BEE Control System Principles 4

Question 1

In a feedback control system, what is the effect of increasing proportional gain Kp on steady-state error for a step input in a Type 0 system?

Accepted Answer

Decreases but does not eliminate steady-state error

Answer

For a Type 0 system, steady-state error = 1/(1+Kp), so increasing Kp reduces error but it approaches zero only as Kp → ∞.

Question 2

Which condition must be satisfied for a system to be both controllable and observable?

Accepted Answer

The controllability matrix and observability matrix must both have full rank

Answer

Controllability requires rank(C) = n and observability requires rank(O) = n, where n is the system order.

Question 3

If a system's Bode phase plot crosses -180° at 10 rad/s and the magnitude at that frequency is -10 dB, what is the gain margin?

Accepted Answer

10 dB

Answer

Gain margin is the negative of the magnitude at the phase crossover frequency: GM = 0 - (-10 dB) = +10 dB.

Question 4

In discrete-time control systems, what is the z-transform equivalent of an integrator (1/s)?

Accepted Answer

z/(z-1)

Answer

The bilinear or exact z-domain equivalent of 1/s using the forward Euler method maps to z/(z-1), while Tustin's method gives (z+1)T/[2(z-1)].

Question 5

What is the percent overshoot for a second-order system with damping ratio ζ = 0.5?

Accepted Answer

16.3%

Answer

Percent overshoot = exp(-πζ/√(1-ζ²)) × 100 = exp(-π×0.5/√0.75) × 100 ≈ 16.3%.

BEE - Bachelor of Electrical Engineering Practice Test