The integrator is used to reduce the overall error of the response so that it reaches the constant steady state 1. The low-pass is used to reduce the overshoot caused by the integrator. If i didn't get it wrong in the control engineering class. Probably have to check the notes again and run thru the MATLAB script again.
The response of TA1.jpg was made during a Lab (control engineering) at University and the Prof checked it.
Are you sure you are not confusing the step response of a transfer function with the step response of a looped system containing an integrator ? Once you close the loop, the global transfer function is not the one you mentionned but H = G/(1+G) for a unity feedback (for example), which exhibits the oscillation and the unity steady state. What you did in your control engineering classes may be the closed-loop system... -- Fabrice Silva