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Settling Time (approx.)

Time for a control response to settle within 2% of target.

Formula

t_s \approx \frac{4}{\zeta \omega_n}

Variables

t_sSettling time (s)

ζDamping ratio

ω_nNatural frequency (rad/s)

Example

ζ=0.7, ω_n=10: t_s ≈ 0.57 s

Did You Know?

A damping ratio near 0.7 gives the sweet spot — fast settling with barely any overshoot.

robotics control settling

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