# Smith's Second-Order Method in Process Dynamics

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Consider an overdamped model with a step response represented by , where and are the time constant and the damping coefficient, respectively. It is possible to use the step-response data in order to obtain approximate values for and . Such a method was developed by Smith [1, 2] and uses the times at which the normalized response reaches 20% and 60% (at times and . Indeed, the ratio gives (red curve) and (blue curve). It is found that the approximate values of the time constant and the damping coefficient ( and ) match the exact values, which are selected by the user, perfectly. A separate plot (select "output") shows the exact response of the second-order process to a unit step, as well as the values of and , identified by the blue and red dots.

Contributed by: Housam Binous, Mohammad Mozahar Hossain, and Ahmed Bellagi (November 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

References

[1] C. L. Smith, *Digital Computer Process Control*, Scranton: Intext Educational Publishers, 1972.

[2] D. E. Seborg, T. F. Edgar, D. A. Mellichamp, and F. J. Doyle III, *Process Dynamics and Control*, 3rd ed., New York: Wiley, 2011.

## Permanent Citation

"Smith's Second-Order Method in Process Dynamics"

http://demonstrations.wolfram.com/SmithsSecondOrderMethodInProcessDynamics/

Wolfram Demonstrations Project

Published: November 10 2015