Challenges faced in resolving Algebraic Loops in SIMULINK models

[poster]

Problem Faced:

I have a SIMULINK model that has got two algebraic loops.
In order to overcome this I have set the model configuration properties as "warning".
The model runs well and has got the expected dynamics as shown in below image.

enter image description here

Now I need to convert this model to .exe which will be accessed by a GUI.
In order to do so I have to break this algebraic loop by usin a unit delay block else the build process does not execute EVEN IF the configuration properties of the simulation model has been set to "none/warning".
But in the process of using a unit delay block, entire dynamics of the solution changes which shows that its a numerical error as shown in below image..

enter image description here

I request, somebody please suggest a suitable solution in dissolving this algebraic loop error without changing the dynamics of the model.

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