System identification for second order overdamped systems

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System identification for second order overdamped
systems

• Method of Incomplete Response

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Second Order Overdamped Response
Consider a second order overdamped system where
For a unit step input
And we can readily find a,b,c to be
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Second Order Overdamped Response Solution
And inverting
For a step of A
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Calculation of Incomplete
Assuming one time constant is much larger than
the other, that is t1gtgt t2 , for large time
This may be written as
This is in the form of
A classic linear form.
The slope m-1/t1 can be determined by plotting
on simi-log paper and using the slope for large
time.
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Procedure for incomplete response
Use a step of magnitude A to excite the system.
Plot PIR on a log scale vs. time on a linear
scale. Use large times to plot a linear curve of
constant slope. This curve is the response for
the t1 term.
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Procedure for incomplete response
Plot the difference between the first linear
curve and the actual response. This difference
is the response for the t2 term. Plot a linear
curve for this difference.
For both linear curves, take each intercept at
t0 as 100 response. Determine the time at 100
-0.368100 response (this is the 63.2 response
point). These times will be t1, and t2