Second Order Differential Equation with Constant to Transfer Function

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r-b0
r-b0 2020-10-3
回答： Paul 2020-10-8
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?

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回答（2 个）

Aman Vyas
Aman Vyas 2020-10-6
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 !
  1 个评论
r-b0
r-b0 2020-10-8
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.

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Paul
Paul 2020-10-8
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.

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