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Unformatted text preview: De La Salle University - Dasmarifias College of Engineering, Architecture and Technology Engineering Department Quiz No.1 in Feedback Control Systems General Directions: I X (1) Read and analyze each item carefully (2) Answer the following items Ionlyfiiftheprovided SOLUTION SHEETS and NOWHERE ELSE (3) Strictly NO TALKING or BORROTWING of examination paraphemaiia‘s with your classmate during the examination (5) QUESTIONS of any nature should be addressed TO YOUR PROFESSORHNSTRUCTOR (6) Only pERMANENT PEN, PENCIL. ERASER and CALCULATOR are ALLOWED Oil top of an examinees armchair during the examination. (7) All BAGS and other PERSONAL BELONGINGS must be pLACED m FRONT of the examination room in clear sight of the examination proctor (8) The use of ELECTRONIC GADGETS. NOTES, HAND-OUTS and other materials which may be construed as Cheating '5 STRICTLY PROHIBITED (9) Anyone caught usmg such items will automatically be given a FAILED GRADE as prescribed by the university student handbook. Part 1: Essay Type (1 0 pts. each) 8 1. Discuss and explain the analysis and deSign objectives of control system. Site a particular example of a control system in your explanation. 8 2. Enumerate and explain the typical deSign process undertaken in the design of feedback and control systems. (BONUS QUESTION) Part 2: Problem Solving Type (10 pts. each) . I . Directions: (1) Number your solutions accordingly. (2) Write your solutions Iegibiy\ - and cross-out any unwanted solution (3) Box your final answer. L4) Only one final new “- answer is allowed per item. 300 3 5 F . 'i .i K‘s. '. " . -. ' l. r . :i Q 1. Find the transfer {HH— .—r--*\ = function Vo(s)/V,(s). \‘4 . i i is . “RH .7 l 1 g - "1N , ‘ f . i aka." 1). . . i". A“ It I / - \ "( )A + M“ 5/ \f ‘v an Edi K K i s a" ;.:- ‘ a. (’H ._ -3? {I if 5.; : i H" 1- ‘ I. -! . ' .__' {a}. ' / ,5. 0 5 a i: I" . - i ' "LE 2. Given the following equations. ( 2 k , , . 5 +1 5 ~ C .. 5 = R S Solve for the transfer function (1(5) =C2Ksy. Rm). ‘( ) -'( ) ( ) Draw the schematic diagram of the translational - C 1 (s)+ (3‘ + 3 +1k2(5)— 5C3 (s) = 0 mechanical system when its equations of motion a are of the same form as the given equations. — 5C2 (5)+ (5" + 5k} (3) = 0 “' 3. Find the transfer function, G6) = Qifiswiiafls), for the motor and load in the figure shown. The torque-speed curve is given by 7]., -20),.,, 4 800 when the input voltage is 100 volts. ii in I), = 400 Nan—shit] .-——i———— i J; —t<00ke—in- 'l—fi :. j __._. J“ = 5 kg-m3 D = | Nun-sired I‘l' O 4. Given the rotational system shown in the figure below, find the transfer function 6(5) = 66¢¢)/’8;(e). (BONUS QUESTION) 0|“) “Honesty is the cemerstone Of a" E! ‘ NI success. 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GOOmA/Sec VAR OFF/Edi sHk cult GI“ ‘W‘is «long-35 {00 N-m 6¥‘%r1u{ _ wk img‘k‘n uh, cg Mngarmqhm Mg 7 kj-mn am! 3 N'mfiS/Y‘M I, rcheC/‘hvcly, ‘Find fit q ' ‘ ‘ ‘ \ “Mgr . “ti a; '9n(9)/Efi(g) 0; 4w, mm a? .# am an ma—w ma or 105 L3 gm. 1 ‘ml c: "(ram 06 shown. 11. “l W Yr.&5ec.* eICtL/Jjglémm- LE‘E’LlE F- PWal (W % 1, Which of the following gives an INCORRECT expression for the current? 1 (A) (ll l : (7] ll: )dz I (C) W l 2 ill!) . R a, cl’i‘ If (B) l(.((=( a: ) (D) none of the above 9/ 2. The following are advantages of a Control System EXCEPT (A) power amplification - (C) remote control (B) convenience of input form (D) portability 3/ 3. When the number of teeth of a gear is quadrupled, which of the followrng is TRUE? (A) T(t) doubles * '. . (C) r decreases to 4x its original value (B) ~(t) decreases by 1/4 ' (D) T(t) remains the same g, 4. What do you call the difference between the input signal and the output signal? (A) dlstUrbance '_'. ' .1 (C) stimulus " (B) reference l (D) controlled variable I. F " '- / fix k 5- The following expression shows you what Laplace Transform theorem [,[f ((101: 1— i" i a ' (I k (I /r g- (A) Scaling (B) Linearity 1 .. ,l (C) Final value (D) Frequency shift. 6. What ancient civilization started engineering} feedback system using a water clock? E (A) Mesopotamians (B) Egyptians “I (C) GI'EEK (D). PhoeniClans 7‘ This We of reSponse remains after the transient response has decayed to zero. 1 C 8 (A) residual (B) null - '- (C) stability (D) natural Wthh Of the following gives the forcejvelocity relationship for a viscous damper? h (0):.71-(“0l’f (B).f(I):.f;.l‘(I) . (c) .r-ll‘l=.r.““(’l (m _ d! i 9' The restilting torque can be effectively reflefited through gear trains by multiplying . _ . ' l It by the ratio (A C(C.\‘IHMH()H\: .S'l'HH'CiC‘I' . " dcsMra/r'nn (D) WW1”? 6: ) ~ HERE—J f ' I q yourcc (/L’SHHHHUH ‘ "If H ’ "(1’ c cxrmrl JON . _ _ c 1 x - i . l dIS lacement l 0. Based on the Voltage-charge relationship pf an electric network, the meChan‘Ca D a _ P (Ei‘ogous to What electrical quantity? i (D) electrIc voltage electricDower (B) electric current 1 (C) Electric charge Ill l r:.'1l‘ *‘..l v. Feedback and Control System ExamCo|mmlttee l (.1 ' I. I Igfgfisfigfifi“gradgfie'mdy-diagfam, the direction of positive motion is - . '_‘ l- p . n ' ‘ (C) always to the right of the diagram B) col ear With the resultant (D) m any direction possible 'a-mhichl I: the following is the definition of a Laplace Transform? In "(If J: sift” Jun w J" Jr“ )ltr (h. ;;The total response of any system is the sum of the i (A) trans'ent 8' SteadV'State (C) transient & natural (3) natural & forced response (0) forced & steady-state I); The followmg expression shows you what Laplace Transform theorem 4ka )1 = 1' (5)7 E (A) Scaling (3) Initial valve . . (C) Final value (D) Frequencv shift -' awmm 0f the fonowmg test wave formsrcan only be used to evaluate the steady-state error of a COHtFOl 1 System? (A) impulse (B) step 2 I. (C) ramp ([3) Slnusoid “if; '1“ ‘3 meChan'Cal SYStem. the number of equations of motion is dependent on the " ,L number ,of _, ; (A) direa‘Y COUPlECl impedances 3' ' (C) linearly independent motion -) moment of inertial mass f - (D) all of the above fiiLWhBt is the main purpose of implementing gear trains? if (A) eiiminate gears with large radii ' ' ‘ '- (C) minimize frictional losses (B) addition of load couplings i (D) mitigate additional inertial reaction 1... Which of the following analogy between electrical and mechanical quantities w a; is INCORRECT using the force—displacement and voltage-charge relationships? ,5 ,2 ) spring : capacitor (B) damper : resist0r (C) mass : inductor (D) all of the above ' V At what shaft should impedances be reflected to when using the derived formula of an _ _ all ' 1%" {J 'i‘: 1. - I 1;; electromechanical SYStem? (A) at any shaft - (C) at the load shaft (B) at the input shaft - (D) none of the above What is a major advantage of frequency domain over the time domain techniques? ‘ (A) unifies designing of a system . . .' (C) rapid transient response information (B) handles nonzero initial condition ' ' - '1 (D) it can model multiple input system one the problem below for items no. 21 - 23) (5pts) "7 l The differential equation shown below has the following initial condition: x(0) = 2; x’(0) : 1 I:va Eh : 2; ——-—;+2—-+.\"=5c’ +1“ "F. 53-; - {If ' d! v 21-. hat will be X(s)? I I. _ I. ’ 3.x" +95} +153: + .s' + 2 i 2.54 +155" +93: +5 + 2 (A) —————-————.——..—* a (C) (.5'e-2X5— l)'.s“ ' - : (5"2Xb— l) a" 2.5" + 9.3": +1552 + S + 2 I (D) 23“ -— 953 + 933 + 3- - 2 _._.-————————'—‘— i _ fl 3 ' i ‘. (s + 2X5 + l)“ .s" (s + 2X3 + l)2 i: What Will be the equwalent partial fraction of X(s)? , 9 l 5 2 l 5 +—1——-—-——~9——+Z'- i (C) ,+——-—— +-—+— 11): 5+1 5+2 5 .5" I. * (5—1) 5—1 5—2 s v ' ' 'i . s l 9 2 l 9 +-—1*——"-'§'—+: -1—1-| . a+ " +'—"'-'T i .. _ (5+1): 5 + 2 s +l .s' .s" (s — l)" .8 - l s — 2 .5 i :1; is the solution, x(t)? '. *' i n; m _f I I Skiff—e r+ge :r—a2+f II 58* ‘6 +919 “2+! 1 .- (3)6913" — e '3' + Se” + 2 H “a .i ii (D) 9’94 ‘ 9" + 5‘5" + 2 +’ . .5 . . 3 problem below for items no: 24 '— 25) (5195) I -. if???” a circuit shown in Figure 1 is known'as the lead-lag Clrcwt. isi’the transfer function V2(s)Nl(S)? " I ‘ ‘ - "ff g- i 1 ' 1 I + _-R C 1+ S}{_‘( 2): «3;... _‘ is: __ "1 i . 1-; , . ; IC l5 .I v Rl‘ :5 l - (i R C )(1 *R t‘ ) ‘3 y -, v- -", ' SIM" I, " I i T "-' I) , i: i. R4125. Page 2 of 3 Qlf\w\"'n‘ r (21"an I C». =1/QF , C1: 0'1»? What islthe output response v;~(t) when v10) is a unit step input? I 1 (A) w r _c r (B) I: _U :i (C) w 2! “c 2: (D) e —! r3 . r} to the problem below for items no. 26 — 27) (5pm) , . ' A loaded a truck results in a force F on the support spring. and the tire flexes as shown an Flhgolgf igel-firmss of the truck and the tire is represented by M.r and M respectively. The reaction oft e s is in fin and k1 while for the tire the reaction. is; and k2. rile“. " ' . are the equations of motion of the truok and tire assembly? 35% (B) 2.81 % ~l (C) 4.72 0/0 (D) 1-25 % at is the transfer function X1(s)/F(s)? D ‘ (A) 96-5 % (a) 96.9 (C) 97.1 0/0 (D) 97.4 /o gr to the'circuit below for items no. 28 - 30) (Sp‘ts) _ i ' The motor whose torque-speed characteristics are snown in Figure 3 drives the load shown In -.:j-.!:-ri.3-fé.l * r m . What are the values of the motor inertia "and damping respectively? -‘ ) 2 and 3 (B) 1 and 2 (C) 3 and 2 (D) 2 and 2 What (actuation reoresents the torque-Speed cu me? i (A) 1" = mire,” +8 k ' (c) 71"" = -360”. + 4 . I'" 'I‘J 1h. : r 7‘!” I: In + S 'l I 7‘"! = —0 25(1)!" + What is? the transfer function 112(5) [545)? 0.75 ' i 12 .3?- (A) “"‘T—T: ‘- . i (C) 1————.c— S(S-+ 0.33.) | - . 3(5 +1 33.1) i 0.333 ': ' . 1.333 (B) —— l ' ‘ (D) — 5(3 + 0.75) .r(.s +12) :5: _ _ . I :-.*t System 33$; (Jiommlttee ' 1" .._ . ’1! 'l ' - r 4. I .- _. - I ‘l ll 'L 12-7" ;.-.;.'_--. r___ I '.-I*_ .~ "L ' ', l _ -- ,__. _;;5,.:_-. thin-rm, . -.-:."_z- 3.. :- . 2m?) + m3 _ji+ra;-n,.xbons n mm; L '19 " “fr {WW (0 x0 5 ‘9 * ° - 5 4" 51 ) -|Cb 1.8"} E? a; It. I. . H Eh.‘{51+25\’l)(5*3) ¥ 349%:st w» C(51)(sn)4 v(s*)fsms*1>~'9 9" (Wm!) .-(c“+4s’+s:..1425)* 0( +31% 9(3'1435’09) +E( finsas‘) His" -. (s) g 1 2 q .. .L L i Pfl¢?[0 A ' CPE‘H Quiz No.1 part 1: Essay Type (10 pts. each) Discuss and ex Part 2: Problem Solving Type (f0 pts. each) Directions: (1) Number your solutions accordingly. (2) Write your solutions leginy and cross-out any (3) Box your final answer. (4) Only one fine unwanted solution. De La Salle University ~ Dosma" College of Engineering, Architecture and Technology Engineering Department plain about the modern approach used in-Feedback Control Systems in the analysis and demgn of control systems. I answer is allowed per item. I .\'-m su’rzld 1 Km": “rad N: :2 100 F I itg-n'i2 .L—n—J L——{ V1: in r' titll‘.‘ flax” = 1. Draw the (a) series analog (b) p of mechanical system shown above. i ' "1 N4: Intfifhi___ Oil-1 \i-m-s-nidLJ arallel analog 2. Represent the electrical network shown in is the output. . l I ‘ \i‘u his} I H Li 1H Q L11};- “in C O 3. Obtain the transfer matnfiitfiie syst i'fi” ':1e figure below in state space. Miere vort) i it: ern defi nee—by x. 0 l 0 II 0 0‘1 H .v |_l 0 0 xl . | . I _ .‘t‘I — 0 0 I I: + U 1 [Hz] [yjr-LO ] OJ 2 I1 *2 ‘4 ‘6 x1 1 SJ r lg‘hmr 9,5ka M“ '1' Sfb fiffbgln} 373%; MW “mun; in} MAFJYiWS‘ .1. i sowmc, -s Bis) 4: (9 *1) 91(5) - 9:50-29 «01(5) ¢ Lmfl) 3.15? ' ' _L———-.-.—_ ____.-.__. _.__._.—+_ GATE» 97pm REPRESmTATIm De La Salle University — Dasmarinas College of Engineering, Architecture and Technology Engineering Department Name (JUAng a'olo . . Yr & SEC (IVE:le Instructor: QUESTIONAIRE . 1' General Directions: / 1. Read and answer the following items carefu||y_ / 2. The exam consists of two parts, PART 1 and PART 2. 3. For both parts, mark the corresponding letter of your answer on the provided SCANTRON ANSWER SHEET. 5. For Part 1, there is NO SOLUTIONS REQUIRED for each question and each item is equivalent to lot. 6. For PART 2, PROVIDE an appropriate SOLUTION to items that require it. 7. Write your solutions on the provided SOLUTION SHEETS and NOWHERE ELSE. 8. NO POINTS WILL BE AWARDED FOR ITEMS WITHOUT SOLUTIONS EVEN IF THE CORRECT LETTER WAS MARKED ON THE ITEM. 9. Solutions should be numbered accordingly and the FINAL ANSWER BOXED. 10.The equivalent point for each item in for PART 2 is indicated at the end of each question. PART 1 , .5 t5 1. In state variable analysis a nth order differential equation is L: e] (A) “:1” partial expansion in terms of its state variables 3 -l 25...... l T (B) “n” first order differential equations in terms of its state variables [5 stio ‘3 *5 5 l (B) “n” simultaneous algebraic equations in terms of its state variables chi - stoic.) to (D) “n” polynomial equations in terms of its state variables r. _'_ is: i 5' C 2. What single-input, single-output system has 0 1 ii i=5” “re-1'. f_ ‘ or: the state variable representation *7 I [F 5 _ [JHLJJH P = [0 “’l‘f * — so _ 5 — so _ 5t, (A) 71(5): 33+532+505 “wars-5 (C)7(3)—32+105+5 (0);“): s: +Ss+5 B 3. The state variables In passwe electrical networks is usually taken as the (A) currents through inductors and capacitors (8) current through inductors and voltage across capacitors (C) voltage across the inductors and current through capacitors (D) voltages across resistors and across capacitors i5 4. In state—space representation, which of the following matrix is associated with comparing the input and the output? (A) input matrix (B) output matrix (C) system matrix (D) feedfonvard matrix A 5. The direction of the current source in a Parallel Analog follows the: (A) direction of the force (C) number of degrees of freedom (B) polarity of the impedance (D) storage elements E 6. A first order dynamic system is represented by the differential equation 5x'(t) + x(t) = u(t). The corresponding transfer function and state-space representation are: 3... x (A) G(s) = 10/(1 + 55) and x' = 0.5u; y = 0.4x (*5 o. 0 ice) .. or.) M“ 3?; (B) (3(5) 2 1 1 (1 + 55)’and x' = -0.2x + 0.5u; y = 0.4x . 5,}, 7, f U .1: N (C) G(s) = 10/(1 + 55) and x’ = -0.2x + u; y = x sot a: *‘ (D)G(s)=1/(s+5) and x’=-5x+u;y=x ' $.go—Ev % D 7. In a Series Analog, impedances between adjacent motions are drawn as: ,5, y, l'. i : H: 1", (A) parallel electrical impedances between two corresponding nodes is} 1 ti 4F HA L, (3) series electrical impedances between two corresponding meshes it“ _. ~,( 3 ; y, (C) series electrical impedances between two corresponding nodes in; i (D) parallel electrical impedances between two corresponding meshes U C 8. In the phase variable method, it.” I = (A) 2,, (B) 56,, (C) X... (D) 13..-, C 9, If xir y and z are variables, which of the following expression shows linear independence? (A)2XY+2 Ht.- (B)X-—2Y+4Z'~" (C)XYZ (D)X/Y—3Z Prepared by: Feedback and Control System Exam Committee ' Page 1 of 4 ‘t l). ’t I {1“ it ‘5‘ ‘ 1‘ [if . For a parallel LC CirCUit With an inductanc A 10 the state variable ectuations are e or L and CaDflcltance of C (A) i '(t) = 1/1- Vc(t) and vc"(t) = -ini L I I (B) it"(t) = 1/L Yea) and ye’(t) = 1/C tag-13112228) (C) if“) = “L '1“) 3"“ Vc'tt) = -1/c wit) + 0c i(t (D) W) = 1’ L "m and V5“) = 1/C yen) l~ 1/c 1(1)) 1. Given the transfer function of a Systel-n' w _ _ .L + a .1 H. D 1 state-space rePresentation? he“ “Elf-“Wines the number or state yariabl r '- (A) the coefficients of the numerator (C) [h e or “5 (B) the coefficrents of the denominator 8 degree of the numerator - ‘ ‘ (D) the de r . 12, WhICh of the followrng 15 one advantage or _ 9 Be or the denommatOr C approaCh? the frequent)! domain over the time domain (A) uses a much thorough analysis of a contr (B) is used to model time-varying SystEmS ol system systems are (C) velocity and friction (B) acceleration and displacement (D) displacement and yelooty E 15-The fouowmg Statements are true for state space a roach ' EX : (A) it can be used to represent nonlinear systems ,pp CE” (3) mU'tiDle input/output System can be re _ _ presented com actl / (C) used In systems wrth nonzero initial conditiom p Y (D) time-variant systems can be modeled using state space approach / PART 2 (Refer to the circuit below and Figure 1 for items no. 16 — 18 5 is When R1_= 100 Q, R; = 300 Q, L = 1mH, C 2 Inc )( p ) f) 16. What variables will be chosen as the state variables? (A) it and it (B) ye and i1L c v and V . . nun-'- II D l: 17- What '5 the Output equation of the network? ( ) c L ( ) I“ and I“ v 0.25 1.00 ' _ (A) '82 : *3 H. + 0.25 (0) {Hi-L 1R2 VG V 3 ) __ 3 (B) -R2 = 3.00 0.84x10 it + 0'34X10 i0) ’32 1.00 4.00 v0 4 (C) 1:322 Z 4.00 "3 1.00 lip 4 in 0.84810 3.00 rm _ . a (D) em 2 "—0.25 —3.34x10‘ [1L]+[0.25] IR; -1196 1.00 :C 1196 E 18. What is the state equation of the network? 1' 250.85 0.84 r' ~250.85_ (A) L : L]+[ ]:(z) vC —100.25 8.36 vc 100.25 . 4 —250.85 _ (B) vL : 250.85 08 [1:3le kt) _ 1}: —100.25 8.36 :C 100.25 9 - ' -—250.35 , a (c) zL : 250.85 0.84 1L]+[ kt) ' vc -—100.25 8.36 vC 100.25 ' — 0.85 (D) vL : 250.85 0.84 yy]+[ 25 1M ‘ —1...
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