Different bode plots for the same input in mathematica, wolfram alpha

Questions
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1

The phase diagrams of both look wrong to me.
What am I missing?

wolframalpha.png
wolframalpha.png972Ă—688 32 KB

mathematica.png
mathematica.png783Ă—660 20.5 KB

2

Thank you, we will look into this.

3

I would also be grateful for responses to this from those with experience using Mathematica for control theory. In the code below, I treat the transfer function as that of the complete system. (Not a component with feedback around it.)

I observe that the transfer function is unstable, with conjugate poles on the axis. The OutputResponse to a step is oscillatory. I don’t think a Bode plot of such a system is meaningful.

syss = (1 + 0.001 s)/(s^2 + 0.5);

sys = TransferFunctionModel[{{syss}}, s];

BodePlot[sys, FeedbackType -> None, PhaseRange -> {-Pi, Pi}]

bode.png
bode.png180Ă—237 1.81 KB

In[4]:= (* poles on the axis == unstable *)
TransferFunctionPoles[sys]

Out[4]= {{{0. - 0.707107 I, 0. + 0.707107 I}}}

In[5]:= sysOutput = OutputResponse[sys, UnitStep[t], t] // Chop

Out[5]= {2. (-1. Cos[0.707107 t] UnitStep[t] + 
    1. Cos[0.707107 t]^2 UnitStep[t] + 
    0.000707107 Sin[0.707107 t] UnitStep[t] + 
    1. Sin[0.707107 t]^2 UnitStep[t])}

In[6]:= Plot[sysOutput, {t, 0, 100}]

response.png
response.png360Ă—226 9.25 KB

4

You can get, what I think you are looking for, by doing the following.

BodePlot[tf, PlotLayout -> "Phase", PhaseRange -> {-\[Pi], \[Pi]}]

ScreenShot2015-06-22at12.28.25PM.png
ScreenShot2015-06-22at12.28.25PM.png379Ă—238 5.52 KB

In v10, an unnecessary (but mathematically not incorrect) phase lag of 360 gets added.

5

Hi David,

I got an error from sysOutput line and I don’t know why?
See file attached.

Can you help…Thanks

6

Hi Jos,

I don’t get an error when I evaluate your notebook. Perhaps some variable is defined. I suggest starting with a fresh kernel.

Best,
David

In[6]:= sysOutput = 
 OutputResponse[sys, UnitStep[t], t] // Chop  (* ERROR ?? *)

Out[6]= {2. (-1. Cos[0.707107 t] UnitStep[t] + 
    1. Cos[0.707107 t]^2 UnitStep[t] + 
    0.000707107 Sin[0.707107 t] UnitStep[t] + 
    1. Sin[0.707107 t]^2 UnitStep[t])}
7

Hi David,

Thanks, all works fine…Jos