How to simulate the time response of a linear dynamic system?

Hello forum, I have a dynamic model of a linear system (A, B, C and D matrices) and so it is known the FRF (H) of it. In particular, H is known for the whole range of frequency and it is as follows:

Now, I would define a certain input signal (let say D1) so that the response of my system is equal to a signal with a constant amplitude of 5 (for example) and phase 0. For this reason, my drive is designed as follows:

But the time response of my system, calculated with lsim it is something completely different.

Can you explain why?

[Star Strider]

‘Can you explain why?’

Perhaps, but definitely not without seeing your code.