF NON-LINEAR EQUATIONS Itoduto Gaphal Method Cloe Method Ope Method Polomal Root Stem o Multvaale Equato Chapte Stem o No-Lea Equato /. Itoduto Polem volvg o-lea equato egeeg lude optmato olvg
Mathematical Statistics
7 75 Ode Sttistics The ode sttistics e the items o the dom smple ed o odeed i mitude om the smllest to the lest Recetl the impotce o ode sttistics hs icesed owi to the moe equet use o opmetic ieeces d
On Almost Increasing Sequences For Generalized Absolute Summability
Joul of Applied Mthetic & Bioifotic, ol., o., 0, 43-50 ISSN: 79-660 (pit), 79-6939 (olie) Itetiol Scietific Pe, 0 O Alot Iceig Sequece Fo Geelized Abolute Subility W.. Suli Abtct A geel eult coceig bolute
UNIT V: Z-TRANSFORMS AND DIFFERENCE EQUATIONS. Dr. V. Valliammal Department of Applied Mathematics Sri Venkateswara College of Engineering
UNIT V: -TRANSFORMS AND DIFFERENCE EQUATIONS D. V. Vllimml Deptmet of Applied Mthemtics Si Vektesw College of Egieeig TOPICS:. -Tsfoms Elemet popeties.. Ivese -Tsfom usig ptil fctios d esidues. Covolutio
African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 4, No. 2, pp GENERALISED DELETION DESIGNS
Af Joul of See Tehology (AJST) See Egeeg See Vol. 4, No.,. 7-79 GENERALISED DELETION DESIGNS Mhel Ku Gh Joh Wylff Ohbo Dee of Mhe, Uvey of Nob, P. O. Bo 3097, Nob, Key ABSTRACT:- I h e yel gle ele fol
Centroids & Moments of Inertia of Beam Sections
RCH 614 Note Set 8 S017ab Cetrods & Momets of erta of Beam Sectos Notato: b C d d d Fz h c Jo L O Q Q = ame for area = ame for a (base) wdth = desgato for chael secto = ame for cetrod = calculus smbol
CBSE SAMPLE PAPER SOLUTIONS CLASS-XII MATHS SET-2 CBSE , ˆj. cos. SECTION A 1. Given that a 2iˆ ˆj. We need to find
BSE SMLE ER SOLUTONS LSS-X MTHS SET- BSE SETON Gv tht d W d to fd 7 7 Hc, 7 7 7 Lt, W ow tht Thus, osd th vcto quto of th pl z - + z = - + z = Thus th ts quto of th pl s - + z = Lt d th dstc tw th pot,,
2012 GCE A Level H2 Maths Solution Paper Let x,
GCE A Level H Maths Solutio Pape. Let, y ad z be the cost of a ticet fo ude yeas, betwee ad 5 yeas, ad ove 5 yeas categoies espectively. 9 + y + 4z =. 7 + 5y + z = 8. + 4y + 5z = 58.5 Fo ude, ticet costs
Union, Intersection, Product and Direct Product of Prime Ideals
Globl Jourl of Pure d Appled Mthemtcs. ISSN 0973-1768 Volume 11, Number 3 (2015), pp. 1663-1667 Reserch Id Publctos http://www.rpublcto.com Uo, Itersecto, Product d Drect Product of Prme Idels Bdu.P (1),
On EPr Bimatrices II. ON EP BIMATRICES A1 A Hence x. is said to be EP if it satisfies the condition ABx
Iteatoal Joual of Mathematcs ad Statstcs Iveto (IJMSI) E-ISSN: 3 4767 P-ISSN: 3-4759 www.jms.og Volume Issue 5 May. 4 PP-44-5 O EP matces.ramesh, N.baas ssocate Pofesso of Mathematcs, ovt. ts College(utoomous),Kumbakoam.
ANSWER KEY PHYSICS. Workdone X
ANSWER KEY PHYSICS 6 6 6 7 7 7 9 9 9 0 0 0 CHEMISTRY 6 6 6 7 7 7 9 9 9 0 0 60 MATHEMATICS 6 66 7 76 6 6 67 7 77 7 6 6 7 7 6 69 7 79 9 6 70 7 0 90 PHYSICS F L l. l A Y l A ;( A R L L A. W = (/ lod etesio
Overview. Review Superposition Solution. Review Superposition. Review x and y Swap. Review General Superposition
ylcal aplace Soltos ebay 6 9 aplace Eqato Soltos ylcal Geoety ay aetto Mechacal Egeeg 5B Sea Egeeg Aalyss ebay 6 9 Ovevew evew last class Speposto soltos tocto to aal cooates Atoal soltos of aplace s eqato
The Linear Probability Density Function of Continuous Random Variables in the Real Number Field and Its Existence Proof
MATEC Web of Cofeeces ICIEA 06 600 (06) DOI: 0.05/mateccof/0668600 The ea Pobablty Desty Fucto of Cotuous Radom Vaables the Real Numbe Feld ad Its Estece Poof Yya Che ad Ye Collee of Softwae, Taj Uvesty,
Collapsing to Sample and Remainder Means. Ed Stanek. In order to collapse the expanded random variables to weighted sample and remainder
Collapg to Saple ad Reader Mea Ed Staek Collapg to Saple ad Reader Average order to collape the expaded rado varable to weghted aple ad reader average, we pre-ultpled by ( M C C ( ( M C ( M M M ( M M M,
Municipality of Central Elgin User Fee Committee Agenda
ult f etl Elg Use Fee ttee ge Pge 11:.. ttee R # ll t e slsue f Peu Iteest the Geel tue Theef -6 7-18 t f utes t f the utes f eetgs te etebe, 14, Ju 7, 15. suss Ites Reve f the 14 Use Fee heule e Busess
Advanced Higher Maths: Formulae
Advced Highe Mths: Fomule Advced Highe Mthemtics Gee (G): Fomule you solutely must memoise i ode to pss Advced Highe mths. Rememe you get o fomul sheet t ll i the em! Ame (A): You do t hve to memoise these
FRACTIONAL MELLIN INTEGRAL TRANSFORM IN (0, 1/a)
Ieol Jol o Se Reeh Pblo Volme Ie 5 y ISSN 5-5 FRACTIONAL ELLIN INTEGRAL TRANSFOR IN / S.. Kh R..Pe* J.N.Slke** Deme o hem hh Aemy o Egeeg Al-45 Pe I oble No.: 98576F No.: -785759 Eml-mkh@gml.om Deme o
6.6 Moments and Centers of Mass
th 8 www.tetodre.co 6.6 oets d Ceters of ss Our ojectve here s to fd the pot P o whch th plte of gve shpe lces horzotll. Ths pot s clled the ceter of ss ( or ceter of grvt ) of the plte.. We frst cosder
ENGINEERING MATHEMATICS I QUESTION BANK. Module Using the Leibnitz theorem find the nth derivative of the following : log. e x log d.
ENGINEERING MATHEMATICS I QUESTION BANK Modle Usig the Leibit theoem id the th deivtive o the ollowig : b si c e d e Show tht d d! Usig the Leibit theoem pove the ollowig : I si b the pove tht b I si show
Laplace Transform. Definition of Laplace Transform: f(t) that satisfies The Laplace transform of f(t) is defined as.
Lplce Trfor The Lplce Trfor oe of he hecl ool for olvg ordry ler dfferel equo. - The hoogeeou equo d he prculr Iegrl re olved oe opero. - The Lplce rfor cover he ODE o lgerc eq. σ j ple do. I he pole o
AGENDA REPORT. Payroll listing conforms to the approved budget except as noted and has been paid WILLIAM A HUSTON CITY MANAGER
Age e 4 AGEDA RERT Reewe ge Fce Dec EETG DATE Al 2 2 T FR A A T T AAGER AEA ARED KG FAE DRETR BET RATFAT F AR AR The cl h e he e f Gee e ec 728 eee he e f f T Reeele Agec blg h e ccce wh he e bge ce e
ELEC 6041 LECTURE NOTES WEEK 3 Dr. Amir G. Aghdam Concordia University
ecre Noe Prepared b r G. ghda EE 64 ETUE NTE WEE r. r G. ghda ocorda Uer eceraled orol e - Whe corol heor appled o a e ha co of geographcall eparaed copoe or a e cog of a large ber of p-op ao ofe dered
IO Gender and natural history
LNA HEBNGER Gede d tul hty The tylu f the fele [plt] the v hle the vulv d the Veu epd t the t Thu the uteu v d vulv ke up the ptl the e tht de btt ve t ll the fele pt f plt A f e e e eed quk lk euh f Ppu
Area, Volume, Rotations, Newton s Method
Are, Volume, Rottio, Newto Method Are etwee curve d the i A ( ) d Are etwee curve d the y i A ( y) yd yc Are etwee curve A ( ) g( ) d where ( ) i the "top" d g( ) i the "ottom" yd Are etwee curve A ( y)
Certain Expansion Formulae Involving a Basic Analogue of Fox s H-Function
vlle t htt:vu.edu l. l. Mth. ISSN: 93-9466 Vol. 3 Iue Jue 8. 8 36 Pevouly Vol. 3 No. lcto d led Mthetc: Itetol Joul M Cet Exo Foule Ivolvg c logue o Fox -Fucto S.. Puoht etet o c-scece Mthetc College o
The use of linear parametric approximation in numerical solving of nonlinear non-smooth Fuzzy equations
vlle ole t www.choleechl.co chve o ppled Scece Reech 5 6:49-6 http://choleechl.co/chve.htl ISSN 975-58X CODEN US SRC9 The ue o le petc ppoto uecl olvg o ole o-ooth uzz equto Mjd Hllj e Ze d l Vhd Kd Nehu
Fairing of Parametric Quintic Splines
ISSN 46-69 Eglad UK Joual of Ifomato ad omputg Scece Vol No 6 pp -8 Fag of Paametc Qutc Sples Yuau Wag Shagha Isttute of Spots Shagha 48 ha School of Mathematcal Scece Fuda Uvesty Shagha 4 ha { P t )}
Born-Oppenheimer Approximation. Kaito Takahashi
o-oppehee ppoato Kato Takahah toc Ut Fo quatu yte uch a ecto ad olecule t eae to ue ut that ft the=tomc UNT Ue a of ecto (ot kg) Ue chage of ecto (ot coulob) Ue hba fo agula oetu (ot kg - ) Ue 4pe 0 fo