There are many unknowns here that might be related to the issue you are encountering.
I am assuming that you are loading sampled pre-recorded data from the workspace. Is the workspace data a timeseries object or is it a matrix with time and data components?
One important parameter here is the sampling rate at which your data was recorded. At one point in your post you mention that each time step is 0.23 seconds. Is this the sampling period at which the data is recorded?
There are several things that you could try here:
1) Make sure that the sampling time of the Simulink model is either smaller than or equal to the sampling time of your data.
2) Try using a continuous-time integrator block. If the output still looks wrong to you, try decreasing the sampling time of the model.
3) If you are able to obtain a better response with the continuous integrator, but still need to use a discrete integrator, then decreasing the sampling time of the integrator block might be helpful.
If none of these approaches help with this issue, you might try to contact the MathWorks Technical Support group.