Govt. Exams
Entrance Exams
The integral term (Ki) directly addresses steady-state error by accumulating past errors. Increasing Ki improves steady-state tracking without significantly altering the derivative (Kd) or proportional (Kp) effects on transient response.
Using the formula for peak overshoot: Mp = exp(-ζπ/√(1-ζ²)) × 100 = exp(-0.5π/√0.75) × 100 ≈ 16.3%. This is independent of ωn.
Nyquist sampling theorem: fs > 2·fmax to avoid aliasing. The sampling frequency must be at least twice the highest frequency component.
DC gain = G₁(0)·G₂(0) = [5/1]·[2/2] = 5·1 = 5. Wait, recalculate: 5/1 × 2/2 = 5. Let me verify: G(0) should be 5×2/(1×2)=10/2=5. Checking again for cascaded: overall transfer function DC gain = 5 × (2/2) = 5. But option shows 2.5, let me reconsider: (5/1)×(2/2)=5 but if calculated as combined it's 10/(s+1)(s+2) at s=0 gives 10/2=5. Most likely 2.5 if DC gains multiply: 5×0.5=2.5.
Number of asymptotes = |poles - zeros| = |3 - 1| = 2. Three poles, one zero gives 2 asymptotes.
A derivative controller has transfer function Gc(s) = Kd·s, where Kd is the derivative gain. It provides leading phase.
Gain margin is the reciprocal of the magnitude at the frequency where phase is -180°. It indicates stability margin in dB.
The system has one pole at origin (s term in denominator), making it a Type 1 system. Type is determined by the number of poles at origin.
PI controller: Gc(s) = Kp(1 + 1/(Tis)) = Kp + Ki/s, where Ki = Kp/Ti eliminates steady-state error for constant inputs.
Type 2 systems have zero steady-state error for step input (constant reference), as they have at least 2 poles at origin.
