BEE Control Systems Theory 5

Question 1

The controllability matrix for a system with matrices A and B is formed as [B, AB, A²B, ...]. A system is controllable if this matrix has:

Accepted Answer

Rank equal to the order n of the system

Answer

A system is controllable (Kalman's criterion) if and only if the controllability matrix [B AB A²B ... Aⁿ⁻¹B] has full rank n.

Question 2

In a discrete-time control system with sampling period T, the z-transform variable z and the Laplace variable s are related by:

Accepted Answer

z = e^(sT)

Answer

The mapping between continuous and discrete domains is z = e^(sT), which maps the left-half s-plane to the interior of the unit circle in the z-plane.

Question 3

A system exhibiting limit cycle behavior is best classified as:

Accepted Answer

Nonlinear, with a sustained oscillation at a fixed amplitude and frequency

Answer

Limit cycles are self-sustained oscillations characteristic of nonlinear systems, with fixed amplitude and frequency independent of initial conditions within a region.

Question 4

Which of the following actions does a lead compensator primarily perform on the Bode plot?

Accepted Answer

Adds phase lead near the crossover frequency to improve phase margin

Answer

A lead compensator contributes positive phase (phase lead) near the crossover frequency, improving phase margin and transient response speed.

Question 5

For an underdamped second-order system, the percent overshoot depends only on:

Accepted Answer

The damping ratio ζ

Answer

Percent overshoot = exp(−πζ/√(1−ζ²)) × 100%, which depends solely on the damping ratio ζ.

BEE - Bachelor of Electrical Engineering Practice Test

BEE - Bachelor of Electrical Engineering Practice Test

BEE Control Systems Theory 5