BEE Signals and Control Systems 4

Question 1

The state-space representation ẋ = Ax + Bu, y = Cx + Du describes a system. The eigenvalues of matrix A correspond to:

Accepted Answer

The poles of the transfer function

Answer

The eigenvalues of the system matrix A are identical to the poles of the transfer function, determining the system's natural modes and stability.

Question 2

Which of the following correctly describes the difference between discrete Fourier Transform (DFT) and the continuous Fourier Transform (CFT)?

Accepted Answer

DFT operates on a finite number of samples and produces a periodic discrete spectrum

Answer

The DFT takes N discrete-time samples and outputs N discrete frequency samples, effectively treating the signal as periodic with period N.

Question 3

A closed-loop control system is said to be type 1 if its open-loop transfer function has:

Accepted Answer

One pole at the origin

Answer

The system type equals the number of open-loop poles at the origin (s = 0); a type 1 system has exactly one integrator in the open-loop path.

Question 4

The steady-state error for a type 1 system subjected to a ramp input (r(t) = t·u(t)) is:

Accepted Answer

1/Kv (a finite constant)

Answer

A type 1 system tracks a ramp with a finite steady-state error equal to 1/Kv, where Kv is the velocity error constant.

Question 5

The unilateral Laplace transform is preferred over the bilateral transform for analyzing systems with initial conditions because:

Accepted Answer

It automatically incorporates initial conditions into the transform

Answer

The unilateral Laplace transform, starting the integral at t = 0⁻, naturally incorporates initial conditions through derivative transform properties.

BEE - Bachelor of Electrical Engineering Practice Test