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

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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?

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