The Routh–Hurwitz criterion provides information about:

 

Q401. The number of roots of the characteristic equation lying in the right half of the s-plane indicates:
A) System order
B) Number of unstable poles
C) Damping ratio
D) Time constant

✅ Answer: B) Number of unstable poles
Explanation:
Poles on the right half of the s-plane correspond to exponentially growing terms in the time response, meaning instability.

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Q402. The Routh–Hurwitz criterion provides information about:
A) Magnitude response
B) System type
C) Stability without solving the equation
D) Frequency domain behavior

✅ Answer: C) Stability without solving the equation
Explanation:
Routh–Hurwitz allows determination of how many roots lie in the right half-plane without finding the roots explicitly.

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Q403. If all elements in the first column of the Routh array are positive, then the system is:
A) Unstable
B) Conditionally stable
C) Stable
D) Marginally stable

✅ Answer: C) Stable
Explanation:
All positive elements in the first column indicate that all poles lie in the left half of the s-plane.

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Q404. The unit step response of a first-order system is:
A) Oscillatory
B) Linear
C) Exponential
D) Parabolic

✅ Answer: C) Exponential
Explanation:
For $G(s) = \frac{1}{\tau s + 1}$, the response is $1 - e^{-t/\tau}$.

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Q405. The settling time of a second-order system decreases if:
A) Damping ratio increases
B) Natural frequency increases
C) Both A and B
D) None

✅ Answer: C) Both A and B
Explanation:
Higher natural frequency speeds up response; moderate damping avoids oscillations, thus decreasing settling time.

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Q406. The gain margin of a stable system must be:
A) 0 dB
B) Positive
C) Negative
D) Infinite

✅ Answer: B) Positive
Explanation:
Positive gain margin ensures system remains stable even if gain increases up to that margin.

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Q407. The phase margin is measured at the frequency where:
A) Phase is 0°
B) Magnitude is 0 dB
C) Gain is 1
D) Phase is −90°

✅ Answer: B) Magnitude is 0 dB
Explanation:
Phase margin = 180° + phase angle at gain crossover frequency (where |G(jω)H(jω)| = 1).

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Q408. In a Bode plot, a single pole contributes a slope of:
A) +20 dB/decade
B) −20 dB/decade
C) +40 dB/decade
D) −40 dB/decade

✅ Answer: B) −20 dB/decade
Explanation:
Each pole decreases the slope by 20 dB/decade after its corner frequency.

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Q409. The Nyquist plot helps determine:
A) Gain
B) Stability using the encirclement of (−1,0) point
C) Damping ratio
D) Phase angle only

✅ Answer: B) Stability using encirclement of (−1,0)
Explanation:
According to the Nyquist stability criterion, the number of clockwise encirclements of (−1,0) point determines closed-loop stability.

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Q410. A phase-lead compensator improves:
A) Steady-state error
B) Speed of response
C) Phase margin
D) All of these

✅ Answer: D) All of these
Explanation:
Phase-lead increases system bandwidth, phase margin, and improves transient response and accuracy.

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Q411. The transfer function of a tachometer is proportional to:
A) Displacement
B) Velocity
C) Acceleration
D) None

✅ Answer: B) Velocity
Explanation:
A tachometer produces voltage proportional to rotational speed.

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Q412. The derivative controller acts on:
A) Present error
B) Past error
C) Rate of change of error
D) Integral of error

✅ Answer: C) Rate of change of error
Explanation:
Derivative control anticipates future error trend, improving stability and damping.

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Q413. A proportional controller increases:
A) System gain
B) Steady-state error
C) Oscillations
D) System order

✅ Answer: A) System gain
Explanation:
Proportional control multiplies error by gain $K_p$, reducing steady-state error but may increase overshoot.

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Q414. The integral controller reduces:
A) Overshoot
B) Steady-state error
C) Transient response
D) System order

✅ Answer: B) Steady-state error
Explanation:
Integral control accumulates error over time, driving the steady-state error to zero.

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Q415. Which controller adds one zero and one pole to the system?
A) PI
B) PD
C) PID
D) Proportional

✅ Answer: C) PID
Explanation:
PID combines proportional, integral, and derivative actions, contributing both a zero and pole.

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Q416. The type of system determines:
A) Stability
B) Steady-state error for standard inputs
C) Damping ratio
D) Order of response

✅ Answer: B) Steady-state error for standard inputs
Explanation:
System type (number of integrators) defines steady-state error for step, ramp, and parabolic inputs.

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Q417. A system with two poles at the origin is a:
A) Type 1 system
B) Type 2 system
C) Type 0 system
D) Unstable system

✅ Answer: B) Type 2 system
Explanation:
Type number equals number of poles at the origin (integrators).

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Q418. A second-order system with damping ratio >1 is called:
A) Underdamped
B) Critically damped
C) Overdamped
D) Undamped

✅ Answer: C) Overdamped
Explanation:
Overdamped systems have no oscillations and slower response.

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Q419. The characteristic equation of a closed-loop system is given by:
A) 1 + GH = 0
B) GH = 1
C) G = 1 + H
D) 1 − GH = 0

✅ Answer: A) 1 + GH = 0
Explanation:
The condition for closed-loop poles comes from denominator $1 + G(s)H(s) = 0$.

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Q420. The open-loop transfer function of a unity feedback system is $G(s) = \frac{10}{s(s+2)}$. The system type is:
A) 0
B) 1
C) 2
D) 3

✅ Answer: B) 1
Explanation:
There is one pole at the origin → Type 1 system.