In a Bode plot, the magnitude plot slope in dB/decade for a pole at origin is:
Answer: A
Each pole contributes -20 dB/decade slope. A single pole at origin contributes -20 dB/decade.
Q.22Easy
A second-order system has damping ratio ζ = 0.5. This system is classified as:
Answer: B
For ζ < 1, the system is underdamped with oscillatory response. ζ = 0.5 falls in this category.
Q.23Easy
Which of the following is a characteristic of a lag compensator?
Answer: B
Lag compensator reduces steady-state error by increasing the DC gain without significantly affecting transient response or stability margins.
Q.24Easy
For a Type 2 system with step input, the steady-state error is:
Answer: A
Type 2 systems have zero steady-state error for step input (constant reference), as they have at least 2 poles at origin.
Q.25Easy
The transfer function of a proportional-integral (PI) controller is:
Answer: C
PI controller: Gc(s) = Kp(1 + 1/(Tis)) = Kp + Ki/s, where Ki = Kp/Ti eliminates steady-state error for constant inputs.
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Q.26Easy
A negative feedback control system has an open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)]. What is the type of the system?
Answer: B
The system has one pole at origin (s term in denominator), making it a Type 1 system. Type is determined by the number of poles at origin.
Q.27Easy
In Bode plot analysis, what does the gain margin represent?
Answer: B
Gain margin is the reciprocal of the magnitude at the frequency where phase is -180°. It indicates stability margin in dB.
Q.28Easy
The transfer function of an ideal derivative controller is:
Answer: A
A derivative controller has transfer function Gc(s) = Kd·s, where Kd is the derivative gain. It provides leading phase.
Q.29Easy
For a system G(s) = K(s+2)/[s(s+1)(s+3)], the number of asymptotes in root locus is:
Answer: B
Number of asymptotes = |poles - zeros| = |3 - 1| = 2. Three poles, one zero gives 2 asymptotes.
Q.30Easy
In digital control systems, the sampling theorem requires sampling frequency to be:
Answer: A
Nyquist sampling theorem: fs > 2·fmax to avoid aliasing. The sampling frequency must be at least twice the highest frequency component.
Q.31Easy
A second-order system has natural frequency ωn = 10 rad/s and damping ratio ζ = 0.5. The peak overshoot percentage is approximately:
Answer: A
Using the formula for peak overshoot: Mp = exp(-ζπ/√(1-ζ²)) × 100 = exp(-0.5π/√0.75) × 100 ≈ 16.3%. This is independent of ωn.
Q.32Easy
A PID controller Gc(s) = Kp + Ki/s + Kd·s is applied to a process. Which parameter adjustment would primarily reduce steady-state error without affecting transient response significantly?
Answer: B
The integral term (Ki) directly addresses steady-state error by accumulating past errors. Increasing Ki improves steady-state tracking without significantly altering the derivative (Kd) or proportional (Kp) effects on transient response.
