Settling time
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In control theory, the settling time of a dynamical system, such as an amplifier or other output device, is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error band. Settling time includes a propagation delay, plus the time required for the output to slew to the vicinity of the final value, recover from the overload condition associated with slew, and finally settle to within the specified error. Systems with energy storage cannot respond instantaneously and will exhibit transient responses when they are subjected to inputs or disturbances.
In control theory, the settling time of a dynamical system, such as an amplifier or other output device, is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error band. Settling time includes a propagation delay, plus the time required for the output to slew to the vicinity of the final value, recover from the overload condition associated with slew, and finally settle to within the specified error. Systems with energy storage cannot respond instantaneously and will exhibit transient responses when they are subjected to inputs or disturbances. T_s = -\frac{\ln (\text{tolerance fraction})}{\text{damping ratio} \times \text{natural freq}} A general form is T_s = -\frac{\ln (\text{tolerance fraction} \times \sqrt{1-\zeta^2} )}{\text{damping ratio} \times \text{natural freq}} Thus, if the damping ratio \zeta \ll 1 , settling time to within 2% = 0.02 is: T_s = -\frac{\ln(0.02)}{\zeta \omega_n}\approx\frac{3.9}{\zeta \omega_n}
See also
Rise time Time constant
External links
Second-Order System Example Op Amp Settling Time Graphical tutorial of Settling time and Risetime MATLAB function for computing settling time, rise time, and other step response characteristics Settling Time Calculator
Text derived from https://en.wikipedia.org/w/index.php?oldid=1372794727 under CC BY-SA 4.0; modifications have been made.