Steady-state tracking & sys. types

Size: px
Start display at page:

Download "Steady-state tracking & sys. types"

Transcription

1 Sty-tt trcking & y. ty Unity fck control: um CL tl lnt r C y - r - o.l. y y r ol ol o.l. m m n n n N N N N N, N,, ut N N, m,

2 ol.. clo-loo: y r ol.. trcking rror: r y r ty-tt trcking: t r ol.. ol.. For t inut: r to t ol..

3 A ytm of ty or highr cn trck t inut with zro. o.. l o.. l For unit t inut: for ty for ty or highr R If t i not unit: r, thn R for ty for ty or highr

4 cont cll ttic locity rror not : to rm rm : i unit If r r r ol ol ol ol ol rt t

5 ignl. trck rm inut ty ytm cn not to rm ty ytm, For n m m N,,

6 . non- zro ty tt rror tyytm trckrm with finit to rm finit, ty: For n m m n m m N,!,,,

7 For ty or highr, N,3, m n, to rm m m n 3 3 cncl on till h fctor m ty or highr ytm cn trck rm inut with no 3.

8 ty if thn : unit, rm i not If ty if ty if ty if : rm inut unit For R R r

9 : 3 t t t r r cclrtion inut unit r 3 to cc rt t

10 i th cclrtion rror contnt. For ty ytm, no fctor of in n. to cc m m n

11 ig. cc. trct t ytm cn' ty or to cc u i.. in n. of i..on fctor. in of on fctor tyytm, For n n n m m,

12 ty : N, two fctor of in or, two fctor of in n. or,, m m n n n to cc ty ytm cn trct cc ig. with finit.. rror.

13 Sty-tt trcking & y. ty lnt r C y - o.l. m m n n n N N N N Sytm ty N #fctor of in nomintor Ty : N,, /, Ty :N,,,, /, Ty :N,,,, /

14 Sttic oition rror cont : Sttic locity rror cont : to t Sttic cclrtion rror cont : to rm to cc Auming clo-loo ytm tility ol ol ol

15 y. ty rf. inut rtu t r/ rttu t r/ rt ½t u t r/ 3 ty N / / ty N / / ty, N / /, ty 3, N 3

16 Exml: wtr tnk ll control P P P l o P P R R N RA R H C C RA R H to cc to rm to t, ty,, control :.. H - C

17 PI control: m H, I P I ut C P P I R CH RA on fctor of in n, N ty, R, I to t to rm R to cc I

18 y toty tt trckingiy. ty. y. ty w.r.t. r i # in i.. # in th on loo T.F. # in th th from following th loo to th r.g. I r ω n ξ ω - n T count # in th : ty w.r.t. r

19 xml fin ytm ty, rror contnt & ty tt rror to t. rm. cc. Not : No inut or it. cifi. Tk fult : r y thr i on, ty

20 for ty to cc for to t to rm ty for for ty ty 4. 4.

21 5 5, 5 5 to cc ty to rm to t ty ty, # Exml :

22 Exml : ut c. l, #, ty. 3 h o. ol for ny clo - loo ytm i untl. for ny inut. h to h c.l. tility.

23 yt. ty w.r.t. iturnc inut : # long th th from to " " whr th it. ntr. If thr r multil it., r multil yt.ty. ty h finit tycn rjct cont it. h finit thr to tit. to rm or cc it. to rm it

24 h ty cn rjct t or rm it. h finit ty 3 or highr cn rjct t or rm or cc it. cn h imilr tl only iffrnc : to cc it. to cc it to t for. for it

25 I - r ω n ζ ω n T A B 3,, ;, A I I I if if if u to ty on to th th from t look to With rct

26 3 ; : B n I n I n n I if or if u to ytm i ty w.r.t of totl to th th from t look to. r. W. ω ζ ζ ω ζω ω

27 Totl ty tt rror u to r u to u to r,, cn ny com. of t, rm, cc, or zro. If ithr comonnt, thn

28 Exml c : r t,, ty w.r.t r i cn rjct t c : r t t, gin ty w.r.t r u to rm c 3 : r t, t, u tot r ty u tot ty w.r.t

29 & c 4 : r totl t, u to t r u to rm ty w.r.t. not rnt. totl inot rnt I t t, ty I

30 c 5 : r t t, not rnt u to ty w.r.t r t t, u to rm r ty w.r.t totl u to cc

31 T V I in V T m - L R J - V T V I in V T m - L R J - V

STEADY STATE ERRORS IN UNITY FEEDBACK CONTROL SYSTEMS

STEADY STATE ERRORS IN UNITY FEEDBACK CONTROL SYSTEMS VU -lrning Courwr Control Enginring (ME55) SEADY SAE ERRORS I UIY FEEDBAC COROL SYSEMS Error in control yt y ttriutd to ny fctor. Chng in th rfrnc inut will cu unoidl rror during trnint riod, nd lo cu

More information

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then

[ ] 1+ lim G( s) 1+ s + s G s s G s Kacc SYSTEM PERFORMANCE. Since. Lecture 10: Steady-state Errors. Steady-state Errors. Then SYSTEM PERFORMANCE Lctur 0: Stady-tat Error Stady-tat Error Lctur 0: Stady-tat Error Dr.alyana Vluvolu Stady-tat rror can b found by applying th final valu thorm and i givn by lim ( t) lim E ( ) t 0 providd

More information

The Theory of Small Reflections

The Theory of Small Reflections Jim Stils Th Univ. of Knss Dt. of EECS 4//9 Th Thory of Smll Rflctions /9 Th Thory of Smll Rflctions Rcll tht w nlyzd qurtr-wv trnsformr usg th multil rflction viw ot. V ( z) = + β ( z + ) V ( z) = = R

More information

Chapter #3 EEE Subsea Control and Communication Systems

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)

More information

1.2. Linear Variable Coefficient Equations. y + b "! = a y + b " Remark: The case b = 0 and a non-constant can be solved with the same idea as above.

1.2. Linear Variable Coefficient Equations. y + b ! = a y + b  Remark: The case b = 0 and a non-constant can be solved with the same idea as above. 1 12 Liner Vrible Coefficient Equtions Section Objective(s): Review: Constnt Coefficient Equtions Solving Vrible Coefficient Equtions The Integrting Fctor Method The Bernoulli Eqution 121 Review: Constnt

More information

EE Control Systems LECTURE 8

EE Control Systems LECTURE 8 Coyright F.L. Lewi 999 All right reerved Udted: Sundy, Ferury, 999 EE 44 - Control Sytem LECTURE 8 REALIZATION AND CANONICAL FORMS A liner time-invrint (LTI) ytem cn e rereented in mny wy, including: differentil

More information

Systems Analysis and Control

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 21: Stability Margins and Closing the Loop Overview In this Lecture, you will learn: Closing the Loop Effect on Bode Plot Effect

More information

Chapter #5 EEE Control Systems

Chapter #5 EEE Control Systems Sprig EEE Chpter #5 EEE Cotrol Sytem Deig Bed o Root Locu Chpter / Sprig EEE Deig Bed Root Locu Led Cotrol (equivlet to PD cotrol) Ued whe the tedy tte propertie of the ytem re ok but there i poor performce,

More information

LINKÖPINGS TEKNISKA HÖGSKOLA. Fluid and Mechanical Engineering Systems

LINKÖPINGS TEKNISKA HÖGSKOLA. Fluid and Mechanical Engineering Systems (6) Fluid nd Mechnicl Engineering Sytem 008086. ) Cvittion in orifice In hydrulic ytem cvittion occur downtrem orifice with high preure drop. For n orifice with contnt inlet preure of p = 00 br cvittion

More information

Floating Point Number System -(1.3)

Floating Point Number System -(1.3) Floting Point Numbr Sstm -(.3). Floting Point Numbr Sstm: Comutrs rrsnt rl numbrs in loting oint numbr sstm: F,k,m,M 0. 3... k ;0, 0 i, i,...,k, m M. Nottions: th bs 0, k th numbr o igts in th bs xnsion

More information

Floating Point Number System -(1.3)

Floating Point Number System -(1.3) Floting Point Numbr Sstm -(.3). Floting Point Numbr Sstm: Comutrs rrsnt rl numbrs in loting oint numbr sstm: F,k,m,M 0. 3... k ;0, 0 i, i,...,k, m M. Nottions: th bs 0, k th numbr o igits in th bs xnsion

More information

sin sin 1 d r d Ae r 2

sin sin 1 d r d Ae r 2 Diffction k f c f Th Huygn-Fnl Pincil tt: Evy unobtuct oint of vfont, t givn intnt, v ouc of hicl cony vlt (ith th m funcy tht of th imy v. Th mlitu of th oticl fil t ny oint byon i th uoition of ll th

More information

12.7 Steady State Error

12.7 Steady State Error Lecture Notes on Control Systems/D. Ghose/01 106 1.7 Steady State Error For first order systems we have noticed an overall improvement in performance in terms of rise time and settling time. But there

More information

Control Systems. Transient and Steady State Response.

Control Systems. Transient and Steady State Response. Corol Sym Trai a Say Sa Ro chibum@oulch.ac.kr Ouli Tim Domai Aalyi orr ym Ui ro Ui ram ro Ui imul ro Chibum L -Soulch Corol Sym Tim Domai Aalyi Afr h mahmaical mol of h ym i obai, aalyi of ym rformac i.

More information

Chapter 12. Feedback Control Characteristics of Feedback Systems

Chapter 12. Feedback Control Characteristics of Feedback Systems Chapter 1 Feedbac Control Feedbac control allows a system dynamic response to be modified without changing any system components. Below, we show an open-loop system (a system without feedbac) and a closed-loop

More information

positive definite (symmetric with positive eigenvalues) positive semi definite (symmetric with nonnegative eigenvalues)

positive definite (symmetric with positive eigenvalues) positive semi definite (symmetric with nonnegative eigenvalues) Chter Liner Qudrtic Regultor Problem inimize the cot function J given by J x' Qx u' Ru dt R > Q oitive definite ymmetric with oitive eigenvlue oitive emi definite ymmetric with nonnegtive eigenvlue ubject

More information

n r t d n :4 T P bl D n, l d t z d th tr t. r pd l

n r t d n :4 T P bl D n, l d t z d   th tr t. r pd l n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R

More information

Higher Order Linear Equations Lecture 7

Higher Order Linear Equations Lecture 7 Higher Order Linear Equations Lecture 7 Dibyajyoti Deb 7.1. Outline of Lecture General Theory of nth Order Linear Equations. Homogeneous Equations with Constant Coefficients. 7.2. General Theory of nth

More information

Fault Modeling. EE5375 ADD II Prof. MacDonald

Fault Modeling. EE5375 ADD II Prof. MacDonald Fult Modeling EE5375 ADD II Prof. McDonld Stuck At Fult Models l Modeling of physicl defects (fults) simplify to logicl fult l stuck high or low represents mny physicl defects esy to simulte technology

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse

What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse Animls shp T h i nk Wht o you know? 2 2:29 Listn n fin. hors Wht s this? Wht s this? It s got ig nos. It s ig n gry. It s hors! YES! 2 Wht r ths? Wht r ths? Thy v got two lgs. Thy r smll n rown. Thy r

More information

The Z transform techniques

The Z transform techniques h Z trnfor tchniqu h Z trnfor h th rol in dicrt yt tht th Lplc trnfor h in nlyi of continuou yt. h Z trnfor i th principl nlyticl tool for ingl-loop dicrt-ti yt. h Z trnfor h Z trnfor i to dicrt-ti yt

More information

,. *â â > V>V. â ND * 828.

,. *â â > V>V. â ND * 828. BL D,. *â â > V>V Z V L. XX. J N R â J N, 828. LL BL D, D NB R H â ND T. D LL, TR ND, L ND N. * 828. n r t d n 20 2 2 0 : 0 T http: hdl.h ndl.n t 202 dp. 0 02802 68 Th N : l nd r.. N > R, L X. Fn r f,

More information

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th n r t d n 20 0 : T P bl D n, l d t z d http:.h th tr t. r pd l 46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l

More information

Construction 11: Book I, Proposition 42

Construction 11: Book I, Proposition 42 Th Visul Construtions of Euli Constrution #11 73 Constrution 11: Book I, Proposition 42 To onstrut, in givn rtilinl ngl, prlllogrm qul to givn tringl. Not: Equl hr mns qul in r. 74 Constrution # 11 Th

More information

828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t

828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t 2Â F b. Th h ph rd l nd r. l X. TH H PH RD L ND R. L X. F r, Br n, nd t h. B th ttr h ph rd. n th l f p t r l l nd, t t d t, n n t n, nt r rl r th n th n r l t f th f th th r l, nd d r b t t f nn r r pr

More information

Ed H. H w H Ed. en 2: Ed. o o o z. o o. Q Ed. Ed Q to. PQ in o c3 o o. Ed P5 H Z. < u z. Ed H H Z O H U Z. > to. <! Ed Q. < Ed > Es.

Ed H. H w H Ed. en 2: Ed. o o o z. o o. Q Ed. Ed Q to. PQ in o c3 o o. Ed P5 H Z. < u z. Ed H H Z O H U Z. > to. <! Ed Q. < Ed > Es. d n 2: d t d t d! d d 52 d t d d P in t d. d P5 d - d d , d P il 0) m d p P p x d d n N r -^ T) n «n - P & J (N 0 ' 4 «"«5 -» % «D *5JD V 9 * * /J -2.2 " ^ 0 n 0) - P - i- 0) G V V - 1(2). i 1 1 & i '

More information

Non-homogeneous equations (Sect. 3.6).

Non-homogeneous equations (Sect. 3.6). Non-homogeneous equations (Sect. 3.6). We study: y + p(t) y + q(t) y = f (t). Method of variation of parameters. Using the method in an example. The proof of the variation of parameter method. Using the

More information

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! 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

More information

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.

More information

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n R P RT F TH PR D NT N N TR T F R N V R T F NN T V D 0 0 : R PR P R JT..P.. D 2 PR L 8 8 J PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D.. 20 00 D r r. Pr d nt: n J n r f th r d t r v th

More information

UNIT # 08 (PART - I)

UNIT # 08 (PART - I) . r. d[h d[h.5 7.5 mol L S d[o d[so UNIT # 8 (PRT - I CHEMICL INETICS EXERCISE # 6. d[ x [ x [ x. r [X[C ' [X [[B r '[ [B [C. r [NO [Cl. d[so d[h.5 5 mol L S d[nh d[nh. 5. 6. r [ [B r [x [y r' [x [y r'

More information

Chapter 4: Higher Order Linear Equations

Chapter 4: Higher Order Linear Equations Chapter 4: Higher Order Linear Equations MATH 351 California State University, Northridge April 7, 2014 MATH 351 (Differential Equations) Ch 4 April 7, 2014 1 / 11 Sec. 4.1: General Theory of nth Order

More information

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016 Wintr 2016 COMP-250: Introduction to Computr Scinc Lctur 23, April 5, 2016 Commnt out input siz 2) Writ ny lgorithm tht runs in tim Θ(n 2 log 2 n) in wors cs. Explin why this is its running tim. I don

More information

Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ

Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ Ğ Ü Ü Ü ğ ğ ğ Öğ ş öğ ş ğ öğ ö ö ş ğ ğ ö ğ Ğ ğ ğ Ğ ğ Öğ ç ğ ö öğ ğ ŞÇ ğ ğ l _.j l L., c :, c Ll Ll, c :r. l., }, l : ö,, Lc L.. c l Ll Lr. 0 c (} >,! l LA l l r r l rl c c.r; (Y ; c cy c r! r! \. L : Ll.,

More information

QUADRATIC EQUATIONS OBJECTIVE PROBLEMS

QUADRATIC EQUATIONS OBJECTIVE PROBLEMS QUADRATIC EQUATIONS OBJECTIVE PROBLEMS +. The solution of the eqution will e (), () 0,, 5, 5. The roots of the given eqution ( p q) ( q r) ( r p) 0 + + re p q r p (), r p p q, q r p q (), (d), q r p q.

More information

CONTROL SYSTEMS LABORATORY ECE311 LAB 3: Control Design Using the Root Locus

CONTROL SYSTEMS LABORATORY ECE311 LAB 3: Control Design Using the Root Locus CONTROL SYSTEMS LABORATORY ECE311 LAB 3: Control Deign Uing the Root Locu 1 Purpoe The purpoe of thi lbortory i to deign cruie control ytem for cr uing the root locu. 2 Introduction Diturbnce D( ) = d

More information

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations.

PH427/PH527: Periodic systems Spring Overview of the PH427 website (syllabus, assignments etc.) 2. Coupled oscillations. Dy : Mondy 5 inuts. Ovrviw of th PH47 wsit (syllus, ssignnts tc.). Coupld oscilltions W gin with sss coupld y Hook's Lw springs nd find th possil longitudinl) otion of such syst. W ll xtnd this to finit

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

Humanistic, and Particularly Classical, Studies as a Preparation for the Law

Humanistic, and Particularly Classical, Studies as a Preparation for the Law University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1907 Humanistic, and Particularly Classical, Studies as a Preparation for the Law

More information

Weighted Graphs. Weighted graphs may be either directed or undirected.

Weighted Graphs. Weighted graphs may be either directed or undirected. 1 In mny ppltons, o rp s n ssot numrl vlu, ll wt. Usully, t wts r nonntv ntrs. Wt rps my tr rt or unrt. T wt o n s otn rrr to s t "ost" o t. In ppltons, t wt my msur o t lnt o rout, t pty o ln, t nry rqur

More information

Grain Reserves, Volatility and the WTO

Grain Reserves, Volatility and the WTO Grain Reserves, Volatility and the WTO Sophia Murphy Institute for Agriculture and Trade Policy www.iatp.org Is v o la tility a b a d th in g? De pe n d s o n w h e re yo u s it (pro d uc e r, tra d e

More information

Numerical methods for PDEs FEM implementation: element stiffness matrix, isoparametric mapping, assembling global stiffness matrix

Numerical methods for PDEs FEM implementation: element stiffness matrix, isoparametric mapping, assembling global stiffness matrix Platzhaltr für Bild, Bild auf Titlfoli hintr das Logo instzn Numrical mthods for PDEs FEM implmntation: lmnt stiffnss matrix, isoparamtric mapping, assmbling global stiffnss matrix Dr. Nomi Fridman Contnts

More information

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S.

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S. ConTst Clikr ustions Chtr 19 Physis, 4 th Eition Jms S. Wlkr ustion 19.1 Two hrg blls r rlling h othr s thy hng from th iling. Wht n you sy bout thir hrgs? Eltri Chrg I on is ositiv, th othr is ngtiv both

More information

Equil. Properties of Reacting Gas Mixtures. So far have looked at Statistical Mechanics results for a single (pure) perfect gas

Equil. Properties of Reacting Gas Mixtures. So far have looked at Statistical Mechanics results for a single (pure) perfect gas Shool of roa Engnrng Equl. Prort of Ratng Ga Mxtur So far hav lookd at Stattal Mhan rult for a ngl (ur) rft ga hown how to gt ga rort (,, h, v,,, ) from artton funton () For nonratng rft ga mxtur, gt mxtur

More information

Class Diagrams. CSC 440/540: Software Engineering Slide #1

Class Diagrams. CSC 440/540: Software Engineering Slide #1 Class Diagrams CSC 440/540: Software Engineering Slide # Topics. Design class diagrams (DCDs) 2. DCD development process 3. Associations and Attributes 4. Dependencies 5. Composition and Constraints 6.

More information

Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v

Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v ll f x, h v nd d pr v n t fr tf l t th f nt r n r

More information

APPH 4200 Physics of Fluids

APPH 4200 Physics of Fluids APPH 42 Physics of Fluids Problem Solving and Vorticity (Ch. 5) 1.!! Quick Review 2.! Vorticity 3.! Kelvin s Theorem 4.! Examples 1 How to solve fluid problems? (Like those in textbook) Ç"Tt=l I $T1P#(

More information

Systems Analysis. Prof. Cesar de Prada ISA-UVA

Systems Analysis. Prof. Cesar de Prada ISA-UVA Sytem Analyi Prof. Cear de Prada ISAUVA rada@autom.uva.e Aim Learn how to infer the dynamic behaviour of a cloed loo ytem from it model. Learn how to infer the change in the dynamic of a cloed loo ytem

More information

Solutions to Homework 3

Solutions to Homework 3 Solutions to Homework 3 Section 3.4, Repeated Roots; Reduction of Order Q 1). Find the general solution to 2y + y = 0. Answer: The charactertic equation : r 2 2r + 1 = 0, solving it we get r = 1 as a repeated

More information

Quadratic Residues. Chapter Quadratic residues

Quadratic Residues. Chapter Quadratic residues Chter 8 Qudrtic Residues 8. Qudrtic residues Let n>be given ositive integer, nd gcd, n. We sy tht Z n is qudrtic residue mod n if the congruence x mod n is solvble. Otherwise, is clled qudrtic nonresidue

More information

Properties of Demand

Properties of Demand AGEC 5733 LECTURE NOTES DR. SHIDA HENNEBERR ROERTIES OF DEMAND AGEC 5733 cl ot /4 /9 d / rort of Dmd Grl rort of Dmd:. El Arto. Homoty 3. Courot d 4. Symmtry Mtr of Eltct M α α M M α L LL M M wr dtur Q

More information

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano RIGHT-ANGLE WEAVE Dv mons Mm t look o ts n rlt tt s ptvly p sn y Py Brnkmn Mttlno Dv your mons nto trnls o two or our olors. FCT-SCON0216_BNB66 2012 Klm Pulsn Co. Ts mtrl my not rprou n ny orm wtout prmsson

More information

l f t n nd bj t nd x f r t l n nd rr n n th b nd p phl t f l br r. D, lv l, 8. h r t,., 8 6. http://hdl.handle.net/2027/miun.aey7382.0001.001 P bl D n http://www.hathitrust.org/access_use#pd Th r n th

More information

AN INTRODUCTION TO THE CONTROL THEORY

AN INTRODUCTION TO THE CONTROL THEORY Open-Loop controller An Open-Loop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, non-linear dynamics and parameter

More information

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples Root Locu Content Root locu, ketching algorithm Root locu, example Root locu, proof Root locu, control example Root locu, influence of zero and pole Root locu, lead lag controller deign 9 Spring ME45 -

More information

ECEN 605 LINEAR SYSTEMS. Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability 1/27

ECEN 605 LINEAR SYSTEMS. Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability 1/27 1/27 ECEN 605 LINEAR SYSTEMS Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability Feedback System Consider the feedback system u + G ol (s) y Figure 1: A unity feedback system

More information

Ch 1.2: Solutions of Some Differential Equations

Ch 1.2: Solutions of Some Differential Equations Ch 1.2: Solutions of Som Diffrntil Equtions Rcll th fr fll nd owl/mic diffrntil qutions: v 9.8.2v, p.5 p 45 Ths qutions hv th gnrl form y' = y - b W cn us mthods of clculus to solv diffrntil qutions of

More information

Solutions Problem Set 2. Problem (a) Let M denote the DFA constructed by swapping the accept and non-accepting state in M.

Solutions Problem Set 2. Problem (a) Let M denote the DFA constructed by swapping the accept and non-accepting state in M. Solution Prolem Set 2 Prolem.4 () Let M denote the DFA contructed y wpping the ccept nd non-ccepting tte in M. For ny tring w B, w will e ccepted y M, tht i, fter conuming the tring w, M will e in n ccepting

More information

CS 188: Artificial Intelligence Fall Announcements

CS 188: Artificial Intelligence Fall Announcements CS 188: Artificil Intelligence Fll 2009 Lecture 20: Prticle Filtering 11/5/2009 Dn Klein UC Berkeley Announcements Written 3 out: due 10/12 Project 4 out: due 10/19 Written 4 proly xed, Project 5 moving

More information

n

n p l p bl t n t t f Fl r d, D p rt nt f N t r l R r, D v n f nt r r R r, B r f l. n.24 80 T ll h, Fl. : Fl r d D p rt nt f N t r l R r, B r f l, 86. http://hdl.handle.net/2027/mdp.39015007497111 r t v n

More information

Language Processors F29LP2, Lecture 5

Language Processors F29LP2, Lecture 5 Lnguge Pocessos F29LP2, Lectue 5 Jmie Gy Feuy 2, 2014 1 / 1 Nondeteministic Finite Automt (NFA) NFA genelise deteministic finite utomt (DFA). They llow sevel (0, 1, o moe thn 1) outgoing tnsitions with

More information

TABLE OF CONTENTS ASSEMBLY INSTRUCTIONS SHEET 1 OF 8 TABLE OF CONTENTS PAGE NUMBER DESCRIPTION B 2 PARTS LIST AND LAYOUT 3-5 PARTS A-D DETAIL DRAWINGS

TABLE OF CONTENTS ASSEMBLY INSTRUCTIONS SHEET 1 OF 8 TABLE OF CONTENTS PAGE NUMBER DESCRIPTION B 2 PARTS LIST AND LAYOUT 3-5 PARTS A-D DETAIL DRAWINGS TL O ONTNTS SHT O TL O ONTNTS PG NUMR SRIPTION PRTS LIST N LYOUT - PRTS - TIL RWINGS - STP Y STP SSMLY INSTRUTIONS TH INORMTION ONTIN IN THIS RWING IS TH SOL PROPRTY O STGING IMNSIONS IN. NY RPROUTION

More information

CONSTACYCLIC CODES OF LENGTH OVER A FINITE FIELD

CONSTACYCLIC CODES OF LENGTH OVER A FINITE FIELD Jorl o Algbr Nbr Tory: Ac Alco Vol 5 Nbr 6 Pg 4-64 Albl ://ccc.co. DOI: ://.o.org/.864/_753 ONSTAYLI ODES OF LENGTH OVER A FINITE FIELD AITA SAHNI POONA TRAA SEHGAL r or Ac Sy c Pb Ury gr 64 I -l: 5@gl.co

More information

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f n r t d n 20 2 : 6 T P bl D n, l d t z d http:.h th tr t. r pd l 22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r

More information

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

Chapter 10 Time-Domain Analysis and Design of Control Systems

Chapter 10 Time-Domain Analysis and Design of Control Systems ME 43 Sytm Dynamic & Control Sction 0-5: Stady Stat Error and Sytm Typ Chaptr 0 Tim-Domain Analyi and Dign of Control Sytm 0.5 STEADY STATE ERRORS AND SYSTEM TYPES A. Bazoun Stady-tat rror contitut an

More information

EE3CL4: Introduction to Linear Control Systems

EE3CL4: Introduction to Linear Control Systems 1 / 17 EE3CL4: Introduction to Linear Control Systems Section 7: McMaster University Winter 2018 2 / 17 Outline 1 4 / 17 Cascade compensation Throughout this lecture we consider the case of H(s) = 1. We

More information

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9

Lecture contents. Bloch theorem k-vector Brillouin zone Almost free-electron model Bands Effective mass Holes. NNSE 508 EM Lecture #9 Lctur contnts Bloch thorm -vctor Brillouin zon Almost fr-lctron modl Bnds ffctiv mss Hols Trnsltionl symmtry: Bloch thorm On-lctron Schrödingr qution ch stt cn ccommo up to lctrons: If Vr is priodic function:

More information

H NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f

More information

I I. R E L A T E D W O R K

I I. R E L A T E D W O R K A c c e l e r a t i n g L a r g e S c a l e C e n t r o i d - B a s e d C l u s t e r i n g w i t h L o c a l i t y S e n s i t i v e H a s h i n g R y a n M c C o n v i l l e, X i n C a o, W e i r u L

More information

R k. t + 1. n E t+1 = ( 1 χ E) W E t+1. c E t+1 = χ E Wt+1 E. Γ E t+1. ) R E t+1q t K t. W E t+1 = ( 1 Γ E t+1. Π t+1 = P t+1 /P t

R k. t + 1. n E t+1 = ( 1 χ E) W E t+1. c E t+1 = χ E Wt+1 E. Γ E t+1. ) R E t+1q t K t. W E t+1 = ( 1 Γ E t+1. Π t+1 = P t+1 /P t R k E 1 χ E Wt E n E t+1 t t + 1 n E t+1 = ( 1 χ E) W E t+1 c E t+1 = χ E Wt+1 E t + 1 q t K t Rt+1 E 1 Γ E t+1 Π t+1 = P t+1 /P t W E t+1 = ( 1 Γ E t+1 ) R E t+1q t K t Π t+1 Γ E t+1 K t q t q t K t j

More information

Colby College Catalogue

Colby College Catalogue Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1866 Colby College Catalogue 1866-1867 Colby College Follow this and additional works at: http://digitalcommons.colby.edu/catalogs

More information

The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function

The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function. The Transfer Function A gnraliation of th frquncy rsons function Th convolution sum scrition of an LTI iscrt-tim systm with an imuls rsons h[n] is givn by h y [ n] [ ] x[ n ] Taing th -transforms of both sis w gt n n h n n

More information

::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2...

::::l<r/ L- 1-1>(=-ft\ii--r(~1J~:::: Fo. l. AG -=(0,.2,L}> M - &-c ==- < ) I) ~..-.::.1 ( \ I 0. /:rf!:,-t- f1c =- <I _,, -2... Math 3298 Exam 1 NAME: SCORE: l. Given three points A(I, l, 1), B(l,;2, 3), C(2, - l, 2). (a) Find vectors AD, AC, nc. (b) Find AB+ DC, AB - AC, and 2AD. -->,,. /:rf!:,-t- f1c =-

More information

o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco

o C *$ go ! b», S AT? g (i * ^ fc fa fa U - S 8 += C fl o.2h 2 fl 'fl O ' 0> fl l-h cvo *, &! 5 a o3 a; O g 02 QJ 01 fls g! r«'-fl O fl s- ccco > p >>>> ft^. 2 Tble f Generl rdnes. t^-t - +«0 -P k*ph? -- i t t i S i-h l -H i-h -d. *- e Stf H2 t s - ^ d - 'Ct? "fi p= + V t r & ^ C d Si d n. M. s - W ^ m» H ft ^.2. S'Sll-pl e Cl h /~v S s, -P s'l

More information

1 Routh Array: 15 points

1 Routh Array: 15 points EE C28 / ME34 Problem Set 3 Solution Fall 2 Routh Array: 5 point Conider the ytem below, with D() k(+), w(t), G() +2, and H y() 2 ++2 2(+). Find the cloed loop tranfer function Y () R(), and range of k

More information

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued... Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th

More information

Review: transient and steady-state response; DC gain and the FVT Today s topic: system-modeling diagrams; prototype 2nd-order system

Review: transient and steady-state response; DC gain and the FVT Today s topic: system-modeling diagrams; prototype 2nd-order system Plan of the Lecture Review: transient and steady-state response; DC gain and the FVT Today s topic: system-modeling diagrams; prototype 2nd-order system Plan of the Lecture Review: transient and steady-state

More information

EE Control Systems LECTURE 11

EE Control Systems LECTURE 11 Up: Moy, Ocor 5, 7 EE 434 - Corol Sy LECTUE Copyrigh FL Lwi 999 All righ rrv POLE PLACEMET A STEA-STATE EO Uig fc, o c ov h clo-loop pol o h h y prforc iprov O c lo lc uil copor o oi goo y- rcig y uyig

More information

(tnaiaun uaejna) o il?smitfl?^ni7wwuiinuvitgviisyiititvi2a-a a imaviitjivi5a^ qw^ww^i fiaa!i-j?s'u'uil?g'ijimqwuwiijami.wti. a nmj 1,965,333.

(tnaiaun uaejna) o il?smitfl?^ni7wwuiinuvitgviisyiititvi2a-a a imaviitjivi5a^ qw^ww^i fiaa!i-j?s'u'uil?g'ijimqwuwiijami.wti. a nmj 1,965,333. 0 fltu77jjiimviu«7mi^ gi^"ijhm?'ijjw?flfi^ V m 1 /14 il?mitfl?^i7wwuiinuvitgviiyiititvi2- imviitvi^ qw^ww^i fi!i-j?'u'uil?g'iqwuwiijmi.wti twwrlf^ imii2^

More information

Digital Control: Part 2. ENGI 7825: Control Systems II Andrew Vardy

Digital Control: Part 2. ENGI 7825: Control Systems II Andrew Vardy Digital Control: Part 2 ENGI 7825: Control Systems II Andrew Vardy Mapping the s-plane onto the z-plane We re almost ready to design a controller for a DT system, however we will have to consider where

More information

Time Response Analysis (Part II)

Time Response Analysis (Part II) Time Response Analysis (Part II). A critically damped, continuous-time, second order system, when sampled, will have (in Z domain) (a) A simple pole (b) Double pole on real axis (c) Double pole on imaginary

More information

Multi-Armed Bandits: Non-adaptive and Adaptive Sampling

Multi-Armed Bandits: Non-adaptive and Adaptive Sampling CSE 547/Stt 548: Mchine Lerning for Big Dt Lecture Multi-Armed Bndits: Non-dptive nd Adptive Smpling Instructor: Shm Kkde 1 The (stochstic) multi-rmed bndit problem The bsic prdigm is s follows: K Independent

More information

Digital Control Systems State Feedback Control

Digital Control Systems State Feedback Control Digital Control Systems State Feedback Control Illustrating the Effects of Closed-Loop Eigenvalue Location and Control Saturation for a Stable Open-Loop System Continuous-Time System Gs () Y() s 1 = =

More information

Reinforcement Learning and Policy Reuse

Reinforcement Learning and Policy Reuse Reinforcement Lerning nd Policy Reue Mnuel M. Veloo PEL Fll 206 Reding: Reinforcement Lerning: An Introduction R. Sutton nd A. Brto Probbilitic policy reue in reinforcement lerning gent Fernndo Fernndez

More information

EE750 Advanced Engineering Electromagnetics Lecture 17

EE750 Advanced Engineering Electromagnetics Lecture 17 EE75 Avan Engnrng Eltromagnt Ltur 7 D EM W onr a D ffrntal quaton of th form α α β f ut to p on Γ α α. n γ q on Γ whr Γ Γ Γ th ontour nlong th oman an n th unt outwar normal ot that th ounar onton ma a

More information

Systems Analysis and Control

Systems Analysis and Control Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture 2: Drawing Bode Plots, Part 2 Overview In this Lecture, you will learn: Simple Plots Real Zeros Real Poles Complex

More information

Labor and Capital Before the Law

Labor and Capital Before the Law University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1884 Labor and Capital Before the Law Thomas M. Cooley University of Michigan Law

More information

TABLE OF CONTENTS cont. TABLE OF CONTENTS. Picture & Matching Cards cont. Biomes Flow Charts. freshwater marine wetland desert forest grassland

TABLE OF CONTENTS cont. TABLE OF CONTENTS. Picture & Matching Cards cont. Biomes Flow Charts. freshwater marine wetland desert forest grassland TABLE OF CONTENT Bios Fow Chrts frshwtr rin wtnd dsrt forst grssnd tundr Pictur & Mtching Crds trrstri qutic frshwtr rin (ocn) wtnd dsrt forst grssnd tundr rivrs & strs ks & onds cost/stury/intr-tid ocn

More information

SAMPLE CSc 340 EXAM QUESTIONS WITH SOLUTIONS: part 2

SAMPLE CSc 340 EXAM QUESTIONS WITH SOLUTIONS: part 2 AMPLE C EXAM UETION WITH OLUTION: prt. It n sown tt l / wr.7888l. I Φ nots orul or pprotng t vlu o tn t n sown tt t trunton rror o ts pproton s o t or or so onstnts ; tt s Not tt / L Φ L.. Φ.. /. /.. Φ..787.

More information

Data Structures and Algorithms CMPSC 465

Data Structures and Algorithms CMPSC 465 Dt Structures nd Algorithms CMPSC 465 LECTURE 10 Solving recurrences Mster theorem Adm Smith S. Rskhodnikov nd A. Smith; bsed on slides by E. Demine nd C. Leiserson Review questions Guess the solution

More information

concentration of the chemical species A to activity as shown below:

concentration of the chemical species A to activity as shown below: Fundmentl of Anlyticl Chemitry: th ed. Chpter Chpter - Activity, A, i the effective concentrtion of chemicl ecie A in olution. The ctivity coefficient, A, i the numericl fctor necery to convert the molr

More information

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x)

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x) Chptr 7 INTEGRALS 7. Ovrviw 7.. Lt d d F () f (). Thn, w writ f ( ) d F () + C. Ths intgrls r clld indfinit intgrls or gnrl intgrls, C is clld constnt of intgrtion. All ths intgrls diffr y constnt. 7..

More information

3. Which of the following elements is primarily responsible for the photochemical smog? Chemistry 12, Exam III, Form A, April 4, 2001

3. Which of the following elements is primarily responsible for the photochemical smog? Chemistry 12, Exam III, Form A, April 4, 2001 Chemistry 12, Exam III, Form A, April 4, 2001 In all questions involving gases, assume that the ideal-gas laws hold, unless the question specifically refers to the non-ideal behavior. 1. It takes 21.3

More information

20.2. The Transform and its Inverse. Introduction. Prerequisites. Learning Outcomes

20.2. The Transform and its Inverse. Introduction. Prerequisites. Learning Outcomes The Trnform nd it Invere 2.2 Introduction In thi Section we formlly introduce the Lplce trnform. The trnform i only pplied to cul function which were introduced in Section 2.1. We find the Lplce trnform

More information

How much air is required by the people in this lecture theatre during this lecture?

How much air is required by the people in this lecture theatre during this lecture? 3 NTEGRATON tgrtio is us to swr qustios rltig to Ar Volum Totl qutity such s: Wht is th wig r of Boig 747? How much will this yr projct cost? How much wtr os this rsrvoir hol? How much ir is rquir y th

More information

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths. How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0

More information

k and v = v 1 j + u 3 i + v 2

k and v = v 1 j + u 3 i + v 2 ORTHOGONAL FUNCTIONS AND FOURIER SERIES Orthogonl functions A function cn e considered to e generliztion of vector. Thus the vector concets like the inner roduct nd orthogonlity of vectors cn e extended

More information