BEE Control System Principles 3 โ Questions and Answers
Question 1: The Nyquist stability criterion states that the number of unstable closed-loop poles equals:
- The number of encirclements of -1+j0 minus open-loop RHP poles (Correct answer)
- The number of open-loop zeros in the RHP
- The number of clockwise encirclements of the origin
- The number of gain crossover frequencies
Correct answer: The number of encirclements of -1+j0 minus open-loop RHP poles
N = Z - P, where N is net clockwise encirclements of -1, P is open-loop RHP poles, and Z is closed-loop RHP poles; solving for Z gives stability information.
Question 2: Which of the following describes a marginally stable system?
- All poles in the left-half plane
- Poles on the imaginary axis with no repeated poles there (Correct answer)
- At least one pole in the right-half plane
- All poles at the origin
Correct answer: Poles on the imaginary axis with no repeated poles there
Marginal stability occurs when poles lie on the imaginary axis (non-repeated) and none are in the right-half plane, producing sustained oscillations.
Question 3: For the transfer function G(s) = 100/[(s+1)(s+10)], what is the DC gain?
- 10 (Correct answer)
- 100
- 1
- 0.1
Correct answer: 10
DC gain is G(0) = 100/[(0+1)(0+10)] = 100/10 = 10.
Question 4: In root locus design, where do the branches begin and end as gain K goes from 0 to infinity?
- From zeros to poles
- From poles to zeros (finite or at infinity) (Correct answer)
- From the origin to infinity
- From -1 to the nearest pole
Correct answer: From poles to zeros (finite or at infinity)
Root locus branches originate at open-loop poles (K=0) and terminate at open-loop zeros or at infinity (Kโโ).
Question 5: An integrating element (1/s) in a control loop ensures zero steady-state error to which type of input?
- Ramp
- Parabolic
- Step (Correct answer)
- Impulse
Correct answer: Step
A single integrator (Type 1 system) eliminates steady-state error for step (position) inputs due to the infinite DC gain of the integrator.
Question 6: What does the time constant ฯ represent in a first-order system G(s) = 1/(ฯs+1)?
- The time to reach 63.2% of final value (Correct answer)
- The system settling time
- The peak overshoot time
- The delay before response begins
Correct answer: The time to reach 63.2% of final value
For a first-order system, the time constant ฯ is the time required for the step response to reach 63.2% (1 - eโปยน) of its final value.
Question 7: Which frequency-domain specification directly measures the robustness of a closed-loop system to gain variations?
- Bandwidth
- Gain margin (Correct answer)
- Resonant peak
- Phase crossover frequency
Correct answer: Gain margin
Gain margin indicates how much the open-loop gain can increase before the system becomes unstable, directly measuring gain robustness.
BEE Control System Principles 3
The Nyquist stability criterion states that the number of unstable closed-loop poles equals: