Govt. Exams
Entrance Exams
For a Type-2 system, parabolic error is ess = A/Ka where Ka = lim[s→0] s²G(s)H(s). Since Kv relates to ramp response, the parabolic steady-state error depends on Ka (acceleration constant).
Sensitivity S(s) = ∂Y/∂G ÷ Y/G = 1/[1+G(s)H(s)] for unity feedback systems. It measures effect of parameter variations.
At ω=5: Phase = -90° (from 1/s) - arctan(5/1) - arctan(5/5) = -90° - 78.7° - 45° ≈ -213.7° ≈ -225°
Centroid (center of asymptotes) = [Σpoles - Σzeros]/[number of poles - number of zeros]. Number of asymptotes = 5-2 = 3.
Routh table construction shows all positive elements in first column, indicating all poles in left half plane, making the system stable.
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
Controllability requires the controllability matrix to have full rank n. This ensures all states can be moved from origin to any desired state
When |L(s)| >> 1, the sensitivity function |S(s)| ≈ 1/|L(s)| becomes very small. This shows that high loop gain reduces sensitivity to parameter variations.
Pole-zero excess affects the phase behavior at high frequencies. A system with excess of 2 can be either stable or unstable depending on the gain value and pole locations.
tp = π/(ωn√(1-ζ²)) = π/(5√(1-0.49)) = π/(5×0.714) ≈ 0.88 seconds ≈ 0.89 seconds. Closest answer is B.
