BEE BEE Bachelor of Electrical Engineering Control Systems Theory Questions and Answers 2 — Questions and Answers
Question 1: What is the primary purpose of a lead compensator in a control system?
- Increase phase margin and improve transient response (Correct answer)
- Reduce steady-state error only
- Eliminate all overshoot
- Decrease the system bandwidth
Correct 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.
Question 2: In a Nyquist plot, what does an encirclement of the point (-1, 0) indicate?
- The closed-loop system may be unstable (Correct answer)
- The system has zero steady-state error
- The gain margin is infinite
- The system is always overdamped
Correct 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.
Question 3: Which matrix equation represents the state-space model of a linear time-invariant system?
- ẋ = Ax + Bu, y = Cx + Du (Correct answer)
- ẋ = Ax² + Bu, y = Cx + Du
- ẋ = A + Bx, y = C + Dx
- ẋ = ABx + u, y = CDx + u
Correct 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.
Question 4: What does a system's gain margin represent?
- The factor by which gain can increase before the system becomes unstable (Correct answer)
- The maximum output amplitude at resonance
- The DC gain of the closed-loop transfer function
- The ratio of output to input at the natural frequency
Correct 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.
Question 5: A second-order underdamped system has a damping ratio of 0.5. What is the approximate percent overshoot of its step response?
- 16.3% (Correct answer)
- 5.0%
- 25.4%
- 0%
Correct answer: 16.3%
Percent overshoot is calculated as e^(-πζ/√(1-ζ²)) × 100, which gives approximately 16.3% for ζ = 0.5.
Question 6: What is the transfer function of a PID controller?
- Kp + Ki/s + Kd·s (Correct answer)
- Kp · Ki · Kd · s
- Kp / (1 + Ki·s + Kd·s²)
- Ki·s + Kd/s + Kp·s²
Correct 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.
BEE BEE Bachelor of Electrical Engineering Control Systems Theory Questions and Answers 2
What is the primary purpose of a lead compensator in a control system?