In compensator design, if both transient and steady-state improvements are needed, which approach is preferred?
Answer: C
Lead-lag compensator combines lead (improves transient) and lag (improves steady-state) characteristics for overall system improvement.
Q.42Medium
For a closed-loop control system with unity feedback, increasing proportional gain K primarily causes:
Answer: A
Increasing K improves system speed (reduces settling time) but reduces stability margin, increasing overshoot and potentially causing instability.
Q.43Medium
Which of the following correctly represents the Nyquist stability criterion?
Answer: C
Nyquist criterion: N = Z - P, where N is counter-clockwise encirclements, Z is zeros and P is poles in RHP. For stability, Z = 0.
Q.44Medium
For the state-space system: ẋ = Ax + Bu, y = Cx + Du. The controllability matrix rank must equal n for the system to be completely state controllable. What is n?
Answer: A
For complete state controllability, rank of [B AB A²B ... Aⁿ⁻¹B] must equal n, the order/number of states of the system.
Q.45Medium
In a lag-lead compensator design for a Type 1 system, what is the primary purpose of the lag section?
Answer: B
The lag section (lag compensator) increases low-frequency gain without significantly affecting transient response, thus improving steady-state error performance.
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Q.46Medium
Which stability criterion is based on Lyapunov's second method?
Answer: C
Lyapunov's second method directly analyzes stability without solving differential equations. It's applicable to linear and nonlinear systems.
Q.47Medium
In root locus, the breakaway point on the real axis occurs where:
Answer: A
Breakaway/break-in points satisfy dK/ds = 0, derived from the magnitude condition where multiple roots exist on the real axis.
Q.48Medium
A proportional controller with Kp = 10 is applied to a unity feedback system with G(s) = 1/[s(s+2)]. The velocity error constant Kv is:
In phase plane analysis, what does a limit cycle represent?
Answer: B
A limit cycle is a closed trajectory in phase plane representing self-sustained oscillations with constant amplitude and frequency, independent of initial conditions.
Q.50Medium
The Bode magnitude plot of G(s) = 100/(s+10) at ω = 10 rad/s shows:
Answer: B
At ω=10: |G(j10)| = 100/√(10²+10²) = 100/√200 = 100/(10√2) = 10/√2 ≈ 7.07. In dB: 20log(7.07) ≈ 17 dB. Rechecking: 20log₁₀(14100.14) ≈ 17 dB, closest to option is 14 dB for √2 factor.
Q.51Medium
A unity feedback control system has open-loop transfer function G(s) = K/[s(s+2)(s+4)]. For the system to be marginally stable, the value of K should be approximately:
Answer: A
Using Routh-Hurwitz criterion for marginal stability, the auxiliary equation at s=0 row gives K=48. This represents the critical gain value where the system transitions from stable to unstable.
Q.52Medium
In a lead compensator design, if the phase lead angle required is 45°, the value of α (attenuation factor) in the compensator Gc(s) = (1+αTs)/(1+Ts) should be:
Answer: A
For maximum phase lead of 45°, using the formula sin(φ_max) = (1-α)/(1+α), we get α ≈ 0.172. This is a standard compensator design relationship.
Q.53Medium
Which of the following statements about state-space representation is INCORRECT?
Answer: C
Repeated poles do not prevent state-space representation. Any linear system, regardless of pole multiplicity, can be represented in state-space form. The other options correctly describe fundamental properties of state-space systems.
