ELECTRICAL AND ELECTRONICS ENGINEERING : Root locus branches always terminate at

31. The addition of a pole to a system generally:

a) Increases stability
b) Decreases stability
c) Has no effect
d) Reduces system type
Answer: b) Decreases stability
Explanation: Adding a pole increases system order and reduces relative stability.

32. The damping ratio (ζ) of a second-order system determines:

a) Rise time only
b) Overshoot and settling time
c) Frequency only
d) Gain margin
Answer: b) Overshoot and settling time
Explanation: ζ affects oscillations, thus impacting overshoot and settling time.

33. The breakaway point in a root locus lies:

a) Where two branches intersect
b) Between two real poles
c) On the imaginary axis
d) At infinity
Answer: b) Between two real poles
Explanation: Breakaway points occur where multiple real poles interact and roots separate.

34. A lag compensator improves:

a) Phase margin
b) Steady-state accuracy
c) Transient response
d) Gain margin only
Answer: b) Steady-state accuracy
Explanation: Lag compensators increase low-frequency gain → reduce steady-state error.

35. The steady-state error for a ramp input is zero for:

a) Type 0 system
b) Type 1 system
c) Type 2 system
d) None
Answer: c) Type 2 system
Explanation: Two integrators (Type 2) eliminate error for ramp input.

36. The transfer function of a first-order system is $G(s) = \frac{K}{1 + sT}$ . The time constant $T$ equals:

a) Time to reach 63.2% of final value
b) Time to reach 100%
c) Time to reach 50%
d) Settling time
Answer: a) Time to reach 63.2% of final value
Explanation: For a first-order system, output reaches 63.2% of final value at t = T.

37. The condition for sustained oscillation is given by:

a) |GH| = 1 and ∠GH = 180°
b) |GH| = 0
c) |GH| < 1
d) ∠GH = 0°
Answer: a) |GH| = 1 and ∠GH = 180°
Explanation: Barkhausen criterion defines sustained oscillations.

38. Gain margin (GM) is defined at:

a) 0° phase
b) -180° phase
c) 90° phase
d) None
Answer: b) -180° phase
Explanation: GM is the factor by which gain can increase before instability at -180° phase shift.

39. Phase margin (PM) is defined at:

a) 0 dB gain
b) -180° phase
c) -90° phase
d) +90° phase
Answer: a) 0 dB gain
Explanation: Phase margin is measured at frequency where gain is unity (0 dB).

40. The settling time of a second-order system is approximately:

a) $2T$
b) $4T$
c) $\frac{4}{ζω_n}$
d) $\frac{1}{ζω_n}$
Answer: c) $\frac{4}{ζω_n}$
Explanation: Settling time (2% criterion) ≈ $\frac{4}{ζω_n}$ .

41. A stable system must have all poles:

a) On imaginary axis
b) In left half s-plane
c) In right half s-plane
d) None
Answer: b) In left half s-plane
Explanation: Negative real parts of poles → stable response.

42. The transfer function of a PID controller is:

a) $K_p + K_i/s + K_d s$
b) $K_p s + K_i + K_d/s$
c) $K_p/s + K_i s + K_d$
d) $K_p s^2 + K_i/s$
Answer: a) $K_p + K_i/s + K_d s$
Explanation: PID = proportional + integral (1/s) + derivative (s) actions.

43. The main drawback of derivative control is:

a) Increases steady-state error
b) Amplifies noise
c) Slows down system
d) Reduces gain
Answer: b) Amplifies noise
Explanation: Derivative term reacts to rapid changes, increasing noise sensitivity.

44. In state-space model, output equation is:

a) $x' = Ax + Bu$
b) $y = Cx + Du$
c) $y = Ax + Bu$
d) $x = Ay + Bu$
Answer: b) $y = Cx + Du$
Explanation: Output depends on states and input directly.

45. The canonical form used to represent a system from its transfer function is:

a) Controllable canonical form
b) Observable canonical form
c) Both a and b
d) None
Answer: c) Both a and b
Explanation: Systems can be represented equivalently in controllable or observable forms.

46. In the root locus, complex conjugate poles always move:

a) On imaginary axis
b) Symmetrically about real axis
c) Asymmetrically
d) Only left half
Answer: b) Symmetrically about real axis
Explanation: Conjugate poles mirror about the real axis because coefficients are real.

47. A phase lag network has transfer function $\frac{1 + sT_2}{1 + sT_1}$ , where $T_1 > T_2$ . Its effect is:

a) Phase lead
b) Phase lag
c) No phase change
d) Unstable
Answer: b) Phase lag
Explanation: Since $T_1 > T_2$ , it produces phase lag (negative phase).

48. The open-loop transfer function has one pole at origin. The steady-state error for step input will be:

a) Zero
b) Finite
c) Infinite
d) Depends on gain
Answer: a) Zero
Explanation: One integrator (pole at origin) eliminates step error → Type 1 system.

49. The frequency at which the magnitude plot crosses 0 dB is:

a) Gain crossover frequency
b) Phase crossover frequency
c) Natural frequency
d) Resonant frequency
Answer: a) Gain crossover frequency
Explanation: Gain crossover frequency is where |G(jω)| = 1 (0 dB).

50. In Bode plot, slope of -20 dB/decade corresponds to:

a) One pole
b) One zero
c) Two poles
d) Two zeros
Answer: a) One pole
Explanation: Each pole adds -20 dB/decade slope.

51. The transient response mainly depends on:

a) Zeros
b) Poles
c) Gain
d) Feedback
Answer: b) Poles
Explanation: Pole locations dominate transient behavior (rise, settling, oscillation).

52. A system having characteristic equation $s^3 + 5s^2 + 6s + K = 0$ is stable for:

a) K > 30
b) K < 30
c) K = 0
d) K = ∞
Answer: b) K < 30
Explanation: Using Routh criterion, system remains stable until K = 30.

53. The Nyquist plot of a stable open-loop system does not encircle (-1,0). The closed-loop system is:

a) Stable
b) Unstable
c) Marginally stable
d) Oscillatory
Answer: a) Stable
Explanation: No encirclement → no right-half closed-loop poles → stable.

54. In frequency response, the resonant peak $M_r$ occurs when:

a) Denominator magnitude is minimum
b) Phase is zero
c) ω = ω_n
d) Damping ratio is high
Answer: a) Denominator magnitude is minimum
Explanation: Resonance occurs when denominator’s magnitude is minimum, maximizing |T(jω)|.

55. A Type 0 system can follow which input with zero steady-state error?

a) Step
b) Ramp
c) Parabolic
d) None
Answer: d) None
Explanation: Type 0 has finite error even for step input.

56. A unity feedback system has open-loop transfer function $G(s) = \frac{K(s+2)}{s(s+1)}$ . The system type is:

a) Type 0
b) Type 1
c) Type 2
d) None
Answer: b) Type 1
Explanation: One factor of s → one integrator → Type 1.

57. Root locus branches always terminate at:

a) Poles
b) Zeros or infinity
c) Imaginary axis
d) None
Answer: b) Zeros or infinity
Explanation: Branches start from poles and end at zeros (or infinity if fewer zeros).

58. The number of separate root loci equals:

a) Number of poles
b) Number of zeros
c) Difference of poles and zeros
d) Number of poles (since each branch starts from a pole)
Answer: d) Number of poles
Explanation: Each pole initiates one branch of the root locus.

ELECTRICAL AND ELECTRONICS ENGINEERING

Pages

Monday, November 3, 2025

Root locus branches always terminate at

31. The addition of a pole to a system generally:

32. The damping ratio (ζ) of a second-order system determines:

33. The breakaway point in a root locus lies:

34. A lag compensator improves:

35. The steady-state error for a ramp input is zero for:

36. The transfer function of a first-order system is $G(s) = \frac{K}{1 + sT}$ . The time constant $T$ equals:

37. The condition for sustained oscillation is given by:

38. Gain margin (GM) is defined at:

39. Phase margin (PM) is defined at:

40. The settling time of a second-order system is approximately:

41. A stable system must have all poles:

42. The transfer function of a PID controller is:

43. The main drawback of derivative control is:

44. In state-space model, output equation is:

45. The canonical form used to represent a system from its transfer function is:

46. In the root locus, complex conjugate poles always move:

47. A phase lag network has transfer function $\frac{1 + sT_2}{1 + sT_1}$ , where $T_1 > T_2$ . Its effect is:

48. The open-loop transfer function has one pole at origin. The steady-state error for step input will be:

49. The frequency at which the magnitude plot crosses 0 dB is:

50. In Bode plot, slope of -20 dB/decade corresponds to:

51. The transient response mainly depends on:

52. A system having characteristic equation $s^3 + 5s^2 + 6s + K = 0$ is stable for:

53. The Nyquist plot of a stable open-loop system does not encircle (-1,0). The closed-loop system is:

54. In frequency response, the resonant peak $M_r$ occurs when:

55. A Type 0 system can follow which input with zero steady-state error?

56. A unity feedback system has open-loop transfer function $G(s) = \frac{K(s+2)}{s(s+1)}$ . The system type is:

57. Root locus branches always terminate at:

58. The number of separate root loci equals:

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Pages

Monday, November 3, 2025

Root locus branches always terminate at

31. The addition of a pole to a system generally:

32. The damping ratio (ζ) of a second-order system determines:

33. The breakaway point in a root locus lies:

34. A lag compensator improves:

35. The steady-state error for a ramp input is zero for:

36. The transfer function of a first-order system is G(s)=K1+sTG(s) = \frac{K}{1 + sT}G(s)=1+sTK​. The time constant TTT equals:

37. The condition for sustained oscillation is given by:

38. Gain margin (GM) is defined at:

39. Phase margin (PM) is defined at:

40. The settling time of a second-order system is approximately:

41. A stable system must have all poles:

42. The transfer function of a PID controller is:

43. The main drawback of derivative control is:

44. In state-space model, output equation is:

45. The canonical form used to represent a system from its transfer function is:

46. In the root locus, complex conjugate poles always move:

47. A phase lag network has transfer function 1+sT21+sT1\frac{1 + sT_2}{1 + sT_1}1+sT1​1+sT2​​, where T1>T2T_1 > T_2T1​>T2​. Its effect is:

48. The open-loop transfer function has one pole at origin. The steady-state error for step input will be:

49. The frequency at which the magnitude plot crosses 0 dB is:

50. In Bode plot, slope of -20 dB/decade corresponds to:

51. The transient response mainly depends on:

52. A system having characteristic equation s3+5s2+6s+K=0s^3 + 5s^2 + 6s + K = 0s3+5s2+6s+K=0 is stable for:

53. The Nyquist plot of a stable open-loop system does not encircle (-1,0). The closed-loop system is:

54. In frequency response, the resonant peak MrM_rMr​ occurs when:

55. A Type 0 system can follow which input with zero steady-state error?

56. A unity feedback system has open-loop transfer function G(s)=K(s+2)s(s+1)G(s) = \frac{K(s+2)}{s(s+1)}G(s)=s(s+1)K(s+2)​. The system type is:

57. Root locus branches always terminate at:

58. The number of separate root loci equals:

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36. The transfer function of a first-order system is $G(s) = \frac{K}{1 + sT}$ . The time constant $T$ equals:

47. A phase lag network has transfer function $\frac{1 + sT_2}{1 + sT_1}$ , where $T_1 > T_2$ . Its effect is:

52. A system having characteristic equation $s^3 + 5s^2 + 6s + K = 0$ is stable for:

54. In frequency response, the resonant peak $M_r$ occurs when:

56. A unity feedback system has open-loop transfer function $G(s) = \frac{K(s+2)}{s(s+1)}$ . The system type is: