Govt. Exams
Entrance Exams
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.
In lead compensation, zero is placed to the left of pole (closer to origin), providing phase lead to improve transient response and stability margin.
Centroid σ = (∑poles - ∑zeros)/(n-m), where n and m are number of poles and zeros respectively.
PI controller adds a pole at origin (integral term), increasing system type by 1 and eliminating steady-state error for step and ramp inputs.
Number of asymptotes = n - m = 3 - 1 = 2, where n=3 (poles) and m=1 (zeros).
Maximum power transfer (Pmax = V²/X) occurs when power angle δ = 90°, regardless of absolute voltage magnitudes.
Fault level = MVA base / (Zth in p.u.), where Zth is the equivalent impedance of the entire network.
δcr is the limiting rotor angle; if exceeded during a fault, the machine cannot return to synchronism even after fault clearance.
H is the inertia constant (M/2×SB) representing the kinetic energy relative to the system base power.
