Second Order Differential Equation with Constant to Transfer Function

I wish to obtain the transfer function for the below system:

• 

This would be a simple second order system except for the constant .

Applying the laplace transform assuming a stationary initial condition gives

It is easily seen that the above expression is implicit in and .

Could anyone offer advice on how to obtain the transfer function for this system?

Answer 1

[Aman Vyas]

Hi,

You can simply model the equation in simulink using block level design (integrator for integration purposes, gain block for multiplier etc). This will more or less correspond to solving differential equations.

Alternatively in matlab directly you can define numerator and denominator and then can use commands to calculate in time domain and frequency domain

For more information and good examples on transfer function you can refer to following documentation link:

https://www.mathworks.com/help/control/ref/tf.html

Hope it helps !

[r-b0]

Alternatively in matlab directly you can define numerator and denominator

There in lies the issue. The equation is implicit and it is not possible to factor into a transfer function. The proposed techiniques will not work for the described system.

Answer 2

[Paul]

If c2 is a constant, there is no transfer function from U to Y because that is not the differential equation for a linear, time invariant system.