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x1(t) x2(1) 1 N/m f(t) 1 kg 1 N-s/m 1 kg 1 Frictionless Figure 2-18 1) Find the transfer function, X2/F, for the network shown in Figure 2-18 R L + vi(t) C - Figure 4-6 2) Find the value of R and C in Figure 4-6, where L = 1H so that a unit step voltage input will cause a 20% overshoot and a 1 ms settling time in the voltage across the capacitor. Amp Motor R(s) E(s) K1 25 C(s) s(s + 1) K2S Tachometer Figure 5-12 3) Find the value of K1 and K2 for the system in Figure 5-12 which yields a 16% overshoot and a 200 ms settling time for a unit step input. 4) If a Routh table has two sign changes above the even polynomial and five sign changes 4) below the even polynomial, how may RHP poles does the system have? 5) What is the percent overshoot of a system with the transfer function H(s) = 2 ? s²+2s+6 5) 6) What is the 1% settling time of a system with the transfer function 2s+1 s²+2s+6 6) 7) What is the natural frequency of a system with the transfer function H(s)= 2s+1 ? s2+2s+6 7) 8) A system has a characteristic equation: q(s)=33+2032+58490. How many roots are in the 8) RHP? R(s) 55 + 254 + 45³ + 52 + 4 ((s) + s² + 5 Figure 2-11 9) What is the differential equation for the system shown if Figure 2-11? 9) I + vi(t) + 1H 1 - vo(t) Figure 2-12 10) Find the transfer function, Vo/Vi, for the network shown in figure 2-12 1 1 H 0000 + vi(1) + 1 - 1 F vo(i) Figure 2-13 11) Find the transfer function, Vo/Vi, for the network shown in figure 2-13 - G2 + + + R o G1 E oy - Figure 3-1(a) 12) What is the transfer function for the system shown in Figure 3-1(a) R(s) + E(s) 38343 C(s) s(s + 200) - Figure 5-11 13) Find the settling time for the system in Figure 5 -11 the MULTIPLE answers CHOICE. are correct, Choose write the one alternative that best completes the statement or answers the question. If none "None" in the space provided. (Worth 1 pts each) of 14) If F(s) (s-5)(s-6) (s+4)e-6s what is f(t)? 14) A) Ju(t-6) C) B) D) 15) Which system is stable, given the follosing characteristic equations? A) q(s)=s4+6s²+25 15) B) q(s)=s++8s³+32s²+80s+100 C) Both systems are stable D) Neither system is stable Controller Process Signal 1 Signal 2 Signal 3 Signal 4 Measurement Signal 5 Figure 1-1 16) Many luxury automobiles have thermostatically controlled air-conditioning systems for the comfort of the passengers. Figure 1-1 can be used to represent such a system where the driver sets 16) the desired temperature using a dashboard panel. Which element is the process? A) The measured temperature B) The driver C) The automobile cabin D) The temperature sensor 17) Many luxury automobiles have thermostatically controlled air-conditioning systems for the comfort of the passengers. Figure 1-1 can be used to represent such a system where the driver sets 17) the desired temperature using a dashboard panel. Which element is the Signal 3? A) The measured temperature C) The error signal B) The automobile cabin temperature D) The desired temperature set by the driver 18) Many luxury automobiles have thermostatically controlled air-conditioning systems for the comfort of the passengers. Figure 1-1 can be used to represent such a system where the driver sets 18) the desired temperature using a dashboard panel. Which element is the controller? A) The driver C) The measured temperature B) The temperature sensor D) The automobile cabin 19) A laser is controlled by an input current to yield the power output. A microprocessor compares the desired power level with a measured signal proportional to the laser power output obtained 19) from a power sensor. The microprocessor generates the input current to the laser based upon this comparison. Using the diagram in Figure 1-1, which element is the controller? A) The microprocessor B) The power sensor C) The measured signal D) The laser + R(s) 3 1 Y(S) S + 7 S 2 + Figure 2-3 Y(s) 20) What is the transfer function, for the system shown in Figure 2-3? 20) R(s) A) T(s)= 2s+3 3 B) T(s)= C) 2s+3 D) 3 s2+13s+3 s2+13s+3 s²+7s+3 s²+7s+3 9 1 1 S + 6 S + 5 / R 920 Y 4 -| I Figure 2-4 21) What is the cofactor for path P1 from R to Y for the signal flow graph shown in Figure2-4° 21) A) 41=1 - 15 1 B) A1=1-29 s+6 D) Both A and C are correct 3 e 2-6 22) What is the transfer function from R to Y for the signal flow graph shown in Figure 2-6? kGaGbGc kGaGbGc A) 1-3Ga-3Gb-2Gc+6GaGc+6GbGc B) 1-3Ga-3GaGb-2Gc+6GaGc+6GaGbGc kGaGbGc kGaGbGc C) 1+3Ga-3GaGb-2Gc-6GaGc+6GaGbGc - D) 1+3Ga-3Gb-2Gs-6GaGc+6GbGc - K 1 Go Gb Gc Gd Ro o Y 3 2 2 Figure 2-7 23) What is the transfer function from R to Y for the signal flow graph shown in Figure 2-7? 2 GaGbGcGd GaGbGcGd+kGa A) B) 1-3Ga-k(2Gb-2Gc)+6GaGc 1-3Ga-k(2Gb-2Gc) GaGbGcGd+kGa(1+2Gc GaGbGcGd+kGa(1-2Gc) D) +3Ga+2Gb+2Gc+6GaGc 1-3Ga-2Gb-2Gc+6GaGo TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. (Worth 1 pts each) 24) A control system is an interconnection of components that will provide a desired system response. 24) 25) The transfer function reprents the ratio of the time based output to the time based input. 25) 26) A second order system is characterized by two values, the natuarl frequency and the damping 26) ratio. 27) An underdampled system will not oscillate. 27) 28) An open-loop actuator control to obtain system uses a controller to compare the output to the input. The result is 28) fed to an the desired response. 29) A second order system is characterized by two values, the natuarl frequency and the damping 29) ratio. 30) In order to develop the differential equations for a system, the engineer must first understand the 30) physical laws associated with the system. 31) 31) A first order system reaches 37% of its final value in one time constant. 32) 32) A system with impulse response h(t) is BIBO (bounded input bounded output) stable if and only if 80 s /h(T) dT=0. -00 33) 33) A necessary condition for stability is that all the coeficients of the characteristic polynomial be positive. R(s) + E(s) C(s) G(s) - Figure 7-1 1) What is the %O.S., settling time, and steady-state error to a unit step input for the system in Figure 7-1 - if 5000 s(s+75) 2) Design the values of n,K, & a for the system in Figure 7-1 where K G(s)= to meet the following requirements: 1) Kz=110; and 2) %O.S. = 12%. sn(s+a) R(s) + K ((s) s(s + 1) 1Os K Figure 7-3 3) Design the value of K for the system in Figure 7-3 so that an input of u(t) will have a steady-state error of 0.1. Current Compensator [s + 5) F C G C(s) = 1.42e+003 X (s + 15.2) H - FS Closed X Root Locus Pole Values: -5.06 -13.2 + 1.88i OK * System Data 83 System Name: untitled Plant Model: untitledG Zeros: Poles: 1 10 20 <none> -8 -6 -4 I -2 Figure 9-10 4) Design a lag compensator for the system in Figure 9-10 that will improve the steady - state error by a factor of 5. </none>Current Compensator 219 F C G Q(s) = H FS Closed X Root Locus Pole Values: -13.1 OK System Data x System Name: untitled Plant Model: untitledG Zeros: Poles: <none> -5 5 10 -11 -5 Figure 9-12 5) Design a lead compensator for the system in Figure 9-12 that will place the dominant second-order - ro -4.61+j7.634.. </none>6) What is the static acceleration error constant for a unity feedback control system whose e forward transfer function is G(s) ? S3(st7)(s+14)(s+19) R(s) + E(s) C(s) G(s) - Figure 7-1 7) What is the steady-state - error for the system in Figure 7-1 - if G(s)= 15(s+2)(s+8) and 7) (2(s+8)(s2+5s+15 r(t)=tu(t)? 8) Find the value of a which will yield Kz=5,000 for the system in Figure 7-1 - if 8) G(s)= 100500(s+5)(s+14)(s+23) s(s+27)(s+a)(s+33) 9) What value of K will yield a steady-state - error of 0.08 for the system in Figure 7-1 if 9) and r(t) = 27tu(t)? s(s+6)(s+9)(s+22) 10) What is the static velocity error constant for the system in Figure 7-1 - if G(s)= 10) 250(s+1)(s+5) ? s(s+2)(s²+5s+10) X X Figure 8-11 11) Using figure 8-11, sketch the general shape of the root locus for the pole-zero - plot shown. 11) R(s) + ((s) G(s) - Figure 8-13 12) Sketch the root locus for the system shown in figure 8-13 - when G(s)= K(s+10)(s+20) 12) (s+30)(s²-20s+200 13) Sketch the root locus for the system shown in figure 8-13 when G(s) K(s+8) (s+2)(s+4) (s+6) 13) Current Compensator (s+5) 1.42e+003 F C G C(s) = X (s + 15.2) H FS Closed x Root Locus Pole Values: -5.06 -13.2 + 1.88i -1.9 + 3.29i OK * System Data @ 83 System Name: untitled Plant Model: untitledG Zeros: Poles: I <none> -8 10 20 -6 -4 -2 igure 9-10 14) What is thedamping ratio for the system shown in Figure 9-10? - </none>Current Compensator (s + 0.1) F C G C(s) = 5.84 X S H x FS Closed a X3 Root Locus Pole Values: -0.0612 OK System Data x System Name: untitled Plant Model: untitledG Zeros: Poles: <none> -4 1 1 -1 gure 9-14 15) What is the error constant for the system shown in Figure 9-14? </none>MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. If none of the answers are correct, write "None" in the space provided. (Worth 1 pts each) 16) How can you determine where the root locus crosses the imaginary axis? 16) A) Search along the imaginary axis for points that have odd multiples of 180° angles to the open-loop poles and zeros. B) Apply Routh-Hurwitz to the open-loop transfer function's characteristic equation. C) Apply Routh-Hurwitz to the closed-loop transfer function's characteristic equation D) Search along the imaginary axis for points that have odd multiples of 180° angles to the closed-loop poles and zeros. E) Both A & Care correct. 17) Which compensator represents a lag controller? 17) A) Gd(s)-Sto.05 B) s+0.01 C) D) Gds)=5+5 S 18) A unity feedback control system whose forward transfer function is 18) S3(st7)(s+14)(++19) is what type system? A) Type 3 B) Type 2 C) Type 0 D) Type 1 19) Which rules for plotting the root locus change depending upon whether the system is a 19) positive-feedback or a negative-feedback system? A) Real-axis segments. B) Symmetry. C) Number of branches. D) Starting and ending points. R(s) + E(s) C(s) G(s) - Figure 7-1 20) What is the system type for the system in Figure 7-1 - if 20) G(s)_K(S2+65+6), (s+5) 2 (s+3) A) Type 2 B) Type 1 C) Type 3 D) Type 0 "RUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. (Worth 1 pts each) 21) The Type number of a system is the same regardless whether you look at it relative to a control 21) input or a disturbance input. 22) The poles and zeros of a system change as the gain of the system changes. 22) 23) A PID compensator requires a PD compensator cascaded with a PI compensator. 23) 24) Steady- state error is only relevant for stable systems 24) 25) The angle from a point on the root locus to all the zeros of the open-loop transfer function minus 25) the angle to all the poles of the open-loop transfer function is equal to an odd multiple of 180°.

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