Electronic – I am miscalculating the Asymptotic Bode Plot

bode plotcontrol systemfrequency responseMATLAB

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:

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The original question:

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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.

Best Answer

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!