See that proportional gain alone makes a control loop respond faster but oscillate around the target, while adding derivative gain damps that oscillation — the same natural-frequency/damping-ratio language used for mechanical vibration applies directly to feedback control.
Overshoot
100.0%Settling Time (2%)
—Natural frequency: ωn = √KpDamping ratio: ζ = Kd / (2√Kp)Overshoot: Mp = e^(−ζπ/√(1−ζ²)) × 100% (ζ < 1)Keep derivative gain at 0. Watch the step response overshoot the target and oscillate around it without settling.
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