# How to estimate transfer function given a transmissibility plot?

1. Mar 19, 2014

### annas425

How would I estimate the transfer function for transmissibility given this plot:

I am told that the data does not include phase information, but assume that the phase is 0 deg at low frequency and -180 deg at high frequency. I must provide a brief rationale for each component of the transfer function. Ignore the measurement noise at frequencies larger than 10 Hz. Keep in mind the frequency units; transmissibility in dB is given on the rightside y-axis.

Thank you so much in advance! I really am struggling with this.

All I know is that {transfer function} = {output} / {input}. I do not know how to get a transfer function, just given a transmissibility vs. frequency graph.

2. Mar 19, 2014

### donpacino

so from low freq to 10 hz it looks like a low pass filter. there will be a pole at 0.5 hz. the pole will have a damping ratio higher than 1 due to the large Q you see there. There are ways to calculate what the damping ratio is due to how high that peak gets.
you also nee to incorporate the bump at 3.5 Hz. I'll let you try to figure that out

3. Mar 19, 2014

### AlephZero

Review your notes or textbook on Bode plots. The basic idea is to approximate the plotted data by straight line segments, and then write down the transfer function that corresponds to the approximation. See www.ece.utah.edu/~ee3110/bodeplot.pdf.

4. Mar 19, 2014

### rude man

I would assume real poles and zeros (no complex-conjugate poles) using Bode plots as the basis for determining the transfer function.