Routh-Hurwitz criterion is used to determine the stability of a system by examining the characteristic equation coefficients without calculating poles.
Q.302Easy
In a bode plot, the magnitude is plotted on a scale of:
Answer: B
Bode plots use dB (20log₁₀|G(jω)|) for magnitude on a logarithmic scale and phase in degrees on a semi-log plot.
Q.303Medium
The gain margin of a system can be determined from the bode plot as:
Answer: C
Gain margin = 1/|G(jω)| at phase crossover frequency where phase = -180°. It indicates how much gain can be increased before instability.
Q.304Medium
For a second-order system with natural frequency ωn = 2 rad/s and damping ratio ζ = 0.5, the system is:
Answer: B
When ζ < 1 (0.5 < 1), the system is underdamped with oscillatory transient response.
Q.305Medium
The rise time of a second-order underdamped system decreases with:
Answer: A
Rise time tr ≈ (π - cos⁻¹(ζ))/(ωn√(1-ζ²)). It decreases with higher ωn and appropriate ζ value.
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Q.306Medium
Which compensation technique is used to improve steady-state accuracy?
Answer: B
Lag compensation increases the system type or gain at low frequencies, improving steady-state accuracy without affecting stability significantly.
Q.307Medium
The Nyquist plot is a mapping of:
Answer: B
Nyquist plot maps the frequency response G(jω)H(jω) in the complex plane by varying ω from 0 to ∞.
Q.308Easy
For a system G(s) = 1/(s(s+2)), the number of poles at origin is:
Answer: B
The system has one pole at s=0, making it Type 1. The denominator has s¹ factor representing one integration.
Q.309Medium
The overshoot of a second-order system is independent of:
Answer: C
Overshoot = e^(-πζ/√(1-ζ²)) depends only on damping ratio ζ, not on ωn or system gain K.
Q.310Medium
Which of the following is a state-space representation advantage over transfer function?
Answer: B
State-space representation naturally handles MIMO systems, non-linear systems, and time-varying systems better than transfer functions.
Q.311Easy
The settling time of a control system is defined as the time taken to:
Answer: C
Settling time is the time required for the transient to decay and response to remain within 2% (or 5%) of the steady-state value.
Q.312Hard
For a system with open-loop transfer function G(s)H(s) = K/[s(s+1)(s+2)], the number of asymptotes in root locus is:
Answer: B
Number of asymptotes = n - m = 3 - 1 = 2, where n=3 (poles) and m=1 (zeros).
Q.313Hard
A proportional-integral (PI) controller transfer function is Gc(s) = Kp + Ki/s. Its effect is:
Answer: B
PI controller adds a pole at origin (integral term), increasing system type by 1 and eliminating steady-state error for step and ramp inputs.
Q.314Hard
The centroid of asymptotes in root locus is located at:
Answer: A
Centroid σ = (∑poles - ∑zeros)/(n-m), where n and m are number of poles and zeros respectively.
Q.315Hard
In phase-lead compensation, the zero is placed:
Answer: A
In lead compensation, zero is placed to the left of pole (closer to origin), providing phase lead to improve transient response and stability margin.
Q.316Medium
In a closed-loop control system, the feedback path gain is reduced from 1 to 0.5. How does this affect the system's steady-state error?
Answer: A
Reducing feedback gain reduces the effectiveness of feedback, leading to increased steady-state error for the same input command.
Q.317Easy
Which of the following is NOT a characteristic of a proportional (P) controller?
Answer: B
A proportional controller cannot eliminate steady-state error completely for step inputs in type-0 systems. An integral term is needed for zero steady-state error.
Q.318Easy
For a unity feedback system with G(s) = K/(s(s+3)(s+5)), what is the system type?
Answer: B
The system type equals the number of poles at origin. Here, there is one pole at origin (s in denominator), making it Type 1.
Q.319Easy
A second-order system has damping ratio ζ = 0.5. What is the nature of its response?
Answer: B
For ζ < 1, the system is underdamped and exhibits oscillatory response. At ζ = 0.5, there are definitely oscillations with exponential decay.
Q.320Easy
In root locus analysis, as the gain K increases from 0 to ∞, the closed-loop poles move along specific paths. Where do these paths originate?
Answer: B
The root locus starts at open-loop poles (K=0) and ends at open-loop zeros (K=∞). This is a fundamental property of root locus construction.
