# Finding a transfer function

The frequency response of a linear time invariant system has been measured and can be seen in the attachment file below.

A feedback element with a transfer function, H(s), is to be chosen so that the system steady-state error to a unit step input is equal to 0.07. What is a suitable transfer function to achieve this? I am having a hard time understanding the procedure and finding the suitable evidence.

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#### Solution Preview

Please see the attached file. Also, visit the following website:

http://www.engin.umich.edu/group/ctm/extras/ess/ess.html

It has a good explanation of steady state error.

From the given frequency response.xls file, it can be seen that the frequencies given are in factors of 1.486. The noticeable thing is Magnitude (dB) is just a function of given frequencies. It implies the actual Magnitude is completely the same as the given frequency. It means whatever the frequency is, the magnitude of the frequency response will be completely the same. This is the case for differentiator.

The transfer function is

G(s) = s

The bode ...

#### Solution Summary

This solution is provided in 398 words in an attached .doc file. It describes the transfer function and provides a bode plot for it as well as the transfer function.