Hi, Could anyone tell me how to extract transfer function from a non linear differential equation?

Dear Sir/ Madam,

I need to extract a transfer function from a non linear equation stated below. I have solved the equation by modelling it in simulink. I also understood that I need to use lonear analysis tool to extract transfer function. The problem which I am facing is that I am unable to configure my output port as output port is time. Could you please help me on this?

Equation is dp/dt = -(n*c*sqrt(r*t*gamma)/vs)*((ps^(2*n-1)/n)*av)/(pso^((n-1)/n)) where ps is a variable quatity and rest all values are constants

[Sulaymon Eshkabilov]

Presumably: dp/dt is meant to be d(ps)/dt since your variable is ps, right?

[Sumukh Surya]

Yes. Could you please help me getting the transfer function?

[darova]

what about ode45?

[Star Strider]

System Identification Toolbox

Integrate your differential equation, then use the time variable and integrated function to estimate the transfer function.

[Sumukh Surya]

Could you please elaborate on this?

I have solved for the equation which means I have the variation of ps with respect to time. I now need to calculate Ps(s)/T(s) . Please find attached document using which I have solved the non linear differential equation

Answer 1

[Grufff]

Sorry, my memory of control engineering is VERY hazy... but I think you need to apply the Laplace transform.

The transfer function of a system is the system output over the system input, all represented in the complex s domain. Your function/s are currently in the time domain, so apply the Laplace transform to system input and output and express as a ratio, that's your transfer function.

Answer 2

[Sumukh Surya]

Hi, I understand that I need to take Laplace transform for obtaining the transfer function. But to find the transfer function for the equation shown above, manual effort might take more time. Hence I prefer doing it in MATLAB

[Grufff]

Well, then have you tried using the

laplace

command available within MATLAB?

The documentation, with examples, is here:

https://uk.mathworks.com/help/symbolic/laplace.html?s_tid=doc_ta

Answer 3

[Sumukh Surya]

Thanks I got the transfer function :)

[Marwan Adel]

how could you get it ??????

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