Numerical Simulation Problems Part 1

I just ran a series of tests on the updated model I was discussing yesterday. For the models with constrained and unconstrained inputs, ran the simulation for 15 seconds at at 1 millisecond time step for reference altitudes of zero meters and reference pitch angles of 15, 30, 45, 60, 75,  and 90 degrees. I compared the altitude and roll, pitch, and yaw angle plots between the models with constrained and unconstrained inputs. The following figures are my results:

Altitude plots (left side is unconstrained, right is constrained:

Figure 1: Altitude at 15 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 2: Altitude at 30 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 3: Altitude at 45 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 4: Altitude at 60 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 5: Altitude at 75 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 6: Altitude at 90 degree ref pitch for (left) unconstrained and (right) constrained models

Until the 75 degree pitch angle case, the two models perform equally, as there is no noticeable difference in the plots. For the 75 and 90 degree pitch cases, the model with unconstrained inputs is stable, while the model with constrained inputs goes unstable. The point at which the constrained model goes unstable is approximately 6 seconds for the 75 degree pitch angle case, while it is approximately 4 seconds for the 90 degree pitch angle case. These results likely indicate a problem with numerical instability.

The following plots show the reference pitch angles for the unconstrained vs constrained models:

Figure 7: Pitch at 15 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 8: Pitch at 30 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 9: Pitch at 45 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 10: Pitch at 60 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 11: Pitch at 75 degree ref pitch for (left) unconstrained and (right) constrained models

Figure 12: Pitch at 90 degree ref pitch for (left) unconstrained and (right) constrained models

As was the case when comparing altitude, the two models perform similarly for pitch angles from 15 to 60 degrees, and the constrained model goes unstable for 75 degree and 90 degree pitch angles.

I have more to say, but I apparently can't fit it into a single blog post. Please see "Part 2" for more details.