Re: Help with a function for plotting zeros and poles

• To: mathgroup at smc.vnet.net
• Subject: [mg132450] Re: Help with a function for plotting zeros and poles
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Wed, 19 Mar 2014 04:23:28 -0400 (EDT)
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• References: <20140315074645.B9C5E6A3E@smc.vnet.net>

```Clear[zeroPole]

zeroPole[tf_TransferFunctionModel] :=
{Re[#], Im[#]} & /@
Flatten[
Through@
{TransferFunctionZeros, TransferFunctionPoles}@
tf];

tf1 = TransferFunctionModel[
(3 (13/8 + s))/(2 (3/2 (13/8 + s) + s (1 + s) (2 + s) (5 + s))), s];

tf2 = TransferFunctionModel[
(199 + 344 s)/(16 (s (1 + s) (2 + s) (5 + s) + 1/16 (199 + 344 s))), s];

N@zeroPole[tf1]

{{-1.625, 0.}, {-0.5, 0.}, {-0.5, 0.}, {-5.08114, 0.}, {-1.91886, 0.}}

N@zeroPole[tf2]

{{-0.578488, 0.}, {-0.5, 0.}, {-5.97986,
0.}, {-0.760068, -1.89264}, {-0.760068, 1.89264}}

Bob Hanlon

On Sat, Mar 15, 2014 at 3:46 AM, Eduardo M. A. M. Mendes <
emammendes at gmail.com> wrote:

> Hello
>
> Sometime ago I found a couple of functions that are used for plotting the
> poles and zeros of a transfer function.  Here they are:
>
>
> xyPoints[values_]:=Module[{xy},xy=Flatten[Replace[values,{Complex[x_,y_]:>{x,y},x_?NumericQ:>{x,0}},{3}],1];Cases[xy,{_?NumericQ,_?NumericQ},{2}]
> ];
>
> zeroPole[tf_]:=Module[{zp,zp0},zp0=Through@
> {TransferFunctionZeros,TransferFunctionPoles}@tf;
> zp=FixedPoint[ReplaceAll[#,{}->{-100}]&,zp0];
> xyPoints/@zp];
>
> zeroPole is a modification of the actual plot function (I have only
> removed the plot command).
>
> Here are two examples of using the functions
>
> tf1=TransferFunctionModel[(3 (13/8+s))/(2 (3/2 (13/8+s)+s (1+s) (2+s)
> (5+s))),s]
> tf2=TransferFunctionModel[(199+344 s)/(16 (s (1+s) (2+s) (5+s)+1/16
> (199+344 s))),s]
>
> N@zeroPole[tf1]
> {{{-1.625,0.}},{{-0.5,0.},{-0.5,0.},{-5.08114,0.},{-1.91886,0.}}}
>
> N@zeroPole[tf2]
> {{{-0.578488,0.}},{{-0.5,0.},{-5.97986,0.},{-0.760068-1.89264
> I,0.},{-0.760068+1.89264 I,0.}}}
>
> The functions does what I expected for the first example, but not for the
> second example (the real and imaginary parts of the complex poles are not
> dealt with).
>
> Can someone tell me what is wrong?   And how to modify xyPoints (Although
> I understand what the functions does I am not sure what to do)?
>
> Many many thanks
>
> Ed
>
>
>

```

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