ˆ x ESTIMATOR. state vector estimate
|
|
- Poppy Simmons
- 6 years ago
- Views:
Transcription
1 hapte 9 ontolle Degn wo Independent Step: Feedback Degn ontol Law =- ame all tate ae acceble a lot of eno ae necea Degn of Etmato alo called an Obeve whch etmate the ente tate vecto gven the otpt and npt PLN ONROL LW - mat of contant ˆ ESIMOR tate vecto etmate OMPENSION - ontol Law Degn med tem fo contol law degn =- =- fo an nth ode tem thee ae n feedback gan,, n. choce of the oot can geneall be placed anwhee
2 chaactetc eqaton I Placng Root Eample: Undamped ocllato wth feq. tate pace decpton REVIEW let' place the oot both at - j j j n -j - n j n we want to doble the natal feqenc and nceae dampng fom = to = co deed chaactetc eqaton d det 4 4 I det o 4 eqatng ame coeffcent: 4 4 4
3 Ue of anoncal Fom mple wa of calclatng the gan when ode geate than thee to e pecal canoncal fom of the tate eqaton. he pecal tcte of the tem mat efeed to a companon fom. Eample: hd ode cae: he chaactetc eqaton a a a Recall the phae vaable fom a lowe companon fom G b n... b n b n n a n... a n.... : a a a n n :... b b b n n D he cloed loop tem mat hd ode cae: a a a a a a haactetc eqaton I a a a
4 4 f the deed pole locaton elt n the chaactetc eqaton d eqatng lke coeffcent of and a a a Eample: Dll poblem D9. page 65 of tet 7 6 k k k Fnd k to place the cloed-loop tem pole at = -, -4, -5 NS deed chaactetc polnomal d , 47, 6 we have k a 7 5 k a k a 6 57
5 5 Degn Pocede Gven, and deed d, tanfom to c, c and olve fo gan We then need to tanfom gan back to ognal tate pace note: the pole can onl be placed abtal f the tem fll contollable h pocede encaplated n ckemann fomla ckemann Fomla... M k d whee M n... contollablt mat whee n the ode of the tem o the nmbe of tate and d defned a I n n n n d... whee the ' ae the coeffcent of the deed chaactetc polnomal d n n... n Eample ppl the fomla fo the ndamped ocllato 4 4 d 4, 4 ecall d contol canoncal companon fom.e. phae vaable fom
6 alo M c M c whch the ame a the elt pevol obtaned. ackng Poblem Fo tep npt: Wll fnd N to ene zeo tead-tate eo to tep npt now N N N N N now tead-tate eo e - table nvee et N N to get zeo tead tate eo N 6
7 Integal ontol ed to get zeo tead tate eo R E X U X - Y - ntegato n the fowad path Integato nceae the tem ode b one,.e. agment the plant model b an added tate vaable edt dt dt gmented tem become zeo matce compatble dmenon ontol law he degn now poceed a befoe. Eample Doble Integato G gment the plant 7
8 8 Select pole of the cloed loop tem to be at j,5 N.. pole becae of eta tate 7 Stead tate otpt to a nt tep npt can be deved a follow dt d n tead tate
9 9 Fo the eample 7 7 det adj 7 onl tem of nteet
10 Obeve Degn t, t t, ˆ t ˆ t - L We wll etmate tate athe than meae them PLN U Y - L ˆ X Obeve mlate the ognal tem Ognal Stem Obeve ˆ ˆ ˆ ˆ L ˆ
11 Eo between tate and the etmate ˆ ~ ˆ ˆ L ˆ L ~ ~ ~ Obeve eo wll go to zeo amptotcall -L table.e. egenvale ae n the LHP note: the egenvale of -L ae the obeve pole, whch can be placed abtal f the tem obevable th can be done b choce of the obeve gan L a colmn vecto fo ngle otpt tem Dalt Defnton: a tem detectable f the ntable mode ae obevable Eample a tem tablzable f the ntable mode ae contollable ontol Etmaton ontol Etmaton M M o L M... n dalt M o : n n o n M : n
12 ckemann fomla to fnd obeve gan : e M o L DERIVION USING DULIY ckemann Fomla fo contol poblem... M Dalt o e e o M M L :... : e M o L Eample Degn an obeve fo G Note the tem completel obevable Degn the obeve wth pole at j ctal chaactetc eqaton: l l l l L I
13 Deed chaactetc eqaton: j j 4 8 Eqatng coeffcent l 4 l 8 4 L 8 he obeve eqaton ae ˆ ˆ ˆ 4 ˆ 8 ˆ PLN ˆ ˆ SRUURE OF OSERVER
14 ontol Ung Obeve Plant: Obeve: ˆ ˆ L ˆ ˆ ˆ Etmated tate feedback: ˆ clong the loop ˆ ˆ L ˆ ˆ L L ˆ L ˆ L L ˆ 4
15 Sepaaton Pncple Intodce tanfomaton z I N N P whee P ˆ w IN I N note P P z I N N w I ˆ ˆ N I N heefoe ng th tanfomaton the old agmented tate vecto compng the plant tate and ˆ the etmato ate now become and the etmato eo. he new tem mat P P note ~ block-tangla L ~ Egenvale of a block-tangla mat ae eqal to the egenvale of the dagonal block. So the egenvale of the fll tem compe the egenvale of the plant.e. egenvale of - and the obeve.e. egenvale of -L. ltenatve ppoach ˆ ˆ L L ˆ ˆ ˆ L L ˆ L L ˆ ~ L ~ ˆ now ˆ ˆ ~ ~ 5
16 ompenato anfe Fncton H U Y ompenato otpt, whch the plant npt ompenato npt, whch the plant otpt PLN ompenato Otpt - ˆ OSERVER ompenato Inpt OMPENSOR we have ˆ ˆ ˆ L ˆ ˆ ˆ L Lˆ L ˆ L Xˆ I L LY U I L LY H Degn Ie Poblem wth pole placement that thee no contol ove compento pole and zeo Optmm choce fo obeve ntal condton ˆ '' hoce of obeve pole:. hooe them to be fate than contolle pole. ltenatvel, chooe them to be at plant zeo f the tem ha RHP zeo, e the LHP mage. 6
17 Redced-Ode Obeve Degn If tem ha n tate and m meaement, then an obeve of ode n-m wll be ffcent. If we wll ame ha the tcte: mm I I R, R m I m m nm meaed tate nmeaed tate m m m known npt dnamc of the nmeaed tate alo m known meaement otpt elatonhp Smmazng: known meaement m known npt a b Recall fo fll-ode obeve: Plant: Obeve: ˆ L ˆ ˆ ˆ compang and how the coepondence ˆ 7
18 m 4 btttng 4 nto we get the edced ode eqaton ˆ ˆ ˆ m L 5 let now defne the etmato eo we get ˆ theefoe btactng 5 fom a and ng b.e. ~ L ~ 6 Degn poceed b, gven an and we chooe an L to place etmato pole. Rewtng 5 we have ˆ L ˆ L L L 7 he peence of the devatve of the meaement.e. not good nce th amplfe the noe. o get aond th we ntodce a new tate z whee z ˆ L 8 ˆ z L 9 the eo dnamc ae gven b th eqaton btttng 9 nto 7 lead to the fnal fom of the edced-ode obeve z Dz F G ˆ z L whee D L F DL L G L z the tate of the etmato 8
19 he block dagam of the edced ode obeve hown below ^ Eample Doble ntegato G ^ z Dz F G ˆ whee z L D L F DL L G L Dnamc of edced ode obeve ~ L ~ 9
20 Reqe obeve pole at I L I L whee L D F 4 G ckeman fomla fo edced ode obeve gan L e M : M : n fo eample: e e M L
21 Redced-Ode anfe Fncton m m ˆ z L ˆ now alo z Dz F G z z L L z Dz F G z D G z F G L G L anfe fncton: U Y 'I ' 'D' whee ' D G ' F G G L ' D' L When not of the fom I? D Qz Qz Qz z Q Qz Q Qz D o fnd a tanfomaton Q o that Q of fom I let Q Q Q o Q Q Q I
22 let P be nonngla abta mat f PQ I Q Q I PQ Q Q Q Q I Q P
Detection and Estimation Theory
ESE 54 Detecton and Etmaton Theoy Joeph A. O Sullvan Samuel C. Sach Pofeo Electonc Sytem and Sgnal Reeach Laboatoy Electcal and Sytem Engneeng Wahngton Unvety 411 Jolley Hall 314-935-4173 (Lnda anwe) jao@wutl.edu
More information3. A Review of Some Existing AW (BT, CT) Algorithms
3. A Revew of Some Exstng AW (BT, CT) Algothms In ths secton, some typcal ant-wndp algothms wll be descbed. As the soltons fo bmpless and condtoned tansfe ae smla to those fo ant-wndp, the pesented algothms
More informationPHYS 705: Classical Mechanics. Derivation of Lagrange Equations from D Alembert s Principle
1 PHYS 705: Classcal Mechancs Devaton of Lagange Equatons fom D Alembet s Pncple 2 D Alembet s Pncple Followng a smla agument fo the vtual dsplacement to be consstent wth constants,.e, (no vtual wok fo
More informationExam 1. Sept. 22, 8:00-9:30 PM EE 129. Material: Chapters 1-8 Labs 1-3
Eam ept., 8:00-9:30 PM EE 9 Mateal: Chapte -8 Lab -3 tandadzaton and Calbaton: Ttaton: ue of tandadzed oluton to detemne the concentaton of an unknown. Rele on a eacton of known tochomet, a oluton wth
More informationMultiloop Control Systems
Mltiloop Control Stem. Introdction. The relative gain arra (RG) 3. Pairing inpt-otpt variable 4. Dnamic conideration 5. Mltiloop controller tning 6. Redcing control loop interaction Introdction Mltiloop
More informationRoot Locus Techniques
Root Locu Technque ELEC 32 Cloed-Loop Control The control nput u t ynthezed baed on the a pror knowledge of the ytem plant, the reference nput r t, and the error gnal, e t The control ytem meaure the output,
More informationFall 2004/05 Solutions to Assignment 5: The Stationary Phase Method Provided by Mustafa Sabri Kilic. I(x) = e ixt e it5 /5 dt (1) Z J(λ) =
8.35 Fall 24/5 Solution to Aignment 5: The Stationay Phae Method Povided by Mutafa Sabi Kilic. Find the leading tem fo each of the integal below fo λ >>. (a) R eiλt3 dt (b) R e iλt2 dt (c) R eiλ co t dt
More informationScalars and Vectors Scalar
Scalas and ectos Scala A phscal quantt that s completel chaacteed b a eal numbe (o b ts numecal value) s called a scala. In othe wods a scala possesses onl a magntude. Mass denst volume tempeatue tme eneg
More informationSolving the Dirac Equation: Using Fourier Transform
McNa Schola Reeach Jounal Volume Atcle Solvng the ac quaton: Ung oue Tanfom Vncent P. Bell mby-rddle Aeonautcal Unvety, Vncent.Bell@my.eau.edu ollow th and addtonal wok at: http://common.eau.edu/na Recommended
More informationISOPARAMETRIC ELEMENTS
5. ISOPARAMETRIC ELEMETS Bce Ion, n 968, Revoltonzed the Fnte Element Method b Intodcng a atal Coodnate Refeence Stem 5. ITRODUCTIO Befoe development of the Fnte Element Method, eeache n the feld of tctal
More informationHow to Obtain Desirable Transfer Functions in MIMO Systems Under Internal Stability Using Open and Closed Loop Control
How to Obtain Desiable ansfe Functions in MIMO Sstems Unde Intenal Stabilit Using Open and losed Loop ontol echnical Repot of the ISIS Goup at the Univesit of Note Dame ISIS-03-006 June, 03 Panos J. Antsaklis
More informationMechanical design of IM. Torque Control of. Induction Machines... Slip ring rotor. Mathematical model. r r. Stator same as PMSM Rotor:
Toqe ontol of Incton Machne... a copae to PMSM Intal Electcal Engneeng an Atoaton Mechancal egn of IM Stato ae a PMSM oto: at aln Won coppe /Slp ng Intal Electcal Engneeng an Atoaton n Unvety, Sween Nan
More informationIntegral Control via Bias Estimation
1 Integal Contol via Bias stimation Consie the sstem ẋ = A + B +, R n, R p, R m = C +, R q whee is an nknown constant vecto. It is possible to view as a step istbance: (t) = 0 1(t). (If in fact (t) vaies
More informationEngineering Mechanics. Force resultants, Torques, Scalar Products, Equivalent Force systems
Engneeng echancs oce esultants, Toques, Scala oducts, Equvalent oce sstems Tata cgaw-hll Companes, 008 Resultant of Two oces foce: acton of one bod on anothe; chaacteed b ts pont of applcaton, magntude,
More informationSet of square-integrable function 2 L : function space F
Set of squae-ntegable functon L : functon space F Motvaton: In ou pevous dscussons we have seen that fo fee patcles wave equatons (Helmholt o Schödnge) can be expessed n tems of egenvalue equatons. H E,
More informationIf there are k binding constraints at x then re-label these constraints so that they are the first k constraints.
Mathematcal Foundatons -1- Constaned Optmzaton Constaned Optmzaton Ma{ f ( ) X} whee X {, h ( ), 1,, m} Necessay condtons fo to be a soluton to ths mamzaton poblem Mathematcally, f ag Ma{ f ( ) X}, then
More informationLecture 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.
More informationChapter 23: Electric Potential
Chapte 23: Electc Potental Electc Potental Enegy It tuns out (won t show ths) that the tostatc foce, qq 1 2 F ˆ = k, s consevatve. 2 Recall, fo any consevatve foce, t s always possble to wte the wok done
More informationChapter Fifiteen. Surfaces Revisited
Chapte Ffteen ufaces Revsted 15.1 Vecto Descpton of ufaces We look now at the vey specal case of functons : D R 3, whee D R s a nce subset of the plane. We suppose s a nce functon. As the pont ( s, t)
More informationUsing DP for hierarchical discretization of continuous attributes. Amit Goyal (31 st March 2008)
Usng DP fo heachcal dscetzaton of contnos attbtes Amt Goyal 31 st Mach 2008 Refeence Chng-Cheng Shen and Yen-Lang Chen. A dynamc-pogammng algothm fo heachcal dscetzaton of contnos attbtes. In Eopean Jonal
More information2/24/2014. The point mass. Impulse for a single collision The impulse of a force is a vector. The Center of Mass. System of particles
/4/04 Chapte 7 Lnea oentu Lnea oentu of a Sngle Patcle Lnea oentu: p υ It s a easue of the patcle s oton It s a vecto, sla to the veloct p υ p υ p υ z z p It also depends on the ass of the object, sla
More informationCh. 3: Forward and Inverse Kinematics
Ch. : Fowa an Invee Knemat Reap: The Denavt-Hatenbeg (DH) Conventon Repeentng eah nvual homogeneou tanfomaton a the pout of fou ba tanfomaton: pout of fou ba tanfomaton: x a x z z a a a Rot Tan Tan Rot
More informationChapter 3 Vector Integral Calculus
hapte Vecto Integal alculus I. Lne ntegals. Defnton A lne ntegal of a vecto functon F ove a cuve s F In tems of components F F F F If,, an ae functon of t, we have F F F F t t t t E.. Fn the value of the
More informationThe Backpropagation Algorithm
The Backpopagaton Algothm Achtectue of Feedfowad Netwok Sgmodal Thehold Functon Contuctng an Obectve Functon Tanng a one-laye netwok by teepet decent Tanng a two-laye netwok by teepet decent Copyght Robet
More informationElectrical Circuits II (ECE233b)
Electrcal Crcut II (ECE33b) Applcaton of Laplace Tranform to Crcut Analy Anet Dounav The Unverty of Wetern Ontaro Faculty of Engneerng Scence Crcut Element Retance Tme Doman (t) v(t) R v(t) = R(t) Frequency
More information4. Linear systems of equations. In matrix form: Given: matrix A and vector b Solve: Ax = b. Sup = least upper bound
4. Lnea systes of eqatons a a a a 3 3 a a a a 3 3 a a a a 3 3 In at fo: a a a3 a a a a3 a a a a3 a Defnton ( vecto no): On a vecto space V, a vecto no s a fncton fo V to e set of non-negatve eal nes at
More informationHomework Set 3 Physics 319 Classical Mechanics
Homewok Set 3 Phsics 319 lassical Mechanics Poblem 5.13 a) To fin the equilibium position (whee thee is no foce) set the eivative of the potential to zeo U 1 R U0 R U 0 at R R b) If R is much smalle than
More informationCHAPTER 4 TWO-COMMODITY CONTINUOUS REVIEW INVENTORY SYSTEM WITH BULK DEMAND FOR ONE COMMODITY
Unvety of Petoa etd Van choo C de Wet 6 CHAPTER 4 TWO-COMMODITY CONTINUOU REVIEW INVENTORY YTEM WITH BULK DEMAND FOR ONE COMMODITY A modfed veon of th chapte ha been accepted n Aa-Pacfc Jounal of Opeatonal
More informationB da = 0. Q E da = ε. E da = E dv
lectomagnetic Theo Pof Ruiz, UNC Asheville, doctophs on YouTube Chapte Notes The Maxwell quations in Diffeential Fom 1 The Maxwell quations in Diffeential Fom We will now tansfom the integal fom of the
More informationChapter 19 Webassign Help Problems
Chapte 9 Webaign Help Poblem 4 5 6 7 8 9 0 Poblem 4: The pictue fo thi poblem i a bit mileading. They eally jut give you the pictue fo Pat b. So let fix that. Hee i the pictue fo Pat (a): Pat (a) imply
More informationCOORDINATE SYSTEMS, COORDINATE TRANSFORMS, AND APPLICATIONS
Dola Bagaoo 0 COORDINTE SYSTEMS COORDINTE TRNSFORMS ND PPLICTIONS I. INTRODUCTION Smmet coce of coodnate sstem. In solvng Pscs poblems one cooses a coodnate sstem tat fts te poblem at and.e. a coodnate
More informationSmall signal analysis
Small gnal analy. ntroducton Let u conder the crcut hown n Fg., where the nonlnear retor decrbed by the equaton g v havng graphcal repreentaton hown n Fg.. ( G (t G v(t v Fg. Fg. a D current ource wherea
More informationChapter I Matrices, Vectors, & Vector Calculus 1-1, 1-9, 1-10, 1-11, 1-17, 1-18, 1-25, 1-27, 1-36, 1-37, 1-41.
Chapte I Matces, Vectos, & Vecto Calculus -, -9, -0, -, -7, -8, -5, -7, -36, -37, -4. . Concept of a Scala Consde the aa of patcles shown n the fgue. he mass of the patcle at (,) can be epessed as. M (,
More information8 Baire Category Theorem and Uniform Boundedness
8 Bae Categoy Theoem and Unfom Boundedness Pncple 8.1 Bae s Categoy Theoem Valdty of many esults n analyss depends on the completeness popety. Ths popety addesses the nadequacy of the system of atonal
More informationWell-Posedness of Feedback Loop:
ntena Stabiity We-oedne of Feedback Loop: onide the foowing feedback ytem - u u p d i d y Let be both pope tanfe function. Howeve u n d di 3 3 ote that the tanfe function fom the extena igna n d d to u
More informationKey Mathematical Backgrounds
Ke Mathematical Background Dierential Equation Ordinar Linear Partial Nonlinear: mooth, nonmooth,, piecewie linear Map Linear Nonlinear Equilibrium/Stead-State State Solution Linearization Traner Function
More informationQuestion 1: The dipole
Septembe, 08 Conell Univesity, Depatment of Physics PHYS 337, Advance E&M, HW #, due: 9/5/08, :5 AM Question : The dipole Conside a system as discussed in class and shown in Fig.. in Heald & Maion.. Wite
More information2 dependence in the electrostatic force means that it is also
lectc Potental negy an lectc Potental A scala el, nvolvng magntues only, s oten ease to wo wth when compae to a vecto el. Fo electc els not havng to begn wth vecto ssues woul be nce. To aange ths a scala
More informationIntegral Vector Operations and Related Theorems Applications in Mechanics and E&M
Dola Bagayoko (0) Integal Vecto Opeatons and elated Theoems Applcatons n Mechancs and E&M Ι Basc Defnton Please efe to you calculus evewed below. Ι, ΙΙ, andιιι notes and textbooks fo detals on the concepts
More informationChapter 11. Supplemental Text Material. The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder
S-. The Method of Steepet cent Chapter. Supplemental Text Materal The method of teepet acent can be derved a follow. Suppoe that we have ft a frtorder model y = β + β x and we wh to ue th model to determne
More informationAdditional File 1 - Detailed explanation of the expression level CPD
Addtonal Fle - Detaled explanaton of the expreon level CPD A mentoned n the man text, the man CPD for the uterng model cont of two ndvdual factor: P( level gen P( level gen P ( level gen 2 (.).. CPD factor
More informationStatic Electric Fields. Coulomb s Law Ε = 4πε. Gauss s Law. Electric Potential. Electrical Properties of Materials. Dielectrics. Capacitance E.
Coulomb Law Ε Gau Law Electic Potential E Electical Popetie of Mateial Conducto J σe ielectic Capacitance Rˆ V q 4πε R ρ v 2 Static Electic Field εe E.1 Intoduction Example: Electic field due to a chage
More informationChapter 12: Kinematics of a Particle 12.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS. u of the polar coordinate system are also shown in
ME 01 DYNAMICS Chapte 1: Kinematics of a Paticle Chapte 1 Kinematics of a Paticle A. Bazone 1.8 CURVILINEAR MOTION: CYLINDRICAL COMPONENTS Pola Coodinates Pola coodinates ae paticlaly sitable fo solving
More informationHarmonic oscillator approximation
armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon
More informationPrerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,
R Pena Towe, Road No, Contactos Aea, Bistupu, Jamshedpu 8, Tel (657)89, www.penaclasses.com IIT JEE Mathematics Pape II PART III MATHEMATICS SECTION I Single Coect Answe Type This section contains 8 multiple
More information1. A body will remain in a state of rest, or of uniform motion in a straight line unless it
Pncples of Dnamcs: Newton's Laws of moton. : Foce Analss 1. A bod wll eman n a state of est, o of unfom moton n a staght lne unless t s acted b etenal foces to change ts state.. The ate of change of momentum
More informationIntroduction to Robotics (Fag 3480)
Intouton to Robot (Fg 8) Vå Robet Woo (Hw Engneeeng n pple Sene-B) Ole Jkob Elle PhD (Mofe fo IFI/UIO) Føtemnuen II Inttutt fo Infomtkk Unvetetet Olo Sekjonlee Teknolog Intevenjonenteet Olo Unvetetkehu
More informationUNIT10 PLANE OF REGRESSION
UIT0 PLAE OF REGRESSIO Plane of Regesson Stuctue 0. Intoducton Ojectves 0. Yule s otaton 0. Plane of Regesson fo thee Vaales 0.4 Popetes of Resduals 0.5 Vaance of the Resduals 0.6 Summay 0.7 Solutons /
More informationASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4.
ASTR 3740 Relativity & Comology Sping 019. Anwe to Poblem Set 4. 1. Tajectoie of paticle in the Schwazchild geomety The equation of motion fo a maive paticle feely falling in the Schwazchild geomety ae
More informationˆ 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
More informationStatistical Properties of the OLS Coefficient Estimators. 1. Introduction
ECOOMICS 35* -- OTE 4 ECO 35* -- OTE 4 Stattcal Properte of the OLS Coeffcent Etmator Introducton We derved n ote the OLS (Ordnary Leat Square etmator ˆβ j (j, of the regreon coeffcent βj (j, n the mple
More informationPHY126 Summer Session I, 2008
PHY6 Summe Sesson I, 8 Most of nfomaton s avalable at: http://nngoup.phscs.sunsb.edu/~chak/phy6-8 ncludng the sllabus and lectue sldes. Read sllabus and watch fo mpotant announcements. Homewok assgnment
More informationUnit_III Complex Numbers: Some Basic Results: 1. If z = x +iy is a complex number, then the complex number z = x iy is
Unt_III Comple Nmbes: In the sstem o eal nmbes R we can sole all qadatc eqatons o the om a b c, a, and the dscmnant b 4ac. When the dscmnant b 4ac
More informationgravity r2,1 r2 r1 by m 2,1
Gavtaton Many of the foundatons of classcal echancs wee fst dscoveed when phlosophes (ealy scentsts and atheatcans) ted to explan the oton of planets and stas. Newton s ost faous fo unfyng the oton of
More informationThen the number of elements of S of weight n is exactly the number of compositions of n into k parts.
Geneating Function In a geneal combinatoial poblem, we have a univee S of object, and we want to count the numbe of object with a cetain popety. Fo example, if S i the et of all gaph, we might want to
More informationObserver Based Parallel IM Speed and Parameter Estimation
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 11, No. 3, Octobe 2014, 501-521 UDC: 621.313.333-253:519.853 DOI: 10.2298/SJEE1403501S Obeve Baed Paallel IM Speed and Paamete Etmaton Saša Skoko 1, Dako
More informationCapítulo. Three Dimensions
Capítulo Knematcs of Rgd Bodes n Thee Dmensons Mecánca Contents ntoducton Rgd Bod Angula Momentum n Thee Dmensons Pncple of mpulse and Momentum Knetc Eneg Sample Poblem 8. Sample Poblem 8. Moton of a Rgd
More informationECE Spring Prof. David R. Jackson ECE Dept. Notes 24
ECE 6345 Sprng 015 Prof. Dav R. Jackon ECE Dept. Note 4 1 Overvew In th et of note we erve the SDI formlaton ng a more mathematcal, bt general, approach (we rectly Forer tranform Maxwell eqaton). Th allow
More informationInference for A One Way Factorial Experiment. By Ed Stanek and Elaine Puleo
Infeence fo A One Way Factoial Expeiment By Ed Stanek and Elaine Puleo. Intoduction We develop etimating equation fo Facto Level mean in a completely andomized one way factoial expeiment. Thi development
More informationState Space: Observer Design Lecture 11
State Space: Oberver Deign Lecture Advanced Control Sytem Dr Eyad Radwan Dr Eyad Radwan/ACS/ State Space-L Controller deign relie upon acce to the tate variable for feedback through adjutable gain. Thi
More informationSensorless 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
More informationone primary direction in which heat transfers (generally the smallest dimension) simple model good representation for solving engineering problems
CHAPTER 3: One-Dimenional Steady-State Conduction one pimay diection in which heat tanfe (geneally the mallet dimenion) imple model good epeentation fo olving engineeing poblem 3. Plane Wall 3.. hot fluid
More information(8) Gain Stage and Simple Output Stage
EEEB23 Electoncs Analyss & Desgn (8) Gan Stage and Smple Output Stage Leanng Outcome Able to: Analyze an example of a gan stage and output stage of a multstage amplfe. efeence: Neamen, Chapte 11 8.0) ntoducton
More informationMULTIPLE REGRESSION ANALYSIS For the Case of Two Regressors
MULTIPLE REGRESSION ANALYSIS For the Cae of Two Regreor In the followng note, leat-quare etmaton developed for multple regreon problem wth two eplanator varable, here called regreor (uch a n the Fat Food
More informationRigid Bodies: Equivalent Systems of Forces
Engneeng Statcs, ENGR 2301 Chapte 3 Rgd Bodes: Equvalent Sstems of oces Intoducton Teatment of a bod as a sngle patcle s not alwas possble. In geneal, the se of the bod and the specfc ponts of applcaton
More informationQuick Visit to Bernoulli Land
Although we have een the Bernoull equaton and een t derved before, th next note how t dervaton for an uncopreble & nvcd flow. The dervaton follow that of Kuethe &Chow ot cloely (I lke t better than Anderon).
More informationSession outline. Introduction to Feedback Control. The Idea of Feedback. Automatic control. Basic setting. The feedback principle
Session otline Intodction to Feedback Contol Kal-Eik Åzen, Anton Cevin Feedback and feedfowad PID Contol State-space models Tansfe fnction models Contol design sing pole placement State feedback and obseves
More informationMachine Learning. Spectral Clustering. Lecture 23, April 14, Reading: Eric Xing 1
Machne Leanng -7/5 7/5-78, 78, Spng 8 Spectal Clusteng Ec Xng Lectue 3, pl 4, 8 Readng: Ec Xng Data Clusteng wo dffeent ctea Compactness, e.g., k-means, mxtue models Connectvty, e.g., spectal clusteng
More informationTeam. Outline. Statistics and Art: Sampling, Response Error, Mixed Models, Missing Data, and Inference
Team Stattc and Art: Samplng, Repone Error, Mxed Model, Mng Data, and nference Ed Stanek Unverty of Maachuett- Amhert, USA 9/5/8 9/5/8 Outlne. Example: Doe-repone Model n Toxcology. ow to Predct Realzed
More informationA Simple Approach to Robust Optimal Pole Assignment of Decentralized Stochastic Singularly-Perturbed Computer Controlled Systems
A Sple Appoach to Robst Optal Pole Assgnent of Decentaled Stochastc Snglaly-Petbed Copte Contolled Systes Ka-chao Yao Depatent of Indstal Edcaton and echnology Natonal Chang-ha Unvesty of Edcaton No. Sh-Da
More informationradians). Figure 2.1 Figure 2.2 (a) quadrant I angle (b) quadrant II angle is in standard position Terminal side Terminal side Terminal side
. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an
More informationEE 5337 Computational Electromagnetics (CEM)
7//28 Instucto D. Raymond Rumpf (95) 747 6958 cumpf@utep.edu EE 5337 Computatonal Electomagnetcs (CEM) Lectue #6 TMM Extas Lectue 6These notes may contan copyghted mateal obtaned unde fa use ules. Dstbuton
More informationSYSTEMS 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
More information19 The Born-Oppenheimer Approximation
9 The Bon-Oppenheme Appoxmaton The full nonelatvstc Hamltonan fo a molecule s gven by (n a.u.) Ĥ = A M A A A, Z A + A + >j j (883) Lets ewte the Hamltonan to emphasze the goal as Ĥ = + A A A, >j j M A
More information( ) ( )( ) ˆ. Homework #8. Chapter 27 Magnetic Fields II.
Homewok #8. hapte 7 Magnetic ields. 6 Eplain how ou would modif Gauss s law if scientists discoveed that single, isolated magnetic poles actuall eisted. Detemine the oncept Gauss law fo magnetism now eads
More informationImplementation of RCWA
Instucto D. Ramond Rumpf (915) 747 6958 cumpf@utep.edu EE 5337 Computational Electomagnetics Lectue # Implementation of RCWA Lectue These notes ma contain copighted mateial obtained unde fai use ules.
More informationVEKTORANALYS FLUX INTEGRAL LINE INTEGRAL. and. Kursvecka 2. Kapitel 4 5. Sidor 29 50
VEKTORANAYS Ksecka INE INTEGRA and UX INTEGRA Kaptel 4 5 Sdo 9 5 A wnd TARGET PROBEM We want to psh a mne cat along a path fom A to B. Bt the wnd s blowng. How mch enegy s needed? (.e. how mch s the wok?
More informationCHAPTER 4 EVALUATION OF FORCE-CONSTANT MATRIX
CHAPTER 4 EVALUATION OF FORCE-CONSTANT MATRIX 4.- AIM OF THE WORK As antcpated n the ntodcton the am of the pesent ok s to obtan the nmecal vale of the foce-constant matx fo tantalm. In a fst step expesson
More informationPhysics Exam II Chapters 25-29
Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do
More informationDYNAMICS VECTOR MECHANICS FOR ENGINEERS: Kinematics of Rigid Bodies in Three Dimensions. Seventh Edition CHAPTER
Edton CAPTER 8 VECTOR MECANCS FOR ENGNEERS: DYNAMCS Fednand P. Bee E. Russell Johnston, J. Lectue Notes: J. Walt Ole Teas Tech Unvest Knematcs of Rgd Bodes n Thee Dmensons 003 The McGaw-ll Companes, nc.
More informationSolution of Advection-Diffusion Equation for Concentration of Pollution and Dissolved Oxygen in the River Water by Elzaki Transform
Ameican Jonal of Engineeing Reeach (AJER) 016 Ameican Jonal of Engineeing Reeach (AJER) e-issn: 30-0847 p-issn : 30-0936 Volme-5, Ie-9, pp-116-11 www.aje.og Reeach Pape Open Acce Soltion of Advection-Diffion
More informationSection 25 Describing Rotational Motion
Section 25 Decibing Rotational Motion What do object do and wh do the do it? We have a ve thoough eplanation in tem of kinematic, foce, eneg and momentum. Thi include Newton thee law of motion and two
More informationHistogram Processing
Hitogam Poceing Lectue 4 (Chapte 3) Hitogam Poceing The hitogam of a digital image with gay level fom to L- i a dicete function h( )=n, whee: i the th gay level n i the numbe of pixel in the image with
More informationME 375 FINAL EXAM Wednesday, May 6, 2009
ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.
More informationVariable Structure Control ~ Basics
Varable Structure Control ~ Bac Harry G. Kwatny Department of Mechancal Engneerng & Mechanc Drexel Unverty Outlne A prelmnary example VS ytem, ldng mode, reachng Bac of dcontnuou ytem Example: underea
More informationHierarchical Intelligent Sliding Mode Control: Application to Stepper Motors
Heachcal Intellgent Sldng Mode Contol: Applcaton to Steppe Moto Benado Rncon Maque Aleande G Louanov and Edga N Sanche Membe IEEE Abtact: In th pape one method of obut contol baed on ldng mode and fuy
More informationSignal Recovery - Prof. S. Cova - Exam 2016/02/16 - P1 pag.1
gal Recovery - Pro.. Cova - Exam 06/0/6 - P pag. PROBEM Data ad Note Appled orce F rt cae: tep ple ecod cae: rectaglar ple wth drato p = 5m Pezoelectrc orce eor A q =0pC/N orce-to-charge covero C = 500pF
More informationECE Spring Prof. David R. Jackson ECE Dept.
ECE 6341 Sprng 016 Prof. Da R. Jackon ECE Dept. Note Note 4 44 1 Oerew n th et of note we ere the SD formlaton ng a more mathematcal, bt more general, approach (we rectly Forer tranform Maxwell eqaton).
More informationGravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003
avity David Bawacz 7778 Thonapple Bayou, and Rapid, MI 495 David Bawacz /3/3 http://membe.titon.net/daveb Uing the concept dicued in the peceding pape ( http://membe.titon.net/daveb ), I will now deive
More informationIf there are multiple rxns, use concentrations not conversions. These might occur in combination or by themselves.
hapte 6 MLTIPLE RETIONS If thee ae multiple xns, use concentations not convesions. intemediate. Seies Reactions onsecutive xns. Paallel Reactions. omplex Reactions: Seies and Paallel 4. Independent None
More information= 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
More informationQueuing Network Approximation Technique for Evaluating Performance of Computer Systems with Input to Terminals
6th Intenatonal Confeence on Chemcal Agcultual Envonmental and Bologcal cence CAEB-7 Dec. 7-8 07 Pa Fance ueung Netwo Appoxmaton Technque fo Evaluatng Pefomance of Compute ytem wth Input to Temnal Ha Yoh
More informationCharacterizations of Slant Helices. According to Quaternionic Frame
Appled Mathematcal Scence, Vol. 7, 0, no. 75, 79-78 HIKARI Ltd, www.m-hka.com http://dx.do.og/0.988/am.0.557 Chaactezaton of Slant Helce Accodng to Quatenonc Fame Hüeyn KOCAYİĞİT and Beyza Betül PEKACAR
More informationCFAR BI DETECTOR IN BINOMIAL DISTRIBUTION PULSE JAMMING 1. I. Garvanov. (Submitted by Academician Ivan Popchev on June 23, 2003)
FA BI EEO I BIOMIAL ISIBUIO PULSE JAMMIG I. Gavanov (Submtted by Academcan Ivan Popchev on June 3, 3) Abtact: In many pactcal tuaton, howeve, the envonment peence of tong pule ammng (PJ) wth hgh ntenty;
More informationAE301 Aerodynamics I UNIT B: Theory of Aerodynamics
AE301 Aeodynamics I UNIT B: Theoy of Aeodynamics ROAD MAP... B-1: Mathematics fo Aeodynamics B-2: Flow Field Repesentations B-3: Potential Flow Analysis B-4: Applications of Potential Flow Analysis AE301
More information9/12/2013. Microelectronics Circuit Analysis and Design. Modes of Operation. Cross Section of Integrated Circuit npn Transistor
Mcoelectoncs Ccut Analyss and Desgn Donald A. Neamen Chapte 5 The pola Juncton Tanssto In ths chapte, we wll: Dscuss the physcal stuctue and opeaton of the bpola juncton tanssto. Undestand the dc analyss
More informationExcellent web site with information on various methods and numerical codes for scattering by nonspherical particles:
Lectue 5. Lght catteng and abopton by atmophec patcuate. at 3: Scatteng and abopton by nonpheca patce: Ray-tacng, T- Matx, and FDTD method. Objectve:. Type of nonpheca patce n the atmophee.. Ray-tacng
More informationNonlinear Network Structures for Optimal Control
tomaton & Robotcs Research Insttte RRI Nonlnear Network Strctres for Optmal Control Frank. ews and Mrad Mrad b-khalaf dvanced Controls, Sensors, and MEMS CSM grop System Cost f + g 0 [ ] V Q + dt he Usal
More informationWhy Reduce Dimensionality? Feature Selection vs Extraction. Subset Selection
Dimenionality Reduction Why Reduce Dimenionality? Olive lide: Alpaydin Numbeed blue lide: Haykin, Neual Netwok: A Compehenive Foundation, Second edition, Pentice-Hall, Uppe Saddle Rive:NJ,. Black lide:
More informationINTRODUCTION. 2. Vectors in Physics 1
INTRODUCTION Vectos ae used in physics to extend the study of motion fom one dimension to two dimensions Vectos ae indispensable when a physical quantity has a diection associated with it As an example,
More information