In state-space representation, if eigenvalues of A matrix are at s = -1, -2, -3, the system is:
Answer: B
Stability depends only on eigenvalue locations (all in LHP = stable). Controllability requires rank[B AB A²B] = n, which eigenvalues alone don't determine
Q.345Medium
For an underdamped second-order system, the relationship between settling time ts and damping ratio ζ is:
Answer: C
Settling time ts ≈ 4/(ζωn) for 2% criterion, thus ts ∝ 1/(ζωn)
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Q.346Medium
Which compensator is preferred for improving steady-state error without significantly affecting transient response?
Answer: B
Lag compensator increases DC gain significantly, improving steady-state error, while its phase lag is restricted to lower frequencies, minimizing transient effects
Q.347Easy
The static error constant for a Type-1 system with G(s) = 20/(s(s+5)(s+10)) is:
For a system to be controllable using state feedback u = -Kx, which condition must be satisfied?
Answer: C
Controllability requires the controllability matrix to have full rank n. This ensures all states can be moved from origin to any desired state
Q.349Medium
A system has poles at -2±j3. The natural frequency and damping ratio are approximately:
Answer: A
ωn = √(4+9) = √13 ≈ 3.6 rad/s, ζ = 2/√13 ≈ 0.55
Q.350Medium
In a unity feedback system, increasing loop gain K generally:
Answer: B
Higher K reduces ess proportionally but shifts root locus rightward, potentially crossing into RHP, thus reducing stability margins
Q.351Easy
The corner frequency of a transfer function H(s) = 1/(1 + s/10) occurs at:
Answer: B
Corner frequency = pole frequency. Rewriting: H(s) = 10/(s+10), so pole at -10, corner frequency = 10 rad/s
Q.352Hard
For improving transient response with minimal steady-state error impact, a lead compensator should be designed to add phase lead at:
Answer: B
Lead compensator adds phase lead at its designed center frequency ωm. For transient improvement, it should coincide with gain crossover frequency to increase phase margin
Q.353Easy
A system with characteristic equation s³ + 6s² + 11s + 6 = 0 has poles at:
Answer: A
Factoring: (s+1)(s+2)(s+3) = 0 gives poles at s = -1, -2, -3. All in LHP, so system is stable
Q.354Medium
In a compensated system, if phase margin PM = 30° and gain margin GM = 8 dB, this indicates:
Answer: C
PM = 30° is acceptable (typically 30-60°), GM = 8 dB (>6 dB threshold) indicates good gain stability. Both margins suggest satisfactory performance
Q.355Easy
A control system has an open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)]. What is the type of this system?
Answer: B
The type of a system is determined by the number of poles at origin. Here, there is one pole at origin (s term), making it Type 1.
Q.356Easy
In a Bode plot, the magnitude plot slope in dB/decade for a pole at origin is:
Answer: A
Each pole contributes -20 dB/decade slope. A single pole at origin contributes -20 dB/decade.
Q.357Easy
A second-order system has damping ratio ζ = 0.5. This system is classified as:
Answer: B
For ζ < 1, the system is underdamped with oscillatory response. ζ = 0.5 falls in this category.
Q.358Easy
Which of the following is a characteristic of a lag compensator?
Answer: B
Lag compensator reduces steady-state error by increasing the DC gain without significantly affecting transient response or stability margins.
Q.359Medium
For a unity feedback control system with G(s) = 10/[s(s+5)], the static velocity error constant Kv is:
