What is the primary function of a feedback control system?
Answer: A
Feedback control systems work by comparing the desired output with actual output and reducing the error between them through corrective action.
Q.2Easy
The transfer function of a system is defined as the ratio of:
Answer: B
Transfer function G(s) = Y(s)/U(s) is the ratio of Laplace transforms of output to input assuming zero initial conditions.
Q.3Easy
Which of the following represents a first-order system?
Answer: B
A first-order system has only s¹ as the highest power in the denominator. G(s) = K/(τs + 1) is the standard first-order form.
Q.4Medium
What is the steady-state error for a unit step input to a Type 0 system?
Answer: C
For Type 0 system with unit step input, e_ss = 1/(1 + Kp) where Kp is the position error constant.
Q.5Easy
The characteristic equation of a system is s² + 4s + 3 = 0. The system is:
Answer: C
Roots are s = -1 and s = -3 (both negative). All poles are in the left half-plane, making the system stable.
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Q.6Medium
What does the Routh-Hurwitz criterion determine?
Answer: B
Routh-Hurwitz criterion is used to determine the stability of a system by examining the characteristic equation coefficients without calculating poles.
Q.7Easy
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.8Medium
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.9Medium
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.10Medium
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.
Q.11Medium
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.12Medium
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.13Easy
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.14Medium
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.15Medium
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.16Easy
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.17Hard
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.18Hard
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.19Hard
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.20Hard
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.
