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hope you are all doing well. Right now I am dealing with a homework and I have transfer function and I need to plot the asymptotic Bode Plots of it. I am trying to plot the Magnitude Diagram right now, and I am misevaluating the Magnitude at Low Frequencies. I calculate it as approximately 15dB, whereas MATLAB shows it 35 dB. Here is what I did:

enter image description here

The original question:

enter image description here

What am I missing? I am pretty ill right now, so I am probably missing out a detail, even though I checked it multiple times.

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    \$\begingroup\$ +1 for identifying this as homework and showing what you have tried. \$\endgroup\$
    – Math Keeps Me Busy
    Apr 18, 2021 at 1:31
  • \$\begingroup\$ question. what is log_10 of 6? What is 20 times that? \$\endgroup\$
    – Math Keeps Me Busy
    Apr 18, 2021 at 1:34
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    \$\begingroup\$ I assume that you are trying to plot the asymptotic bode for the open loop system. In that case, there is a pole at the origin and so the zero frequency gain is infinite. You can check by substituting s=0 in the third equation. Due to the pole at origin, the asymptote is a sloping line with —20 dB/decade slope until it reaches the first corner frequency. You can verify by substituting 0.00001 rad/s, 0.0001 rad/s etc for s in the third equation. Matlab result may be wrong. What does dcgain(openlooptransferfunction) give a as output in matlab? \$\endgroup\$
    – AJN
    Apr 18, 2021 at 2:15
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    \$\begingroup\$ If your original question is answered, you can post it as an answer yourself. It is allowed on this site. \$\endgroup\$
    – AJN
    Apr 18, 2021 at 3:24
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    \$\begingroup\$ @jonk In the lessons we dealt with the open loop transfer functions, therefore I assumed that this one require me to deal with the open loop system too. I asked my friends about it and they confirmed me. However, you might be right, I will ask my lecturer about it. Thanks for the heads up! \$\endgroup\$
    – kucar
    Apr 18, 2021 at 12:21

1 Answer 1

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I got what was I missing thanks to everyone who commented. I was not taking the pole at the origin into account. However, the magnitude of this pole starts with a slope of -20dB/decade at infinity, and at w = 0.1 rad/s, it is at 20 dB magnitude. Adding that 20 dB to the 15 dB I had already calculated, yields the starting magnitude as 35 dB, just like on MATLAB. Big thanks to everyone who helped!

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