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?
You can represent a closed loop sytem 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.
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.
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.