BEE BEE Bachelor of Electrical Engineering Control Systems Theory Questions and Answers 2

Question 1

What is the primary purpose of a lead compensator in a control system?

Accepted Answer

Increase phase margin and improve transient response

Answer

A lead compensator adds positive phase shift near the crossover frequency, increasing phase margin and improving transient response speed.

Question 2

In a Nyquist plot, what does an encirclement of the point (-1, 0) indicate?

Accepted Answer

The closed-loop system may be unstable

Answer

Encirclements of the (-1, 0) point relate to closed-loop poles in the right-half plane via the Nyquist stability criterion.

Question 3

Which matrix equation represents the state-space model of a linear time-invariant system?

Accepted Answer

ẋ = Ax + Bu, y = Cx + Du

Answer

The standard LTI state-space representation uses the linear equations ẋ = Ax + Bu for state dynamics and y = Cx + Du for output.

Question 4

What does a system's gain margin represent?

Accepted Answer

The factor by which gain can increase before the system becomes unstable

Answer

Gain margin is the reciprocal of the open-loop gain magnitude at the phase crossover frequency, indicating how much gain increase causes instability.

Question 5

A second-order underdamped system has a damping ratio of 0.5. What is the approximate percent overshoot of its step response?

Accepted Answer

16.3%

Answer

Percent overshoot is calculated as e^(-πζ/√(1-ζ²)) × 100, which gives approximately 16.3% for ζ = 0.5.

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