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Settling Time (5%)

Settling Time (5%) Equation


$$ T_s = \frac{3}{ζ\omega_n} $$
where:

Ts   =   Settling time   (s)

ζ   =   Damping Ratio   (dimensionless)

ωn   =   System Natural Frequency   (rad/s)


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Equation Assumptions


  • The system is a linear time-invarient system.
  • The system is of second order.
  • The resposne is under-damped (ζ < 1).
  • The input is a step input.