How to get a transfer function for a dynamic model that is only a function of time?

Thank you for your time!

If you have a nonlinear dynamic model like this

where y is the output and u is the input. You can linearize it using taylor series in order to be able to get the trasnfer function easier.

What about if you dynamic model that is only a function of time?

and you know y0 = f(t0)

Does matlab have any tool to acomplish this?

I want to get a transfer function for a dynamic model that is enterely a function of time.

Answer 1

[Guru Mohanty]

Hi, I understand you are trying get transfer function from a differential equation having only one variable i.e. time. It can be done using MATLAB symbolic toolbox.

1. Define variables using syms.
2. Form the differential equation.
3. Set Initial Condition.
4. Get the solution using dsolve.

Here is a sample code for your reference.

clc;
clear all;
syms y(t) 
eqn = diff(y,1)==exp(t)*sin(t); % Differential Equation
cond = y(0)==0;                 % Initial Condition
y_sol = dsolve(eqn,cond);