BEE Signals and Control Systems 4 β Questions and Answers
Question 1: The state-space representation αΊ = Ax + Bu, y = Cx + Du describes a system. The eigenvalues of matrix A correspond to:
- The zeros of the transfer function
- The poles of the transfer function (Correct answer)
- The DC gain of the system
- The controllability matrix rank
Correct answer: The poles of the transfer function
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)?
- DFT operates on continuous signals; CFT operates on discrete samples
- DFT produces a continuous spectrum; CFT produces a discrete spectrum
- DFT operates on a finite number of samples and produces a periodic discrete spectrum (Correct answer)
- DFT and CFT are identical for periodic signals
Correct answer: DFT operates on a finite number of samples and produces a periodic discrete spectrum
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:
- No poles at the origin
- One pole at the origin (Correct answer)
- One zero at the origin
- Two poles at the origin
Correct answer: One pole at the origin
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) = tΒ·u(t)) is:
- Zero
- 1/Kv (a finite constant) (Correct answer)
- Infinite
- 1/Kp
Correct answer: 1/Kv (a finite constant)
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:
- It converges for more signal types
- It automatically incorporates initial conditions into the transform (Correct answer)
- It is easier to compute numerically
- It gives real-valued results always
Correct answer: It automatically incorporates initial conditions into the transform
The unilateral Laplace transform, starting the integral at t = 0β», naturally incorporates initial conditions through derivative transform properties.
Question 6: In the Nyquist stability criterion, the number of closed-loop unstable poles Z is given by:
- Z = N + P (Correct answer)
- Z = N β P
- Z = P β N
- Z = N Γ P
Correct answer: Z = N + P
The Nyquist criterion relates Z (unstable closed-loop poles) to N (clockwise encirclements of β1) and P (unstable open-loop poles) by Z = N + P.
Question 7: Which type of signal has a Fourier series representation with discrete spectral components?
- Aperiodic energy signal
- Periodic power signal (Correct answer)
- White noise
- Impulse signal
Correct answer: Periodic power signal
Periodic signals are represented by Fourier series with energy concentrated at discrete harmonically related frequencies.
BEE Signals and Control Systems 4
The state-space representation αΊ = Ax + Bu, y = Cx + Du describes a system.
The eigenvalues of matrix A correspond to: