Control System Engineering (EE301T) Assignment: 2
|
|
|
- Collin Norton
- 6 years ago
- Views:
Transcription
1 Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also calcula Damping raio, Ovrshoo, sling im a ±% and ±5% olranc.. Opn loop ransfr funcion of uniy fdack sysm is (s) whr and T ar s( Ts) consans. Drmin facor y which gain should muliplid so ha ovrshoo of uni sp rspons rducd from 75% o 5%.. Th opn loop ransfr funcion of uniy fdack sysm is (s). For his sysm s Ts ( ) T ovrshoo rducd from 0.6 o 0. du o chang in only. Show ha 4. T whr and ar valus of for 0.6 and 0. ovrshoo rspcivly. 4. Th lock diagram of a simpl srvo sysm is shown in h following figur. Drmin h characrisic quaion of h sysm. Hnc calcula h undampd frquncy of oscillaions, damping raio, damping facor, maximum ovrshoo, firs undrshoo, im inrvals afr which maximum and minimum occurs, sling im and h numr of cycls compld for h oupu is sld wihin % of h final valu. Th inpu o h sysm is a uni sp. 0. 5(s )(0.s ) C( s) 5. A scond ordr conrol sysm is rprsnd y a ransfr funcion is givn y Q T 0( s) ( s) Js fs Whr Q 0 (s) is h proporional oupu and T is h inpu orqu. A sp inpu 0N-m is applid o h sysm and s rsuls ar givn as M p 6%, T p s, h sady sa oupu of h sysm is 0.5 radian. Drmin h valu of J,, and f. 6. A sysm has 40% ovrshoo and rquirs a sling im of 4 sc whn givn a sp inpu. Th sady sa rror is %. Drmin h ransfr funcion of h scond ordr sysm. Also find ris im and pak im. 7. A sandard scond ordr sysm has 50% ovrshoo and sling im of sconds. Drmin ω n, ξ, T p and T r. 5 6 Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag of 5 W: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
2 Conrol Sysm Enginring (EE0T) Assignmn: 8. For a uniy fdack conrol sysm having (s), find h following: s(st ) i.th facor y which h gain mus muliplid so ha h damping raio incrass from 0. o 0.9. ii.th facor y which h im consan T mus muliplid so ha h damping raio dcrass from 0.9 o 0.. T iii.show ha. 9 whn h sysm ovrshoo rducs from 70% o 0% whr and T ar valus of for 70% and 0% ovrshoo. 9. Th figur shown low shows h sp rspons of a scond ordr sysm for an inpu u(). Assuming uniy fdack, drmin ξ, ω n and opn loop ransfr funcion of h sysm. C() Tim (sc) 0. A uniy fdack sysm has h loop ransfr funcion (s). If is im rspons o hav an s s a ( ) ovrshoo of lss han 5% and sling im no xcding 4 sconds, drmin suial valus for and a.. A uniy fdack sysm is characrizd y a opn loop ransfr funcion (s). 0) Drmin h gain so ha h sysm will hav a damping raio of 5.0. For his valu of drmin sling im, pak ovrshoo and im o pak ovrshoo for a uni sp inpu.. Find pak im, sling im, and prcnag of ovrshoo for h approxima scond ordr rspons C() cos(9.796) sin(9.796). 4. A uniy fdack conrol sysm has an opn loop ransfr funcion (s). Drmin h ) ris im, pak im, pak ovrshoo, % of ovrshoo and h sling im whn a sp displacmn of 5 is givn o h sysm. 4. Drmin h valus of and T of h closd loop sysm shown in figur low, so ha h maximum ovrshoo in uni sp rspons is 0% and h pak im is.5s. Assum ha Jkg-m. Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag of 5 W: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
3 Conrol Sysm Enginring (EE0T) Assignmn: Js C( s) Ts 5. Drmin h sling im for h sysm givn in Q. for 4%, 6%, 9%. 6. A posiion conrol sysm is sailizd y mans of acclraion fdack. If h sysm has a momn of inria of 0-5 g-m ; viscous fricional orqu of 0-4 Nm/rad/sc and h moor orqu is givn y dθ0 dθ0 Tm 4 0 N m, whr θi θ0; Acclraion fdack d d i. Draw is lock diagram ii. Drmin h valu of for criical damping iii. Drmin h sady sa rror ss whn h inpu is a consan vlociy of 0rpm. PART-B (Tim Domain Analysis: Sady sa Analysis). Drmin h sp, ramp and paraolic rror consans of h following uniy fdack conrol sysms. Th opn loop ransfr funcions ar givn 00 ( s) ( 0.s)( 0s) s(s (s) s (s 00 00, 0s 00) s( 0.s)( 0.5s) ( s)( 4s) 0s 00) 0)(s 00) s (s s ). Calcula saic rror cofficin for a uniy fdack sysm wih 6 (s).if inpu givn is ) r () 4 hn drmin sady sa rror. For h aov sysm of ss o rducd o 0% of xising valu, wha would h prcnag chang in gain?. Find rror cofficins for h givn uniy fdack sysm having 4. A uniy fdack conrol sysm has 4(s 0s 00) (s). )(s s 0) 0(s 4) (s), if inpu )(s s ) h sysm hn drmin h sady sa rror of h sysm. 5. A uniy fdack conrol sysm has (s) )(s s 5) i. For a uni ramp inpu i is dsird ha ss 0.. Drmin minimum valu of. ii. Drmin ss if inpu r() 4. Assum 0. r() 6 is givn o Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag of 5 W: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
4 Conrol Sysm Enginring (EE0T) Assignmn: 6. Using gnralizd rror sris calcula h sady-sa rror of uniy fdack sysm has 0 (s) for h following xciaion: s i. r () ii. r () iii. r() & iv. r() 7. Using gnralizd rror sris drmin h sady-sa rror of h sysm for h inpu r() 5. s s s s C(s) 5(s ) 8. An opn loop ransfr funcion of a uniy fdack conrol sysm is (s). Using h (s )(s ) gnralizd rror sris, drmin h rror signal and sady sa rror of h sysm whn i is xcid y i. r () ii. r () iii. r() & iv. r() 9. Considr a uniy fdack conrol sysm wih h closd loop ransfr funcion C(s) R(s) s. s as Drmin h opn loop ransfr funcion (s). Show ha h sady sa rror in h uni-ramp a rspons is givn y. 0. Th figur low shows a closd loop conrol sysm which rgulas h gnraor rminal volag E 0. Th valus of and H ar 0 and 0.. Drmin h following i. Th valu of E r o kp E 0 60V. ii. Th prcnag chang in h gnraor rminal volag if h forward pah gain rducs y %. Find h rsuls (i) and (ii) whn h sysm is opn loop and closd loop. ****ALL THE BEST**** Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag 4 of 5 W: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
5 Conrol Sysm Enginring (EE0T) Assignmn:. C() Answrs (Par-A). 9.6., rad/sc, 0.6, 4rad/sc, 9.5%, 0.94%, 0.785sc,.57sc,.sc, 0.85scs. 5..8gm, 6.4Nm/rad/sc , , 0.54, 0.597, , , 0.rad/sc, 4.98) 0., a. 00, 0.8, 6.%, 0.6. sc, 0.07, 0., 5.66%..9,.8,.445, 6.%, 4sc (±%), sc (±5%) , T Answr no givn sc, ο Answrs (Par-B). ( 000,0,0),(,,0),(,0),( ),( 0),( )., ss.5 p v 40., , () 0. 5 () () 7 7. () Answr no givn 9. Answr no givn 0..8V,.8V, %, 0.495% () Prpard y: Mr. Saish Choudhury (Ass. Profssor, Dp. of. EICE Pag 5 of 5 W: saish@schoudhury.n, saishchoudhury@soaunivrsiy.ac.in
Lecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey
cur : Growh and dcay of currn in circui Growh of currn in Circui us considr an inducor of slf inducanc is conncd o a DC sourc of.m.f. E hrough a rsisr of rsisanc and a ky K in sris. Whn h ky K is swichd
whereby we can express the phase by any one of the formulas cos ( 3 whereby we can express the phase by any one of the formulas
Third In-Class Exam Soluions Mah 6, Profssor David Lvrmor Tusday, 5 April 07 [0] Th vrical displacmn of an unforcd mass on a spring is givn by h 5 3 cos 3 sin a [] Is his sysm undampd, undr dampd, criically
Lecture 2: Current in RC circuit D.K.Pandey
Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging
CSE 245: Computer Aided Circuit Simulation and Verification
CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy
Charging of capacitor through inductor and resistor
cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.
UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o
a dt a dt a dt dt If 1, then the poles in the transfer function are complex conjugates. Let s look at f t H t f s / s. So, for a 2 nd order system:
Undrdamd Sysms Undrdamd Sysms nd Ordr Sysms Ouu modld wih a nd ordr ODE: d y dy a a1 a0 y b f If a 0 0, hn: whr: a d y a1 dy b d y dy y f y f a a a 0 0 0 is h naural riod of oscillaion. is h daming facor.
Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors
Boc/DiPrima 9 h d, Ch.: Linar Equaions; Mhod of Ingraing Facors Elmnar Diffrnial Equaions and Boundar Valu Problms, 9 h diion, b William E. Boc and Richard C. DiPrima, 009 b John Wil & Sons, Inc. A linar
MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control
MEM 355 Prformanc Enhancmn of Dynamical Sysms A Firs Conrol Problm - Cruis Conrol Harry G. Kwany Darmn of Mchanical Enginring & Mchanics Drxl Univrsiy Cruis Conrol ( ) mv = F mg sinθ cv v +.2v= u 9.8θ
C From Faraday's Law, the induced voltage is, C The effect of electromagnetic induction in the coil itself is called selfinduction.
Inducors and Inducanc C For inducors, v() is proporional o h ra of chang of i(). Inducanc (con d) C Th proporionaliy consan is h inducanc, L, wih unis of Hnris. 1 Hnry = 1 Wb / A or 1 V sc / A. C L dpnds
AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )
AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc
H is equal to the surface current J S
Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion
EXERCISE - 01 CHECK YOUR GRASP
DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc
Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is
39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h
General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract
Applicaion of Diffrnial... Gnral Aricl Applicaion of diffrnial uaion in - and C- circui analysis by classical mhod. ajndra Prasad gmi curr, Dparmn of Mahmaics, P.N. Campus, Pokhara Email: rajndraprasadrgmi@yahoo.com
Microscopic Flow Characteristics Time Headway - Distribution
CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,
REPETITION before the exam PART 2, Transform Methods. Laplace transforms: τ dτ. L1. Derive the formulas : L2. Find the Laplace transform F(s) if.
Tranform Mhod and Calculu of Svral Variabl H7, p Lcurr: Armin Halilovic KTH, Campu Haning E-mail: armin@dkh, wwwdkh/armin REPETITION bfor h am PART, Tranform Mhod Laplac ranform: L Driv h formula : a L[
Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review
Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an
Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule
Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -
Inverse Fourier Transform. Properties of Continuous time Fourier Transform. Review. Linearity. Reading Assignment Oppenheim Sec pp.289.
Convrgnc of ourir Trnsform Rding Assignmn Oppnhim Sc 42 pp289 Propris of Coninuous im ourir Trnsform Rviw Rviw or coninuous-im priodic signl x, j x j d Invrs ourir Trnsform 2 j j x d ourir Trnsform Linriy
Copyright 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Chapr Rviw 0 6. ( a a ln a. This will qual a if an onl if ln a, or a. + k an (ln + c. Thrfor, a an valu of, whr h wo curvs inrsc, h wo angn lins will b prpnicular. 6. (a Sinc h lin passs hrough h origin
Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016
Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...
5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t
AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =
2. NONLINEAR DYNAMICS MODEL FOR A
Nonlinar Dynamics for Gar Faul Lvl Su Xunwn * Liu Jinhao and Wang Shaoping Snd Ordrs for Rprins o rprins@nhamscinc.a h Opn Mchanical Enginring Journal 04 8 487-496 487 Opn Accss School of chnology Bijing
Review Lecture 5. The source-free R-C/R-L circuit Step response of an RC/RL circuit. The time constant = RC The final capacitor voltage v( )
Rviw Lcur 5 Firs-ordr circui Th sourc-fr R-C/R-L circui Sp rspons of an RC/RL circui v( ) v( ) [ v( 0) v( )] 0 Th i consan = RC Th final capacior volag v() Th iniial capacior volag v( 0 ) Volag/currn-division
S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]
![S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]](/thumbs/92/108666103.jpg "S.Y. B.Sc. (IT) : Sem. III. Applied Mathematics. Q.1 Attempt the following (any THREE) [15]")
S.Y. B.Sc. (IT) : Sm. III Applid Mahmaics Tim : ½ Hrs.] Prlim Qusion Papr Soluion [Marks : 75 Q. Amp h following (an THREE) 3 6 Q.(a) Rduc h mari o normal form and find is rank whr A 3 3 5 3 3 3 6 Ans.:
1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:
![1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:](/thumbs/84/89365453.jpg "1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:")
Rfrncs Brnank, B. and I. Mihov (1998). Masuring monary policy, Quarrly Journal of Economics CXIII, 315-34. Blanchard, O. R. Proi (00). An mpirical characrizaion of h dynamic ffcs of changs in govrnmn spnding
Physics 160 Lecture 3. R. Johnson April 6, 2015
Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx
Chapter 3: Fourier Representation of Signals and LTI Systems. Chih-Wei Liu
Chapr 3: Fourir Rprsnaion of Signals and LTI Sysms Chih-Wi Liu Oulin Inroducion Complx Sinusoids and Frquncy Rspons Fourir Rprsnaions for Four Classs of Signals Discr-im Priodic Signals Fourir Sris Coninuous-im
4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b
![4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b](/thumbs/71/65779443.jpg "4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b")
4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs
CHAPTER 9 Compressible Flow
CHPTER 9 Comrssibl Flow Char 9 / Comrssibl Flow Inroducion 9. c c cv + R. c kcv. c + R or c R k k Rk c k Sd of Sound 9.4 Subsiu Eq. 4.5.8 ino Eq. 4.5.7 and nglc onial nrgy chang: Q WS + + u~ u~. m ρ ρ
2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35
MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h
Let s look again at the first order linear differential equation we are attempting to solve, in its standard form:
Th Ingraing Facor Mhod In h prvious xampls of simpl firs ordr ODEs, w found h soluions by algbraically spara h dpndn variabl- and h indpndn variabl- rms, and wri h wo sids of a givn quaion as drivaivs,
Transfer function and the Laplace transformation
Lab No PH-35 Porland Sa Univriy A. La Roa Tranfr funcion and h Laplac ranformaion. INTRODUTION. THE LAPLAE TRANSFORMATION L 3. TRANSFER FUNTIONS 4. ELETRIAL SYSTEMS Analyi of h hr baic paiv lmn R, and
Midterm exam 2, April 7, 2009 (solutions)
Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions
( ) 2! l p. Nonlinear Dynamics for Gear Fault Level. ( ) f ( x) ( ),! = sgn % " p. Open Access. Su Xunwen *,1, Liu Jinhao 1 and Wang Shaoping 2. !
Nonlinar Dynamics for Gar Faul Lvl Su Xunwn Liu Jinhao and Wang Shaoping Snd Ordrs for Rprins o rprins@bnhamscinc.a Th Opn Mchanical Enginring Journal 04 8 487496 487 Opn Accss School of Tchnology Bijing
On the Speed of Heat Wave. Mihály Makai
On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.
Elementary Differential Equations and Boundary Value Problems
Elmnar Diffrnial Equaions and Boundar Valu Problms Boc. & DiPrima 9 h Ediion Chapr : Firs Ordr Diffrnial Equaions 00600 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /55 ผศ.ดร.อร ญญา ผศ.ดร.สมศ
7.4 QUANTUM MECHANICAL TREATMENT OF FLUCTUATIONS *
Andri Tokmakoff, MIT Dparmn of Chmisry, 5/19/5 7-11 7.4 QUANTUM MECANICAL TREATMENT OF FLUCTUATIONS * Inroducion and Prviw Now h origin of frquncy flucuaions is inracions of our molcul (or mor approprialy
An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT
[Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI
Frequency Response. Lecture #12 Chapter 10. BME 310 Biomedical Computing - J.Schesser
Frquncy Rspns Lcur # Chapr BME 3 Bimdical Cmpuing - J.Schssr 99 Idal Filrs W wan sudy Hω funcins which prvid frquncy slciviy such as: Lw Pass High Pass Band Pass Hwvr, w will lk a idal filring, ha is,
+ d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
Chapter 5 Digital PID control algorithm. Hesheng Wang Department of Automation,SJTU 2016,03
Chaper 5 Digial PID conrol algorihm Hesheng Wang Deparmen of Auomaion,SJTU 216,3 Ouline Absrac Quasi-coninuous PID conrol algorihm Improvemen of sandard PID algorihm Choosing parameer of PID regulaor Brief
Institute of Actuaries of India
Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6
ECE 145A / 218 C, notes set 1: Transmission Line Properties and Analysis
class nos, M. Rodwll, copyrighd 9 ECE 145A 18 C, nos s 1: Transmission in Propris and Analysis Mark Rodwll Univrsiy of California, Sana Barbara rodwll@c.ucsb.du 85-893-344, 85-893-36 fax Transmission in
On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument
Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn
Dynamic Effects of Feedback Control!
Dynamic Effecs of Feedback Conrol! Rober Sengel! Roboics and Inelligen Sysems MAE 345, Princeon Universiy, 2017 Inner, Middle, and Ouer Feedback Conrol Loops Sep Response of Linear, Time- Invarian (LTI)
Problem 2. Describe the following signals in terms of elementary functions (δ, u,r, ) and compute. x(t+2) x(2-t) RT_1[x] -3-2 = 1 2 = 1
![Problem 2. Describe the following signals in terms of elementary functions (δ, u,r, ) and compute. x(t+2) x(2-t) RT_1[x] -3-2 = 1 2 = 1](/thumbs/81/83830149.jpg "Problem 2. Describe the following signals in terms of elementary functions (δ, u,r, ) and compute. x(t+2) x(2-t) RT_1[x] -3-2 = 1 2 = 1")
EEE 03, HW NAME: SOLUTIONS Problm. Considr h signal whos graph is shown blow. Skch h following signals:, -, RT [], whr R dnos h rflcion opraion and T 0 dnos shif dlay opraion by 0. - RT_[] - -3 - Problm.
fiziks Institute for NET/JRF, GATE, IIT JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES MATEMATICAL PHYSICS SOLUTIONS are
MTEMTICL PHYSICS SOLUTIONS GTE- Q. Considr an ani-symmric nsor P ij wih indics i and j running from o 5. Th numbr of indpndn componns of h nsor is 9 6 ns: Soluion: Th numbr of indpndn componns of h nsor
EE 350 Signals and Systems Spring 2005 Sample Exam #2 - Solutions
EE 35 Signals an Sysms Spring 5 Sampl Exam # - Soluions. For h following signal x( cos( sin(3 - cos(5 - T, /T x( j j 3 j 3 j j 5 j 5 j a -, a a -, a a - ½, a 3 /j-j -j/, a -3 -/jj j/, a 5 -½, a -5 -½,
Lab 10: RC, RL, and RLC Circuits
Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in
4.3 Design of Sections for Flexure (Part II)
Prsrssd Concr Srucurs Dr. Amlan K Sngupa and Prof. Dvdas Mnon 4. Dsign of Scions for Flxur (Par II) This scion covrs h following opics Final Dsign for Typ Mmrs Th sps for Typ 1 mmrs ar xplaind in Scion
More on FT. Lecture 10 4CT.5 3CT.3-5,7,8. BME 333 Biomedical Signals and Systems - J.Schesser
Mr n FT Lcur 4CT.5 3CT.3-5,7,8 BME 333 Bimdicl Signls nd Sysms - J.Schssr 43 Highr Ordr Diffrniin d y d x, m b Y b X N n M m N M n n n m m n m n d m d n m Y n d f n [ n ] F d M m bm m X N n n n n n m p
Sinusoidal Response Notes
ECE 30 Sinusoidal Rspons Nots For BIBO Systms AStolp /29/3 Th sinusoidal rspons of a systm is th output whn th input is a sinusoidal (which starts at tim 0) Systm Sinusoidal Rspons stp input H( s) output
MATH 308: Diff Eqs, BDP10 EXAMPLES [Belmonte, 2019] 1 Introduction 1.1 Basic Mathematical Models; Direction Fields
![MATH 308: Diff Eqs, BDP10 EXAMPLES [Belmonte, 2019] 1 Introduction 1.1 Basic Mathematical Models; Direction Fields](/thumbs/93/113091114.jpg "MATH 308: Diff Eqs, BDP10 EXAMPLES [Belmonte, 2019] 1 Introduction 1.1 Basic Mathematical Models; Direction Fields")
MATH 308: Diff Eqs, BDP0 EXAMPLES Blmon, 09 Mos problms ar from NSS9 Inroducion Basic Mahmaical Modls; Dircion Filds / Plo a dircion fild for dy/dx = 4x/y (a) Vrify ha h sraigh lins y = ±x ar soluions
Linear Systems Analysis in the Time Domain
Liar Sysms Aalysis i h Tim Domai Firs Ordr Sysms di vl = L, vr = Ri, d di L + Ri = () d R x= i, x& = x+ ( ) L L X() s I() s = = = U() s E() s Ls+ R R L s + R u () = () =, i() = L i () = R R Firs Ordr Sysms
RC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER
A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:
CHE302 LECTURE VI DYNAMIC BEHAVIORS OF REPRESENTATIVE PROCESSES. Professor Dae Ryook Yang
CHE30 LECTURE VI DYNAMIC BEHAVIORS OF REPRESENTATIVE PROCESSES Professor Dae Ryook Yang Fall 00 Dep. of Chemical and Biological Engineering orea Universiy CHE30 Process Dynamics and Conrol orea Universiy
Some Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
6.003 Homework #8 Solutions
6.003 Homework #8 Soluions Problems. Fourier Series Deermine he Fourier series coefficiens a k for x () shown below. x ()= x ( + 0) 0 a 0 = 0 a k = e /0 sin(/0) for k 0 a k = π x()e k d = 0 0 π e 0 k d
2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
Logistic equation of Human population growth (generalization to the case of reactive environment).
Logisic quaion of Human populaion growh gnralizaion o h cas of raciv nvironmn. Srg V. Ershkov Insiu for Tim aur Exploraions M.V. Lomonosov's Moscow Sa Univrsi Lninski gor - Moscow 999 ussia -mail: srgj-rshkov@andx.ru
LAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
On General Solutions of First-Order Nonlinear Matrix and Scalar Ordinary Differential Equations
saartvlos mcnirbata rovnuli akadmiis moamb 3 #2 29 BULLTN OF TH ORN NTONL DMY OF SNS vol 3 no 2 29 Mahmaics On nral Soluions of Firs-Ordr Nonlinar Mari and Scalar Ordinary Diffrnial uaions uram L Kharaishvili
Wave Equation (2 Week)
Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris
INC 693, 481 Dynamics System and Modelling: Linear Graph Modeling II Dr.-Ing. Sudchai Boonto Assistant Professor
INC 69, 48 Dynamics Systm and Modlling: Linar Graph Modling II Dr.-Ing. Sudchai Boonto Assistant Profssor Dpartmnt of Control Systm and Instrumntation Enginring King Mongkut s Unnivrsity of Tchnology Thonuri
Section 2: The Z-Transform
Scion : h -rnsform Digil Conrol Scion : h -rnsform In linr discr-im conrol sysm linr diffrnc quion chrcriss h dynmics of h sysm. In ordr o drmin h sysm s rspons o givn inpu, such diffrnc quion mus b solvd.
10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
CHAPTER 9. Compressible Flow. Btu ft-lb lbm ft-lb c p = = ft-lb slug- R. slug- R. 1 k. p p. p v p v. = ρ ρ
CHPTER 9 Cmrssibl Flw 9 Bu f-lb lbm f-lb c 778 6 lbm- R Bu slug slug- R f-lb cv c R 6 76 96 96 slug- R Bu 7 lbm R f-lb slug- R Bu 778 f - lb slug lbm c 9 c cv + R c cv c + R r c R c R / ( ) 9 If s, Eq
PRELIMINARY DEFINITIONS AND RELATIONS
Prliinary Dfiniions and Rlaions 1 CHAPTER 2 PRELIMINARY DEFINITIONS AND RELATIONS يتكون حجم معيه مه التربة مه حبيبات صلببة هولواو هملاو اميلاي جوفيللة أه ميللاي (.للصدر همقلل ) ال للو فللي التربللة وللو
ELECTRIC VELOCITY SERVO REGULATION
ELECIC VELOCIY SEVO EGULAION Gorg W. Younkin, P.E. Lif FELLOW IEEE Indusril Conrols Consuling, Di. Bulls Ey Mrking, Inc. Fond du Lc, Wisconsin h prformnc of n lcricl lociy sro is msur of how wll h sro
Revisiting what you have learned in Advanced Mathematical Analysis
Fourir sris Rvisiing wh you hv lrnd in Advncd Mhmicl Anlysis L f x b priodic funcion of priod nd is ingrbl ovr priod. f x cn b rprsnd by rigonomric sris, f x n cos nx bn sin nx n cos x b sin x cosx b whr
10. If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve
0. If p and q ar h lnghs of h prpndiculars from h origin on h angn and h normal o h curv + Mahmaics y = a, hn 4p + q = a a (C) a (D) 5a 6. Wha is h diffrnial quaion of h family of circls having hir cnrs
Why Laplace transforms?
MAE4 Linar ircui Why Lalac ranform? Firordr R cc v v v KVL S R inananou for ach Subiu lmn rlaion v S Ordinary diffrnial quaion in rm of caacior volag Lalac ranform Solv Invr LT V u, v Ri, i A R V A _ v
Electrical Circuits. 1. Circuit Laws. Tools Used in Lab 13 Series Circuits Damped Vibrations: Energy Van der Pol Circuit
V() R L C 513 Elecrical Circuis Tools Used in Lab 13 Series Circuis Damped Vibraions: Energy Van der Pol Circui A series circui wih an inducor, resisor, and capacior can be represened by Lq + Rq + 1, a
Boyce/DiPrima 9 th ed, Ch 7.8: Repeated Eigenvalues
Boy/DiPrima 9 h d Ch 7.8: Rpad Eignvalus Elmnary Diffrnial Equaions and Boundary Valu Problms 9 h diion by William E. Boy and Rihard C. DiPrima 9 by John Wily & Sons In. W onsidr again a homognous sysm
This is an example to show you how SMath can calculate the movement of kinematic mechanisms.
Dec :5:6 - Kinemaics model of Simple Arm.sm This file is provided for educaional purposes as guidance for he use of he sofware ool. I is no guaraeed o be free from errors or ommissions. The mehods and
3.4 Repeated Roots; Reduction of Order
3.4 Rpd Roos; Rducion of Ordr Rcll our nd ordr linr homognous ODE b c 0 whr, b nd c r consns. Assuming n xponnil soluion lds o chrcrisic quion: r r br c 0 Qudric formul or fcoring ilds wo soluions, r &
EE 435 Lecture 42. Phased Locked Loops and VCOs
EE 435 Lecure 42 d Locked Loops and VCOs Basis PLL Archiecure Loop Filer (LF) Volage Conrolled Oscillaor (VCO) Frequency Divider N Applicaions include: Frequency Demodulaion Frequency Synhesis Clock Synchronizaion
Solution: APPM 1360 Final (150 pts) Spring (60 pts total) The following parts are not related, justify your answers:
APPM 6 Final 5 pts) Spring 4. 6 pts total) Th following parts ar not rlatd, justify your answrs: a) Considr th curv rprsntd by th paramtric quations, t and y t + for t. i) 6 pts) Writ down th corrsponding
Section 3.8, Mechanical and Electrical Vibrations
Secion 3.8, Mechanical and Elecrical Vibraions Mechanical Unis in he U.S. Cusomary and Meric Sysems Disance Mass Time Force g (Earh) Uni U.S. Cusomary MKS Sysem CGS Sysem fee f slugs seconds sec pounds
University of Cyprus Biomedical Imaging and Applied Optics. Appendix. DC Circuits Capacitors and Inductors AC Circuits Operational Amplifiers
Universiy of Cyprus Biomedical Imaging and Applied Opics Appendix DC Circuis Capaciors and Inducors AC Circuis Operaional Amplifiers Circui Elemens An elecrical circui consiss of circui elemens such as
Section 5 Exercises, Problems, and Solutions. Exercises:
Scion 5 Exrciss, Problms, and Soluions Exrciss: 1. Tim dpndn prurbaion hory provids an xprssion for h radiaiv lifim of an xcid lcronic sa, givn by τ R : τ h- R 4 c 4(E i - E f ) µ fi, whr i rfrs o h xcid
Q1) [20 points] answer for the following questions (ON THIS SHEET):
![Q1) [20 points] answer for the following questions (ON THIS SHEET):](/thumbs/87/96063197.jpg "Q1) [20 points] answer for the following questions (ON THIS SHEET):")
Dr. Anas Al Tarabsheh The Hashemie Universiy Elecrical and Compuer Engineering Deparmen (Makeup Exam) Signals and Sysems Firs Semeser 011/01 Final Exam Dae: 1/06/01 Exam Duraion: hours Noe: means convoluion
RESONANT CAVITY. Supplementary Instructions
UNIEITY OF TOONTO Dparmn of Elcrical and ompur Enginring Filds and Wavs aboraory ourss EE 3F and EE 357 III Yar EONANT AITY upplmnary Insrucions EONANE Pag of 3 Pag 3 of 3. Inroducion, gnral rsonanc A
Homework: Introduction to Motion
Homwork: Inroducon o Moon Dsanc vs. Tm Graphs Nam Prod Drcons: Answr h foowng qusons n h spacs provdd. 1. Wha do you do o cra a horzona n on a dsancm graph? 2. How do you wak o cra a sragh n ha sops up?
Instructors Solution for Assignment 3 Chapter 3: Time Domain Analysis of LTIC Systems
Inrucor Soluion for Aignmn Chapr : Tim Domain Anali of LTIC Sm Problm i a 8 x x wih x u,, an Zro-inpu rpon of h m: Th characriic quaion of h LTIC m i i 8, which ha roo a ± j Th zro-inpu rpon i givn b zi
555 Timer. Digital Electronics
555 Timer Digial Elecronics This presenaion will Inroduce he 555 Timer. 555 Timer Derive he characerisic equaions for he charging and discharging of a capacior. Presen he equaions for period, frequency,
Solutions to FINAL JEE MAINS/IITJEE
Soluions o FINAL JEE MAINS/IIJEE - [CHEMISRY].(C By consrvaion of mols PV P V P V + R R R P + P am..(a.(d.(b KMnO will rac wih FSO only. mols 5 mols χ FSO / N (g + H (g NH (g a a a a q a a P PNH P. a AgNO
Laplace Transforms recap for ccts
Lalac Tranform rca for cc Wha h big ida?. Loo a iniial condiion ron of cc du o caacior volag and inducor currn a im Mh or nodal analyi wih -domain imdanc rianc or admianc conducanc Soluion of ODE drivn
UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED
006-0 Asian Rsarch Publishing work (ARP). All righs rsrvd. USTEADY FLOW OF A FLUID PARTICLE SUSPESIO BETWEE TWO PARALLEL PLATES SUDDELY SET I MOTIO WITH SAME SPEED M. suniha, B. Shankr and G. Shanha 3
Reliability Analysis of a Bridge and Parallel Series Networks with Critical and Non- Critical Human Errors: A Block Diagram Approach.
Inrnaional Journal of Compuaional Sin and Mahmais. ISSN 97-3189 Volum 3, Numr 3 11, pp. 351-3 Inrnaional Rsarh Puliaion Hous hp://www.irphous.om Rliailiy Analysis of a Bridg and Paralll Sris Nworks wih
Module 4: Time Response of discrete time systems Lecture Note 2
Module 4: Time Response of discree ime sysems Lecure Noe 2 1 Prooype second order sysem The sudy of a second order sysem is imporan because many higher order sysem can be approimaed by a second order model
Examples of Dynamic Programming Problems
M.I.T. 5.450-Fall 00 Sloan School of Managemen Professor Leonid Kogan Examples of Dynamic Programming Problems Problem A given quaniy X of a single resource is o be allocaed opimally among N producion
where: u: input y: output x: state vector A, B, C, D are const matrices
Sa pac modl: linar: y or in om : Sa q : f, u Oupu q : y h, u u Du F Gu y H Ju whr: u: inpu y: oupu : a vcor,,, D ar con maric Eampl " $ & ' " $ & 'u y " & * * * * [ ],, D H D I " $ " & $ ' " & $ ' " &
Lecture 13 RC/RL Circuits, Time Dependent Op Amp Circuits
Lecure 13 RC/RL Circuis, Time Dependen Op Amp Circuis RL Circuis The seps involved in solving simple circuis conaining dc sources, resisances, and one energy-sorage elemen (inducance or capaciance) are:
Viscous Damping Summary Sheet No Damping Case: Damped behaviour depends on the relative size of ω o and b/2m 3 Cases: 1.
Viscous Daping: && + & + ω Viscous Daping Suary Shee No Daping Case: & + ω solve A ( ω + α ) Daped ehaviour depends on he relaive size of ω o and / 3 Cases:. Criical Daping Wee 5 Lecure solve sae BC s
Gaussian minimum shift keying systems with additive white Gaussian noise
Indian Journal of ur & Applid hysics Vol. 46, January 8, pp. 65-7 Gaussian minimum shif kying sysms wih addiiv whi Gaussian nois A K Saraf & M Tiwari Dparmn of hysics and Elcronics, Dr Harisingh Gour Vishwavidyalaya,