FREE BEE Bachelor of Electrical Engineering Signals and Control Systems Questions and Answers

Question 1

The characteristic equation of a closed-loop control system is given by s³ + 6s² + 11s + K = 0. For the system to be stable, which of the following conditions must be met for the gain K?

Accepted Answer

0 < K < 66

Answer

According to the Routh-Hurwitz stability criterion, for a third-order system with characteristic equation as³ + bs² + cs + d = 0, all coefficients must be positive, and the condition bc > ad must be satisfied for stability. In this case, a=1, b=6, c=11, and d=K. The conditions are K > 0 and (6)(11) > (1)(K), which simplifies to 66 > K. Combining these, the condition for stability is 0 < K < 66.

Question 2

An engineer is analyzing a system's frequency response using a Bode magnitude plot. In a specific frequency range, the plot shows a consistent downward slope of -40 dB/decade. What does this slope most likely indicate about the system's transfer function in that range?

Accepted Answer

Two poles or a double pole

Answer

In a Bode magnitude plot, each pole in the transfer function contributes a slope of -20 dB/decade after its corner frequency. A slope of -40 dB/decade indicates the combined effect of two poles, which could be two distinct poles whose corner frequencies have been passed, or a double pole at the same frequency.

Question 3

A control systems engineer observes that a process under proportional-integral (PI) control exhibits a persistent steady-state error after a step change in the setpoint. Which of the following is the most likely cause?

Accepted Answer

The integral time (Ti) is too large, resulting in weak integral action.

Answer

The primary role of the integral (I) term in a PID controller is to eliminate steady-state error by accumulating the error over time. A very large integral time (Ti) corresponds to a very small integral gain (Ki = 1/Ti), making the integral action too weak to effectively eliminate the offset. Integral windup typically occurs from large, prolonged errors causing saturation, not a persistent small error. Proportional gain affects the speed and stability but doesn't guarantee zero steady-state error on its own. Derivative action is not primarily used for steady-state error.

Question 4

In the context of a system's transfer function in the s-plane, what is the primary significance of a pole's location?

Accepted Answer

It dictates the system's stability and transient response characteristics.

Answer

The location of the poles (roots of the denominator of the transfer function) in the complex s-plane is fundamental to the system's behavior. Poles in the left-half plane result in a stable system where the transient response decays over time. Poles in the right-half plane cause an unstable response that grows without bound. Poles on the imaginary axis lead to marginal stability or sustained oscillations.

Question 5

A continuous-time signal is band-limited to a maximum frequency of 4 kHz. According to the Nyquist-Shannon sampling theorem, what is the minimum sampling rate required to avoid aliasing and allow for perfect reconstruction of the signal?

Accepted Answer

8 kHz

Answer

The Nyquist-Shannon sampling theorem states that to perfectly reconstruct a continuous-time signal from its samples, the sampling frequency (fs) must be at least twice the maximum frequency (f_max) present in the signal. This minimum rate is known as the Nyquist rate. Here, f_max = 4 kHz, so the minimum sampling rate is 2 * 4 kHz = 8 kHz.

BEE - Bachelor of Electrical Engineering Practice Test

BEE - Bachelor of Electrical Engineering Practice Test

FREE BEE Bachelor of Electrical Engineering Signals and Control Systems Questions and Answers