The breakaway point in root locus occurs where:

 Q11. The standard test signals used in control system analysis are:

A) Impulse, step, ramp, parabolic
B) Square, triangular, sinusoidal
C) Impulse, sawtooth, noise
D) DC, AC, transient

✅ Answer: A) Impulse, step, ramp, parabolic
Explanation:
These standard signals help analyze transient and steady-state behavior of control systems.

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Q12. For a unity feedback system, the overall transfer function is:
A) $\frac{G(s)}{1 - G(s)}$
B) $\frac{1}{1 + G(s)}$
C) $\frac{G(s)}{1 + G(s)}$
D) $\frac{1}{G(s)}$

✅ Answer: C) $\frac{G(s)}{1 + G(s)}$
Explanation:
In unity feedback, feedback gain $H(s) = 1$. So, closed-loop TF = $\frac{G(s)}{1 + G(s)}$.

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Q13. The number of poles of a transfer function determines:
A) The system type
B) The order of the system
C) The gain
D) The stability margin

✅ Answer: B) The order of the system
Explanation:
Order = highest power of ‘s’ in the denominator → number of energy-storing elements.

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Q14. Which of the following is not a time-domain specification?
A) Rise time
B) Overshoot
C) Gain margin
D) Settling time

✅ Answer: C) Gain margin
Explanation:
Gain margin is a frequency-domain concept; others are time-domain parameters.

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Q15. The “type” of a control system is determined by:
A) Number of zeros
B) Number of poles at the origin
C) Damping ratio
D) Gain constant

✅ Answer: B) Number of poles at the origin
Explanation:
System type = number of integrators (poles at origin) → affects steady-state error.

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Q16. The steady-state error for a step input in a Type-1 system is:
A) Zero
B) Infinite
C) Finite
D) Depends on damping

✅ Answer: A) Zero
Explanation:
Type-1 systems perfectly track step inputs (error constant $K_p \to \infty$).

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Q17. The damping ratio (ζ) indicates:
A) Gain of the system
B) Type of system
C) Nature of transient response
D) Frequency of oscillation

✅ Answer: C) Nature of transient response
Explanation:
ζ controls overshoot, oscillation, and settling of a second-order system.

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Q18. The effect of increasing the proportional gain in a feedback system is:
A) Slower response
B) Increased overshoot
C) More damping
D) Higher steady-state error

✅ Answer: B) Increased overshoot
Explanation:
Increasing $K_p$ makes the system faster but less stable → more overshoot.

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Q19. Derivative control improves:
A) Steady-state accuracy
B) Stability and damping
C) System gain
D) Steady-state error

✅ Answer: B) Stability and damping
Explanation:
Derivative control anticipates future error, providing damping and improving stability.

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Q20. Integral control is mainly used to:
A) Reduce overshoot
B) Eliminate steady-state error
C) Increase rise time
D) Reduce bandwidth

✅ Answer: B) Eliminate steady-state error
Explanation:
Integral control accumulates error over time and forces steady-state error → 0.

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Q21. The Laplace transform of a unit step function is:
A) 1/s
B) s
C) 1/s²
D) e^(-st)

✅ Answer: A) 1/s
Explanation:
Unit step function $u(t)$ → $1/s$ in Laplace domain.

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Q22. The open-loop transfer function of a unity feedback system is $G(s) = \frac{10}{s(s+2)}$. The steady-state error for a unit step input is:
A) 0
B) 0.1
C) 0.2
D) Infinite

✅ Answer: A) 0
Explanation:
Type = 1 (one pole at origin), so step input error = 0.

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Q23. Routh–Hurwitz criterion gives information about:
A) Transient response
B) Time constant
C) Stability of the system
D) Steady-state error

✅ Answer: C) Stability of the system
Explanation:
It determines the number of roots of the characteristic equation with positive real parts.

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Q24. A system is marginally stable if:
A) Poles lie on imaginary axis
B) Poles lie in left half
C) Poles lie in right half
D) Zeros lie on imaginary axis

✅ Answer: A) Poles lie on imaginary axis
Explanation:
Imaginary-axis poles → sustained oscillations (marginal stability).

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Q25. The Bode plot is a graphical representation of:
A) Time response
B) Frequency response
C) Root locus
D) Step response

✅ Answer: B) Frequency response
Explanation:
Bode plots display magnitude (dB) and phase versus frequency (log scale).

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Q26. Nyquist plot is used for:
A) Determining time-domain specifications
B) Evaluating steady-state error
C) Analyzing stability in frequency domain
D) Calculating damping ratio

✅ Answer: C) Analyzing stability in frequency domain
Explanation:
Nyquist criterion relates open-loop frequency response to closed-loop stability.

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Q27. The root locus starts from:
A) Zeros and ends at poles
B) Poles and ends at zeros
C) Origin
D) Infinity

✅ Answer: B) Poles and ends at zeros
Explanation:
Each branch of root locus starts at open-loop poles and terminates at open-loop zeros.

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Q28. For higher-order systems, dominant poles determine:
A) Gain margin
B) Overall stability
C) Transient behavior
D) Steady-state error

✅ Answer: C) Transient behavior
Explanation:
Dominant poles (closest to imaginary axis) govern the slowest transient response.

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Q29. Which system has infinite steady-state error to ramp input?
A) Type 0
B) Type 1
C) Type 2
D) Type ∞

✅ Answer: A) Type 0
Explanation:
Type-0 systems (no integrator) → infinite ramp error.

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Q30. A system has poles at -1, -2, and -3. The system is:
A) Stable
B) Marginally stable
C) Unstable
D) Oscillatory

✅ Answer: A) Stable
Explanation:
All poles in left half-plane → stable system.

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Q31. The main disadvantage of open-loop control is:
A) Simple design
B) No feedback correction
C) High accuracy
D) Low cost

✅ Answer: B) No feedback correction
Explanation:
Open-loop cannot correct disturbances → low accuracy.

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Q32. Which of the following increases bandwidth?
A) Proportional gain
B) Integral gain
C) Derivative gain
D) Negative feedback

✅ Answer: D) Negative feedback
Explanation:
Negative feedback improves bandwidth and linearity.

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Q33. The transient response is mainly due to:
A) Zero input
B) Poles of the system
C) Zeros of the system
D) Feedback path

✅ Answer: B) Poles of the system
Explanation:
Transient behavior depends on pole location in s-plane.

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Q34. The breakaway point in root locus occurs where:
A) Two poles meet
B) Two branches cross imaginary axis
C) Derivative of gain w.r.t s = 0
D) Gain margin is zero

✅ Answer: C) Derivative of gain w.r.t s = 0
Explanation:
Breakaway/entry points found by solving $\frac{dK}{ds} = 0$.

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Q35. Lead compensator improves:
A) Steady-state error
B) Phase margin and speed
C) Stability only
D) Damping only

✅ Answer: B) Phase margin and speed
Explanation:
Lead compensation adds phase lead → faster response and improved stability.