Operations on transfer function model

Question

Suppose I have a transfer function defined via TransferFunctionModel, e.g. tf == TransferFunctionModel[{{1/s}}, s]. How can I perform operations on tf, e.g. multiplication. As an example, I may want to use it as follows RootLocusPlot[k tf, {k, 0, 10}] which does not work.

Is there a way to extract a transfer function model such that it can be modified, e.g. similar to the way Normal works for StateSpaceModel?

Answer 1

You Just use the tf, with no k multiplied in the call to RootLocusPlot.

The k goes to the tf it self. Like this

sys = TransferFunctionModel[k*(s^2 + 2 s + 4)/(s (s + 4)(s + 6)(s^2 + 1.4 s + 1)), s];
RootLocusPlot[sys, {k, 0, 100}, 
    ImageSize -> 300, 
    GridLines -> Automatic, 
    GridLinesStyle -> Dashed, Frame -> True, AspectRatio -> 1]

Is there a way to extract a transfer function model such that it can be modified, e.g. similar to the way Normal works for StateSpaceModel

I am not sure what you mean. the tf, is the polynomial ratio in s you had at the start, so you have this allready. You can always go First@tf to get it again.

Answer 2

You can do this with the mathematica model connections. For the full list see http://reference.wolfram.com/language/guide/ModelConnections.html

For example using the function SystemsModelSeriesConnect:

tf = TransferFunctionModel[{{1/s}}, s];

SystemsModelSeriesConnect[TransferFunctionModel[k, s], tf]

Output is the gain, k multiplied by the original transfer function. You can do more complex multiplications and parallel combinations, feedback arrangements, etc. with the various connections.

Answer 3

You could try this:

tf = TransferFunctionModel[{{1/s}}, s]
ClearAttributes[Times, Protected];
Times[k_, TransferFunctionModel[m_, s_]] := 
    TransferFunctionModel[k m, s]
SetAttributes[Times, Protected];

But you would have to modify a lot of operations.