Open Loop Representation of Closed Loop System

[QwertyXP]

I remember having studied that closed loop systems can be represented by open loop systems. But that seems weird..if it were possible for both the types of systems to have the same transfer function, why would they behave differently?

 

[TimeToShine]

The transfer functions are not the same. When you close an open loop you create a feedback network which changes the transfer function.

 

[meBigGuy]

You can represent a closed loop system by a cascade of open loop systems which eventually close the loop. Each subsection can be seen as open loop, but the overall system is closed loop. Is it possible that was being said? Or are you referring to something different.

I guess you could also analyse the loop performance in an open loop way by perturbing the input and looking at the response. This is commonly done. For example
http://www.mathworks.com/help/slcon...rol-system-for-stability-margin-analysis.html

 

[QwertyXP]

For the system given on that website:
http://www.mathworks.com/help/releases/R2013b/slcontrol/ug/singleloop_control_block_diagram.png

The closed loop transfer function would be: Tc=C(s)P(s)/(1+C(s)P(s)) as per my understanding. However, couldn't we also make an open loop system having the same transfer function? e.g. an input X(s) goes into a block, and when it comes out, it is equal to X(s)Tc.

 

[meBigGuy]

I don't know how without embedding the closed loop system inside. That isn't to say it isn't possible, just that I don't know how. What you are asking is how to make a system of form Tc=C(s)P(s)/(1+C(s)P(s)) without feedback. I'll have to think about it, but I can't right now. But your question is clear now.

 

[meBigGuy]

http://www.cds.caltech.edu/~murray/books/AM05/pdf/am06-xferfcns_16Sep06.pdf has some stuff on page 256 about block diagram algebra. But it doesn't definitively answer your question. It sort of shows the feedback system as a component.

This ppt sort of addresses it the same way:
http://www.google.com/url?sa=t&rct=...HWqHdb_mMA0pNq1uAZcM70A&bvm=bv.53899372,d.cGE

Basically you can consider a closed loop system as an open loop component whose transfer function is the same as the closed loop system. You can then use this to combine complex multi-loop systems.