Electrical Engg (EEE) - MCQ Practice Questions

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.

The system type equals the number of poles at origin. Here, there is one pole at origin (s in denominator), making it Type 1.

For ζ < 1, the system is underdamped and exhibits oscillatory response. At ζ = 0.5, there are definitely oscillations with exponential decay.

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.

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.

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.

Type of system is determined by the number of poles at origin. Option A has s² in denominator, making it Type-2

Number of root locus branches = max(number of poles, number of zeros) = max(3, 1) = 3

For first-order system, bandwidth ωBW = 1/τ = $\frac{1}{0}$.1 = 10 rad/s (where -3dB occurs)

For Type-1 system, Kv = lim s→0 s·G(s) = 20/(5·10) = $\frac{20}{50}$ = 0.4

Corner frequency = pole frequency. Rewriting: H(s) = 10/(s+10), so pole at -10, corner frequency = 10 rad/s

Factoring: (s+1)(s+2)(s+3) = 0 gives poles at s = -1, -2, -3. All in LHP, so system is stable

The type of a system is determined by the number of poles at origin. Here, there is one pole at origin (s term), making it Type 1.

Each pole contributes -20 dB/decade slope. A single pole at origin contributes -20 dB/decade.

For ζ < 1, the system is underdamped with oscillatory response. ζ = 0.5 falls in this category.

Lag compensator reduces steady-state error by increasing the DC gain without significantly affecting transient response or stability margins.

Type 2 systems have zero steady-state error for step input (constant reference), as they have at least 2 poles at origin.

PI controller: Gc(s) = Kp(1 + 1/(Tis)) = Kp + Ki/s, where Ki = Kp/Ti eliminates steady-state error for constant inputs.

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.

Gain margin is the reciprocal of the magnitude at the frequency where phase is -180°. It indicates stability margin in dB.