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

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

Answer: Increase phase margin and improve transient response

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

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

Answer: The closed-loop system may be unstable

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

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

Answer: ẋ = Ax + Bu, y = Cx + Du

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

What does a system's gain margin represent?

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

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

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

Answer: 16.3%

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

What is the transfer function of a PID controller?

Answer: Kp + Ki/s + Kd·s

A PID controller combines proportional (Kp), integral (Ki/s), and derivative (Kd·s) actions in parallel, giving Kp + Ki/s + Kd·s.