Govt. Exams
Entrance Exams
Number of asymptotes = |number of poles - number of zeros| = |3 - 0| = 3. However, for this specific configuration with two poles at origin, effective asymptotes for root locus are 2.
Lead compensator has zero at -2 and pole at -8 (pole further left). This increases bandwidth and adds phase lead, improving transient response.
When gain crossover frequency equals phase crossover frequency, the system is at the stability boundary (phase = -180°), indicating marginal stability.
Reducing feedback gain reduces the effectiveness of feedback, leading to increased steady-state error for the same input command.
State-space representation naturally handles MIMO systems, non-linear systems, and time-varying systems better than transfer functions.
Overshoot = e^(-πζ/√(1-ζ²)) depends only on damping ratio ζ, not on ωn or system gain K.
Nyquist plot maps the frequency response G(jω)H(jω) in the complex plane by varying ω from 0 to ∞.
Lag compensation increases the system type or gain at low frequencies, improving steady-state accuracy without affecting stability significantly.
Rise time tr ≈ (π - cos⁻¹(ζ))/(ωn√(1-ζ²)). It decreases with higher ωn and appropriate ζ value.
When ζ < 1 (0.5 < 1), the system is underdamped with oscillatory transient response.
