The Nyquist stability criterion states that for stability, the Nyquist plot should not encircle:
Answer: B
The Nyquist criterion checks encirclements of the critical point (-1, 0) in the complex plane. No encirclement indicates stability for minimum phase systems.
Q.182Medium
A control system with gain margin of 6 dB means:
Answer: A
Gain margin in dB = 20log₁₀(GM). Therefore, 6 = 20log₁₀(GM), GM = 10^(206) ≈ 2
Q.183Medium
The settling time of a second-order underdamped system is approximately given by:
Answer: A
For 2% criteria, settling time ts ≈ 4/(ζωₙ). This is the standard formula for second-order systems.
Q.184Medium
In state-space representation, observability matrix rank should be equal to:
Answer: A
For a system to be completely observable, the observability matrix [C; CA; CA²; ...] must have rank equal to n (number of states).
Q.185Medium
A lead compensator with transfer function Gc(s) = (1 + aTs)/(1 + Ts) where a > 1 provides:
Answer: B
Lead compensator (a > 1) provides phase lead in mid-frequency range, improving transient response and system speed, hence used for transient improvement.
Advertisement
Q.186Medium
A system with transfer function H(s) = 100/(s² + 10s + 100) has natural frequency ωₙ and damping ratio ζ respectively as:
Answer: A
Standard form: ωₙ² = 100, so ωₙ = 10 rad/s. 2ζωₙ = 10, so ζ = 10/(2×10) = 0.5
Q.187Medium
Peak overshoot of underdamped second-order system depends on:
Answer: A
Peak overshoot Mp = e^(-πζ/√(1-ζ²)). It depends only on damping ratio ζ, not on ωₙ.
Q.188Medium
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.189Medium
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.190Medium
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.191Medium
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.192Medium
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.
Q.193Medium
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.194Medium
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.195Medium
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.197Medium
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.198Medium
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.199Medium
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.200Medium
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.
