How Can I Determine the Equivalent Transfer Function of Two Active LTI Systems?

[umarkhan]

hello,
If I have two LTI system in G1(s) and G2(s) and I know that for a certain fraction of the time period G1 is active and for the reminaing fraction G2 is active, then is there any method to get the equivalent transfer function ?


Umat.

 

[timthereaper]

I would think you would just have two transfer functions. Since there G1 and G2 are never active at the same time, you can't really describe it that way. At least, I don't think there is a way. Maybe I'm wrong though.

 

[Manchot]

If you're switching between the two systems, the joint system is no longer time-invariant. It's probably going to be not so simple.

 

[timthereaper]

I agree with Manchot. And since you can't have a transfer function for a non-LTI system, you'll have to describe it some other way.

 

[blue_raver22]

Hello,

Thank you for your question. In order to determine the equivalent transfer function for a switched LTI system, we can use the concept of time-averaging. This involves taking the average of the two transfer functions G1(s) and G2(s) over the time period in which they are active. This will give us the overall transfer function for the switched system.

Another method is to use the concept of state-space representation. By representing each LTI system in state-space form, we can combine them using a switching matrix to create a new state-space model for the switched system. From this, we can obtain the equivalent transfer function.

I hope this helps answer your question. If you have any further inquiries, please don't hesitate to ask.

Best regards,