Control Systems practice questions

Answer: C) 1 s

• AIncorrect. That omits \(\zeta\omega_n\).
• BIncorrect. Use \(4/(\zeta\omega_n)\).
• CCorrect. \(T_s \approx 4/(\zeta\omega_n)\).
• DIncorrect. That inverts part of the formula.

Answer: C) Unstable

• AIncorrect. That's poles on the jω axis.
• BIncorrect. Right-half-plane poles are unstable.
• CCorrect. Its response grows without bound.
• DIncorrect. It's unstable.

Answer: C) 0.2 s

• AIncorrect. Take the reciprocal of 5.
• BIncorrect. Take the reciprocal.
• CCorrect. τ = 1/a = 1/5 s.
• DIncorrect. Recheck the reciprocal.

Answer: B) Stable

For a stable, minimum-phase open-loop system, positive gain and phase margins mean the closed loop is stable. Zero margins mean marginal stability, and negative margins mean instability.

• AIncorrect. For a stable, minimum-phase open loop, negative margins would indicate instability. Positive margins mean no closed-loop poles lie in the right half-plane.
• BCorrect. When the open loop is stable and minimum-phase, positive gain and phase margins mean the Nyquist plot does not encircle −1. So the closed-loop system is stable.
• CIncorrect. Sustained constant-amplitude oscillation happens when the margins are zero, meaning the loop gain is exactly 1 at −180°. It does not happen when both margins are positive.
• DIncorrect. A 45° or larger phase margin is a common design guideline for good damping, not a requirement for stability. Any positive margin is enough for stability here.

Answer: C) Eliminates steady-state error

• AIncorrect. That's proportional action.
• BIncorrect. That's derivative action.
• CCorrect. It accumulates past error.
• DIncorrect. It removes steady-state error.

Answer: D) Real axis

• AIncorrect. It's symmetric about the real axis.
• BIncorrect. That isn't required.
• CIncorrect. That isn't required.
• DCorrect. Complex poles occur in conjugate pairs.

Answer: A) Reduces the effect of disturbances and plant parameter changes on the output

Negative feedback lowers the closed-loop system's sensitivity to disturbances and parameter variations, and it usually widens bandwidth. The costs are lower overall gain and a possible risk of instability.

• ACorrect. The controller acts on measured error, so disturbances and parameter variations are cut by roughly the factor 1 + GH (the loop gain plus one).
• BIncorrect. Feedback can destabilize a stable plant if the loop gain is too high or there is too much phase lag.
• CIncorrect. The closed-loop gain G/(1 + GH) is lower than the forward gain G. Feedback trades gain for accuracy and robustness.
• DIncorrect. Negative feedback usually widens bandwidth, trading gain for speed of response.

Answer: D) −180°

• AIncorrect. It's measured at −180°.
• BIncorrect. It's at −180°.
• CIncorrect. It's at −180°.
• DCorrect. The phase crossover frequency.

Answer: B) Disturbance rejection and tracking accuracy

• AIncorrect. That depends on high-frequency gain.
• BCorrect. Errors shrink as loop gain grows.
• CIncorrect. Stability depends on margins.
• DIncorrect. That isn't the main effect.

Answer: C) 2 s

• AIncorrect. Recheck the formula.
• BIncorrect. Divide by \(\zeta\omega_n\).
• CCorrect. \(t_s \approx 4/(\zeta\omega_n)\).
• DIncorrect. Recheck the formula.