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.2Hard
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.3Hard
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.4Hard
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.5Hard
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.
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Q.6Hard
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.7Hard
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.8Hard
For a system to be controllable using state feedback u = -Kx, which condition must be satisfied?
Answer: C
Controllability requires the controllability matrix to have full rank n. This ensures all states can be moved from origin to any desired state
Q.9Hard
For improving transient response with minimal steady-state error impact, a lead compensator should be designed to add phase lead at:
Answer: B
Lead compensator adds phase lead at its designed center frequency ωm. For transient improvement, it should coincide with gain crossover frequency to increase phase margin
Q.10Hard
For the characteristic equation s⁴ + 8s³ + 24s² + 32s + 15 = 0, using Routh-Hurwitz criterion, the system is:
Answer: D
Routh table construction shows all positive elements in first column, indicating all poles in left half plane, making the system stable.
Q.11Hard
In a root locus plot, the asymptotes for a system with 5 poles and 2 zeros meet at a point called:
Answer: B
Centroid (center of asymptotes) = [Σpoles - Σzeros]/[number of poles - number of zeros]. Number of asymptotes = 5-2 = 3.
Q.12Hard
For a system with Gc(s)G(s)H(s) = 100/[s(s+5)], the phase at ω = 5 rad/s is approximately:
The sensitivity function S(s) in a feedback control system is defined as:
Answer: B
Sensitivity S(s) = ∂Y/∂G ÷ Y/G = 1/[1+G(s)H(s)] for unity feedback systems. It measures effect of parameter variations.
Q.14Hard
In a Type-2 system with step, ramp, and parabolic inputs, the steady-state error with parabolic input A·t²/2 and loop gain Kv = 5 is:
Answer: C
For a Type-2 system, parabolic error is ess = A/Ka where Ka = lim[s→0] s²G(s)H(s). Since Kv relates to ramp response, the parabolic steady-state error depends on Ka (acceleration constant).
