MCQOPTIONS
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MCQOPTIONS
This section includes 180 Mcqs, each offering curated multiple-choice questions to sharpen your Control System knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For the transfer functionG(s) = 5(s + 4) s (s + 0.25)(s2 + 4s + 25)The values of the constant gain term and the highest corner frequency of t he Bode plot respectively are |
| A. | 3.2, 5.0 |
| B. | 16.0, 4.0 |
| C. | 3.2, 4.0 |
| D. | 16.0, 5.0 |
| Answer» B. 16.0, 4.0 | |
| 2. |
The maximum phase shift that can be provided by a lead compensator with transfer functionG(s) = 1 + 6s is1 + 2s |
| A. | 15 |
| B. | 30 |
| C. | 45 |
| D. | 60 |
| Answer» C. 45 | |
| 3. |
A linear second-order single-input continuous-time system is described by the following set of differential equations : X1 (t) = 2 X1 (t) + 4 X2 (t) X2 (t) = 2 X1 (t) X2 (t) + u (t) where X1 (t) and X2 (t) are the state variables and u (t) is the control variable. The system is |
| A. | controllable and stable |
| B. | controllable but unstable |
| C. | uncontrollable and unstable |
| D. | uncontrollable but stable |
| Answer» C. uncontrollable and unstable | |
| 4. |
A system with the open loop transfer function G(s) = K s(s + 2)(s2 + 2s + 2)is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is ____ |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» E. | |
| 5. |
The closed-loop transfer function of a system is T(s) = 4 (s2 + 0.4s + 4)The steady state error due to unit step input is ____. |
| A. | 0 to 0 |
| B. | 4 to 3 |
| C. | 1 to 5 |
| D. | None of the above |
| Answer» B. 4 to 3 | |
| 6. |
An open loop control system results in a response of e 2t (sin5t + cos5t) for a unit impulse input. The DC gain of the control system is ______. |
| A. | 241 |
| B. | 0.241 |
| C. | 41 |
| D. | 0.21 |
| Answer» C. 41 | |
| 7. |
For the transfer functionG(s) H(s) = 1 s (s + 1)(s + 0.5)the phase cross-over frequency is_____ rad/sec |
| A. | 0.707 |
| B. | 707 |
| C. | 7.07 |
| D. | None of the above |
| Answer» B. 707 | |
| 8. |
The value of k for a unity feedback system with G(s) = k s(1 + s)to have a peak overshoot of 50% is _______ |
| A. | 53 |
| B. | 0.53 |
| C. | 5.3 |
| D. | None of the above |
| Answer» C. 5.3 | |
| 9. |
The z-transform of a signal is given by c(z) = z 1 (1 - z 4)4(1 - z 1)2Its final value is_______ . |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 10. |
A unity-feedback control system has the open-loop transfer functionG(s) = 4(1 + 2s) s2 (s + 2)If input to the system is a unit ramp, then steadystate error will be_______ |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 11. |
The unit step error coefficient of a system G(s) = 1 (s + 6)(s + 1)with unity feedback is _______ |
| A. | 6 |
| B. | 5/6 |
| C. | 1/6 |
| D. | 5 |
| Answer» D. 5 | |
| 12. |
The transfer function of a system is 101 + sWhen operated as a unity feedback system, the steady state error to a unit step input will be_______ |
| A. | 1 / 11 |
| B. | 4 / 7 |
| C. | 11 / 7 |
| D. | None of the above |
| Answer» B. 4 / 7 | |
| 13. |
The open-loop DC gain of a unity negative feedback system with closed-loop transfer function s + 4 is _______.s2 + 7s + 13 |
| A. | 9 / 4 |
| B. | 1 / 9 |
| C. | 4 / 5 |
| D. | 4 / 9 |
| Answer» E. | |
| 14. |
For a unit step input, a system with forward path transfer function G(s) = 20 s2and feedback path transfer function H (s) = (s + 5), has a steady state output of_______ |
| A. | 7.2 |
| B. | 0.01 |
| C. | 0.002 |
| D. | 0.2 |
| Answer» E. | |
| 15. |
A plant has the following transfer function :G(s) = 1 (s2 + 0.2s + 1)From a step input it is required that the response settles to within 2% of its final value. The plant setting time is _____sec |
| A. | 4 sec |
| B. | 40 sec |
| C. | 10 sec |
| D. | None of the above |
| Answer» C. 10 sec | |
| 16. |
A phase-lead compensator has the transfer function ______ rad/secGC(s) = 10(1 + 0.4s) (1 + 0.01s)The maximum phase angle lead provided by this compensator will occur at a frequency m is equal to |
| A. | 50 |
| B. | 5 |
| C. | 125 |
| D. | 150 |
| Answer» B. 5 | |
| 17. |
The characteristic equation of a feedback system is s 3 + Ks 2 + 5s + 10 = 0 For the system to be critically stable, the value of K should be_______ |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 18. |
In a synchro error detector, the output voltage is proportional to [ (t)]n, where (t) is the rotor velocity and n equals_______ |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 19. |
A system with transfer function G(s) = (s2 + 9)(s + 2) is excited by sin ( t). (s + 1)(s + 3)(s + 4)The steady-state output of the system is zero at |
| A. | = 1 rad/s |
| B. | = 2 rad/s |
| C. | = 3 rad/s |
| D. | = 4 rad/s |
| Answer» D. = 4 rad/s | |
| 20. |
A source vs (t) =V cos 100 t has an internal impedance of (4 + j3) Ω . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be(a) (b) |
| A. | 3 |
| B. | 4 |
| C. | |
| D. | 5 |
| E. | 7 |
| Answer» D. 5 | |
| 21. |
Let the Laplace transform of a function f(t) which exists for t > 0 be F1 (s) and the Laplace transform of its delayed version f(t ) be F2 * (s). Let F1 * (s) be the complex conjugate of F1 (s) with the Laplace variable set as s = + j .G(s) = F2(s).F1*(s) , then the inverse Laplace transform of G(s) is |F1(s)|2 |
| A. | an ideal impulse (t) |
| B. | an ideal delayed impulse (t ) |
| C. | an ideal step function u(t) |
| D. | an ideal delayed step function impulse u(t ) |
| Answer» C. an ideal step function u(t) | |
| 22. |
The frequency response of a linear system G(j ) is provided in the tabular form below | G(j )| 1.3 1.2 1.0 0.8 0.5 0.3 G(j ) 130 140 150 160 180 200 The gain margin and phase margin of the system are |
| A. | 6 dB and 30 |
| B. | 6 dB and 30 |
| C. | 6 dB and 30 |
| D. | 6 dB and 30 |
| Answer» B. 6 dB and 30 | |
| 23. |
For the system 2 the approximate time taken for a step response to (s + 1) reach 98% of its final value is |
| A. | 1 s |
| B. | 2 s |
| C. | 4 s |
| D. | 8 s |
| Answer» D. 8 s | |
| 24. |
A discrete real all pass system has a pole at z = 2 30 : it, therefore |
| A. | has a constant phase response over the zplane: arg | H(z)| = constant |
| B. | is stable only, if it is anticausal |
| C. | has a constant phase response over the unit circle: arg | H(e |
| D. | )| = constant |
| Answer» E. | |
| 25. |
The transfer function of a system is given as 100 s2 + 20s + 100This system is |
| A. | an overdamped system |
| B. | an underdamped system |
| C. | a critically damped system |
| D. | an unstable system |
| Answer» D. an unstable system | |
| 26. |
If x = Re G(j ), and y = lm G(j ) then for 0+, the Nyquist plot for G(s) = 1 s(s + 1)(s + 2)becomes asymptotic to the line |
| A. | x = 0 |
| B. | x = y 1 / 6 |
| Answer» C. | |
| 27. |
The open loop transfer function of a unity feedback system is given byG(s) = (e-0.1s) sThe gain margin of this system is |
| A. | 11.95 dB |
| B. | 17.67 dB |
| C. | 21.33 dB |
| D. | 23.9 dB |
| Answer» E. | |
| 28. |
The transfer function of a linear time invariant system is given asG(s) = 1 s2 + 3s + 2The steady state value of the output of this system for a unit impulse input applied at time instant t = 1 will be |
| A. | 0 |
| B. | 0.5 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 29. |
If the loop gain K of a negative feedback system having a loop transfer functionK(s + 3) (s + 8)2is to be adjusted to induce a sustained oscillation then |
| A. | The frequency of this oscillation must be must be 4 rad/s |
| B. | such a K does not exist |
| Answer» E. | |
| 30. |
The first two rows of Routh's tabulation of a third order equation are as follows.s322s344This means there are |
| A. | two roots at s = j and one root in right half s-plane |
| B. | two roots at s = j2 and one root in left half s-plane |
| C. | two roots at s = j2 and one root in right half s-plane |
| D. | two roots at s = j and one root in left half s-plane |
| Answer» E. | |
| 31. |
Consider a unity feedback system having an open-loop transfer functionG(j ) = K j (j 0.2 + 1)(j 0.05 + 1)For K = 1, GM = 28 dB. When GM at 20 dB, K will be equal to______ |
| A. | 0.25 |
| B. | 25 |
| C. | 5 |
| D. | 2.5 |
| Answer» E. | |
| 32. |
An open loop transfer function G(s) of a system isG(s) = K s (s + 1)(s + 2)For a unity feedback system, the breakaway point of the root loci on the real axis occurs at, |
| A. | 0.42 |
| B. | 1.58 |
| C. | 0.42 and 1.58 |
| D. | None of the above |
| Answer» B. 1.58 | |
| 33. |
The gain margin of the transfer functionG(s) = 0.75 (s + 1)(s + 2)will be _____dB |
| A. | 2 dB |
| B. | 12 dB |
| C. | 16 dB |
| D. | 32 dB |
| Answer» C. 16 dB | |
| 34. |
Consider the following statements regarding a linear system y = f(x1) 1. f (x1 + x2) = f (x1) + f (x2) 2. f [x (t + T)] = f [x (t)] + f [x (T)] 3. f (Kx) = Kf (x). Of these statements |
| A. | 1, 2 and 3 are correct |
| B. | 1 and 2 are correct |
| C. | 3 alone is correct |
| D. | 1 and 3 are correct |
| Answer» E. | |
| 35. |
Consider the following properties attributed to state model of a system : 1. State model is unique 2. State model can be derived from the system transfer function 3. State model can be derived from time variant systems. Of these statements |
| A. | 1, 2 and 3 are correct |
| B. | 1 and 2 are correct |
| C. | 2 and 3 are correct |
| D. | 1 and 3 are correct |
| Answer» D. 1 and 3 are correct | |
| 36. |
The maximum phase shift that can be obtained by using a lead compensator with transfer functionGC(s) = 4(1 + 0.15s) is equal to(1 + 0.005s) |
| A. | 15 |
| B. | 30 |
| C. | 45 |
| D. | 60 |
| Answer» C. 45 | |
| 37. |
Maximum phase-lead of the compensatorD(s) = (0.5s + 1) is(0.5s + 1) |
| A. | 52 deg at 4 rad/sec |
| B. | 52 deg at 10 rad/sec |
| C. | 55 deg at 12 rad/sec |
| D. | none of these |
| Answer» E. | |
| 38. |
The value of A matrix in x = Ax for the system describe by the different equation y + 2 y + 3y = 0, is |
| A. | |
| B. | |
| Answer» E. | |
| 39. |
State representation of a second order system isx1 = -x1 + ux2 = x1 - 2x2 + uConsider the following statements regarding the above system : 1. The system is completely state controllable 2. If x1 is the output, then the system is completely output controllable 3. If x2 is the output, then the system is completely output controllable. Of these statements |
| A. | 1, 2 and 3 are correct |
| B. | 1 and 2 are correct |
| C. | 2 and 3 are correct |
| D. | 1 and 3 are correct |
| Answer» D. 1 and 3 are correct | |
| 40. |
The transfer function of a compensating network is of the form(1 + Ts) .(1 + Ts)If this is a phase-lag network, the value of should be |
| A. | exactly equal to 0 |
| B. | between 0 and 1 |
| C. | exactly equal to 1 |
| D. | greater than 1 |
| Answer» C. exactly equal to 1 | |
| 41. |
Consider the following statements : Lead compensator 1. increases the margin of stability 2. speeds up transient response 3. does not affect the system error constant Of these statements |
| A. | 2 and 3 are correct |
| B. | 1 and 2 are correct |
| C. | 1 and 3 are correct |
| D. | 1, 2 and 3 are correct |
| Answer» C. 1 and 3 are correct | |
| 42. |
Consider a unity feedback control system with open-loop transfer functionG = Ks(s + 1)The steady state error of the system due to a unit step input is |
| A. | zero |
| B. | K |
| C. | 1/ K |
| D. | |
| Answer» B. K | |
| 43. |
The position and velocity error coefficients for the system of transfer functionG(s) = 50(1 + 0.1s)(1 + 2s)respectively are |
| A. | zero and zero |
| B. | zero and infinity |
| C. | 50 and zero |
| D. | 50 and infinity |
| Answer» D. 50 and infinity | |
| 44. |
The close-loop transfer function of a control system is given byC(s) = 1 R(s)1 + sFor the input r(t) = sin t, the steady state value of c(t) is equal to |
| A. | 1 |
| Answer» E. | |
| 45. |
A system is represented bydy + 2y = 4t u(t)dtThe ramp component in the forced response will be |
| A. | t u(t) |
| B. | 2t u (t) |
| C. | 3t u (t) |
| D. | 4t u (t) |
| Answer» C. 3t u (t) | |
| 46. |
Consider a system shown in the given figureU(s) 2 C(s)sIf the system is disturbed so that C(0) = 1, then C (t) for a unit step input will be |
| A. | 1 + t |
| B. | 1 t |
| C. | 1 + 2t |
| D. | 1 2t |
| Answer» D. 1 2t | |
| 47. |
A unity feedback control system has a forward path transfer function equal to42.25 s2(s + 6.5)The unit step response of this system starting from rest, will have its maximum value at a time equal to |
| A. | 0 sec |
| B. | 0.56 sec |
| C. | 5.6 sec |
| D. | infinity |
| Answer» E. | |
| 48. |
The forward-path transfer function of a unity feedback system isG(s) = K(s2 - 4) s3 + 3For the system to be stable the range of K is |
| A. | K > -1 |
| B. | marginal stable |
| Answer» E. | |
| 49. |
The open-loop transfer function of a unity feedback control system isG(s) = K(s + 2)(s + 1)(s - 7)For K > 6, the stability characteristic of the openloop and closed-loop configurations of the system are respectively |
| A. | stable and unstable |
| B. | stable and stable |
| C. | unstable and stable |
| D. | unstable and unstable |
| Answer» D. unstable and unstable | |
| 50. |
Consider the following statements regarding timedomain analysis of a control system : 1. Derivative control improves system s transient performance 2. I ntegral control does not improve system s steady state performance 3. I ntegral control can convert a second order system into a third order system Of these statements |
| A. | 1 and 2 are correct |
| B. | 1 and 3 are correct |
| C. | 2 and 3 are correct |
| D. | 1, 2 and 3 are correct |
| Answer» C. 2 and 3 are correct | |