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Settling time

{{Short description|Time required for the output of an amplifier to stabilize}}

File:High accuracy settling time measurements figure 1.png

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.Modern Control Engineering (5th Edition), Katsuhiko Ogata, p.160

Definition

Tay, Mareels and Moore (1998) defined settling time as "the time required for the response curve to reach and stay within a range of certain percentage (usually 5% or 2%) of the final value."{{Cite book| title = High performance control | last = Tay | first = Teng-Tiow |author2=Iven Mareels |author3=John B. Moore | publisher = Birkhäuser | year = 1998 | isbn = 978-0-8176-4004-0 | page = 93}}

Mathematical detail

Settling time depends on the system response and natural frequency.

The settling time for a second order, underdamped system responding to a step response can be approximated if the damping ratio \zeta \ll 1 by

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

References

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External links

{{wikisourcehas|a paper on settling time measurements.|Wikisource:High accuracy settling time measurements}}

  • [https://web.archive.org/web/20040626102542/http://bass.gmu.edu/~gbeale/ece_421/second_order_04.html Second-Order System Example]
  • [http://www.analog.com/static/imported-files/application_notes/466359863287538299597392756AN359.pdf Op Amp Settling Time]
  • [https://web.archive.org/web/20070705124107/http://www.facstaff.bucknell.edu/mastascu/eControlHTML/SysDyn/SysDyn5.html Graphical tutorial] of Settling time and Risetime
  • [http://www.mathworks.com/help/toolbox/ident/ref/stepinfo.html MATLAB function] for computing settling time, rise time, and other step response characteristics
  • [https://3roam.com/settling-time-calculator/ Settling Time Calculator]

Category:Transient response characteristics

Category:Systems_theory