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.22Easy
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.23Easy
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.24Easy
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.25Easy
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.
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Q.26Medium
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.27Medium
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.28Medium
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.29Medium
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.30Medium
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.
Q.31Easy
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.32Medium
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.33Medium
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.34Hard
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.35Medium
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.36Easy
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.37Hard
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.38Medium
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.39Medium
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.40Hard
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.
