If you want to reproduce the response of "predict" by (manual) simulation, you will need to generate the right prediction model first for the chosen prediction horizon. Note that the prediction model uses both measured inputs and measured outputs as its inputs. That is, if your original model has 2 inputs and 1 output, the predictive model will have 2+1=3 inputs and 1 output.
For 1-step ahead prediction, the prediction model is:
x(t+1) = (A-K*C)x(t) + (B-KD)u_m(t) + Ky_m(t)
y(t) = Cx(t) + Du(t)
Here u_m is measured input signal and y_m is measured output signal. x(t) is the predicted sate sequence and y(t) is the predicted response.
For prediction to horizons N> 1 steps, you can treat is as a sequence of N 1-step ahead predictions, where the results from the previous step are treated as measured output for the next step. You can also do this with a single simulation (as in the case of 1-step ahead prediction), but the model you will need to use will be more complicated. Note that the 3rd output argument of the PREDICT command returns this model. In the help content for PREDICT, you will see:
