Second Order Differential Equation with Constant to Transfer Function
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I wish to obtain the transfer function
for the below system:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370318/image.png)
This would be a simple second order system except for the constant
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370324/image.png)
Applying the laplace transform assuming a stationary initial condition gives
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370327/image.png)
It is easily seen that the above expression is implicit in
and
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370330/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370333/image.png)
Could anyone offer advice on how to obtain the transfer function
for this system?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370318/image.png)
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Réponses (2)
Aman Vyas
le 6 Oct 2020
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:
Hope it helps !
Paul
le 8 Oct 2020
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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