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I looked at your model, one issue that I noticed is that in the External Mode tab, the "decimation" value under "Sampling" is too large. One of my colleagues explained what this setting does in this answer here. In your model, the sample time is 1e-4, and you are asking for 1000 samples. If the decimation setting is 1, you will receive 1000 samples, with each point sampled at 1e-4 sample time. If the decimation setting is 100, you will still receive 1000 samples, but each point is now sampled at 1e-4*100=0.01 sample rate. So you will have lower resolution on the received waveform, if the decimation setting is higher.
For example in your model, if you apply a sine wave of frequency 50 Hz at the Analog In port of the RT Box, with your current decimation setting (100), you will notice a distorted sine wave at the scope of ADC, as shown in the attached screenshot.
If you decrease the "decimation" to 10, or 1, you will see the waveform that you're expecting.
As for applying a constant value, I am seeing a small deviation of about 0.1-1%, which is expected from ADC sampling. How much deviation are you seeing from the requested value? Are you able to share a screenshot?