Initial value and time delay SIMULINK

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I have a system that im trying to create a controller for but I can't make a good model in SIMULINK.
The system looks like the one I drawn below and the output signal should look something like the plot I've drawn. However I can't make the initial value and the time delay work at the same time. Eather I get a system with 0 time delay and with the right initial value or I get a system with 0.5s time delay and 0 as its initial value.
How should I make this system in SIMULINK.
The system is in continious time.

Accepted Answer

Kiran Felix Robert
Kiran Felix Robert on 23 Mar 2021
Hi Karl,
As your System is in continuous time,you can utilize the Transport Delay Block and the Transfer Fcn with initial outputs block (in Simulink extras) to model the initial output and the Time delay.
In order to provide the initial condition for transfer function you can convert it to its controllable canonical state-space (tf2ss) form then use the state-space block. Refer this documentation page.

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