Get transfer function from data and known input

Hey there :)

So this is what I know about the system:

• The system is a second order system
• The input is u(t) = 2·1(t)
• A structure has been given to me with y(t) against t(sec)

When I plot it I get this graph:

What I need:

I need to find the trasnfer function for the conditions above.

I know that I can find it analytically by finding Mp, Zeta, Wn and etc...

Is there a shortcut to find the transfer function?

I tried working with systemIdentification and tfest but both ways ask me to give the number of poles and zeros which I don't know + I can't tell the program that the data is for the input u(t) = 2·1(t).

This is what I get from systemIdentification tool, but I might be using it wrong:

The code:

data = iddata(Struc.y, Struc.time, 1*10^(-4));
plot(Struc.time, Struc.y, '--r');
hold 'all'
step(tf1)

%tf1 is generated from the systemIdentification tool and data

tnx!

[Walter Roberson]

number of poles is 0 unless there are some for negative or complex values.

number of zeros is possibly 1, unless there are more at negative or complex

That said, if you were to subtract approximately 15 you might get an infinite number of 0s.

[Walter Roberson]

What would you get for something like 12*sin(t)*exp(-t)+15 ?

Answer 1

[Star Strider]

If you know that the system is second-order, use the ssest funciton and specify the order as 2. (State space representations are the best optionos in any event.) You can then use the tf function to convert it to a transfer function.

[Or Perez]

It works with 100% fit. but the transfer function I got describes the data, without knowing that the data is plotted for the input u(t) = 2·1(t). So when I use step function on the tf I get a graph that doesn't match the data.

I need somehow to get step(2*tf) to match the plotted data.

thank you for your previous answer!

[Star Strider]

My pleasure!

To change the step amplitude to 2:

opt = stepDataOptions;

opt.StepAmplitude = 2;

figure

step(sys,opt)

This is described in Response to Custom Step Input.

EDIT — (31 May 2022 at 14:31)

Also, use the compare funciton to check the extimation result.

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[Or Perez]

You are truely a life saver.

Thank you sir!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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