Implementing PID Controller into system

Hi, I am currently trying to use Simulink to use a PID to control a closed-loop system, comparing a real out to an approximated one given by a first-order transfer function with delay, as seen in the first attachment.

I know how to design a PID controller in a general case, but trying to integrate it into my system to produce an output for both the real and approximated system is proving difficult and was wondering if anyone could help. The second attachment shows my attempt whilst the third output gives an idea of what I want my output/scope to show.

This is probably too vague but any guidance will help!

Thanks!

[Arkadiy Turevskiy]

It is not clear what you want to do. Do you want the closed loop response to match the putput of that first order transfer function with time delay?