For a control system, the gain crossover frequency and phase crossover frequency are equal. What does this indicate about the system's stability margin?
Answer: C
When gain crossover frequency equals phase crossover frequency, the system is at the stability boundary (phase = -180°), indicating marginal stability.
Q.322Medium
A lead compensator has a transfer function Gc(s) = K(s+2)/(s+8). What is the effect of this compensator?
Answer: B
Lead compensator has zero at -2 and pole at -8 (pole further left). This increases bandwidth and adds phase lead, improving transient response.
Q.323Medium
For a system with transfer function G(s)H(s) = 10/(s²(s+2)), the number of asymptotes in the root locus is:
Answer: B
Number of asymptotes = |number of poles - number of zeros| = |3 - 0| = 3. However, for this specific configuration with two poles at origin, effective asymptotes for root locus are 2.
Q.324Medium
Which statement is correct regarding the Bode plot of a system?
Answer: B
For minimum phase systems, magnitude and phase are related through the Kramers-Kronig relations. Knowledge of magnitude plot uniquely determines phase plot.
Q.325Medium
A PID controller is used for a plant. If only the derivative gain Kd is increased while keeping Kp and Ki constant, what is the primary effect?
Answer: B
The derivative term acts as damping in the system. Increasing Kd increases damping, which reduces overshoot and oscillations without affecting steady-state error significantly.
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Q.326Easy
For the open-loop transfer function G(s)H(s) = K(s+1)/((s+2)(s+3)(s+4)), the system order is:
Answer: B
System order is determined by the highest power of 's' in the characteristic equation denominator. Here, it's (s+2)(s+3)(s+4) = s³+..., so order is 3.
Q.327Medium
In frequency response analysis, what does the gain margin represent?
Answer: B
Gain margin is the factor by which the system gain at phase crossover frequency can be increased before the system becomes unstable (phase reaching -180° at unity gain).
Q.328Medium
A lag compensator has the form Gc(s) = K(s+0.1)/(s+0.01). Which characteristic does it primarily improve?
Answer: B
Lag compensator (zero at -0.1, pole at -0.01, with pole closer to origin) adds gain at low frequencies without significantly affecting phase at crossover, improving steady-state accuracy.
Q.329Hard
For a second-order system with natural frequency ωn = 5 rad/s and ζ = 0.7, the peak time tp is approximately:
Answer: B
tp = π/(ωn√(1-ζ²)) = π/(5√(1-0.49)) = π/(5×0.714) ≈ 0.88 seconds ≈ 0.89 seconds. Closest answer is B.
Q.330Medium
The characteristic equation of a closed-loop system is s³ + 6s² + 11s + 6 = 0. What are the poles?
Answer: A
The polynomial factors as (s+1)(s+2)(s+3) = 0, giving poles at -1, -2, and -3. All poles are in the left half-plane, making the system stable.
Q.331Easy
In a state-space representation, if the system has 4 state variables, what is the dimension of the state vector?
Answer: C
The state vector x(t) contains all state variables. With 4 state variables, it's a 4×1 column vector, so the dimension is 4.
Q.332Hard
A negative feedback system's loop gain L(s) = G(s)H(s) has a pole-zero excess of 2. What can be concluded?
Answer: B
Pole-zero excess affects the phase behavior at high frequencies. A system with excess of 2 can be either stable or unstable depending on the gain value and pole locations.
Q.333Medium
For a unity feedback system, if the open-loop DC gain is 100, what is the closed-loop DC gain?
Answer: C
Closed-loop gain = G(s)/(1+G(s)). At DC, this becomes 100/(1+100) = 101100 ≈ 0.99, showing the effect of feedback on reducing overall gain.
Q.334Medium
In the Routh-Hurwitz stability criterion, if the first column has a sign change, what does it indicate?
Answer: C
The number of sign changes in the first column of the Routh array equals the number of poles in the right half-plane. A sign change indicates at least one pole in RHP, making the system unstable.
Q.335Hard
A feedback system's sensitivity function S(s) = 1/(1+L(s)) where L(s) is loop gain. For large |L(s)|, what happens to |S(s)|?
Answer: B
When |L(s)| >> 1, the sensitivity function |S(s)| ≈ 1/|L(s)| becomes very small. This shows that high loop gain reduces sensitivity to parameter variations.
Q.336Medium
A unity feedback control system has an open-loop transfer function G(s) = 10/(s(s+2)). What is the steady-state error for a unit ramp input?
In a Bode plot, what is the phase margin when the gain crossover frequency equals the phase crossover frequency?
Answer: A
At the gain crossover frequency, magnitude is 0 dB. When this equals phase crossover frequency, the phase is -180°, giving phase margin = -180° - (-180°) = 0°
Q.338Easy
Which of the following transfer functions represents a Type-2 system?
Answer: A
Type of system is determined by the number of poles at origin. Option A has s² in denominator, making it Type-2
Q.339Medium
For a second-order system with ζ = 0.5 and ωn = 4 rad/s, what is the peak overshoot?
