How to reduce a leapfrog block diagram to find transfer function

[pnjbi]

Hi,

I'm having some trouble reducing a leapfrog block diagram shown in the attachment. I want to find the transfer function but I don't know how to reduce the portions which "leapfrog". I can reduce the feedback loops G1 and G4 but not too sure on where to go from there.

Any help is appreciated.
Thanks!

 

[berkeman]

Sorry that I'm not much help on this one, but it would seem that you would need to write simultaneous equations for each summing node, and solve the system of equations. Kind of analogous to using the KCL to solve for the behavior of a circuit.

 

[pnjbi]

Thanks for the response Berkeman.
I think you might be right. Could you show a quick example of how I can proceed using matlab?
I was thinking of using the sym function but I've also been told that I could use ode45 functions (although I'm not familiar with ode45 functions).

Thanks.

 

[user101]

type "help ode45"