Modeling Long-Time Dynamics in Simulink

Modeling long-time dynamics can provide insight into important issues that may be difficult to observe in field experiments. However, simply creating a long time trajectory is not enough, since it must be possible to convert the simulated trajectory data into concrete scientific conclusions. Although this analysis step is often taken for granted, it deserves further attention as large-scale long-term modeling becomes very routine.

From this point of view, I would like to ask the community about approaches to modeling large-scale long-time simulations.

Simple example:

1. Servo drive

2. Reference signal for tracking, which is extended in time by 12 hours. For the entire 12 hours, the servo drive must follow this signal.

Some considerations: it would be possible to introduce a scale-coefficient that scales the derivatives in the system, reducing the simulation time accordingly, but if the model is complex and includes many other subsystems (for example, a power supply), then it becomes difficult to adjust all elements for time scaling.