Fixed time step solver stability

Fixed time step solver stability

Switching from a variable time step solver to a fixed time step solver is a prerequesite for using a model for Real-Time study. To ensure numerical stability and real-time target limitation, the value of the fixed time step has to be in a dedicated range that depends on the model.

For explicit system a criteria for fixed time step simulation with explicit integration method is provided. Four integration methods are available:

• Euler

• Runge-Kutta 2nd order

• Runge-Kutta 3rd order

• Runge-Kutta 4th order

This criteria denotes the possible maximal value to ensure stable fixed time step simulation with a solver using the selected integration method for the current system during the whole simulation time range.

Note

For more information on numerical stability, please refer to the fixedstep_and_stability demo example.

This value of the criteria is displayed at the bottom of the plot. This is the maximal integration time step to be used that guarantees of getting the same results using the selected fixed time step solver. In addition the corresponding linearization time is given so that by using the localization button the cursor is activated and positionned on this time.

Figure 43: Integration method stability conditions

Note

The eigenvalues table includes a dedicated column that lists, for each eigenvalue, the maximum fixed time step to be used depending on the selected integration method.

Eigenvalues stability region

Figure 44: Eigenvalues - Stability region tab

The eigenvalues at a specific time and the stability region contour of the selected integration method are displayed as a graph. The eigenvalues are displayed in green if they are inside the stability region and red otherwise.

Figure 45: Eigenvalues stability region graph

Zooms

To better visualize the eigenvalues, use the button to zoom in, zoom out, or pan the graph.

Note

At animation start, eigenvalues are sometimes superimposed. This is due to a huge stability area, itself due to high damped mode for near pure oscillatory eigenvalues. Use the zoom options to see all eigenvalues.

Eigenvalue position

You can use the button:

• to obtain the precise position of a given eigenvalue,

• to obtain a precise position on the integration method's stability domain contour.

Integration method visualization

As already mentioned, there are four integration methods available. They can be chosen using the Integration method drop-down menu available under Numerical stability region.

Figure 46: Integration methods

Each integration method is parameterized by a time step 'h', the stability domain area of Runge-Kutta nth order is defined as follows:

By default the stability region of the selected integration method is displayed for a time step equal to 0.1 ms. This value corresponds to the minimum integration step that can be used in order to run the model on a Real-Time target.

This time step can be changed using the Target fixed time step field available under Numerical stability region.

Figure 47: Target fixed time step

Changing the time step will automatically update the stability domain in the graphical display.

Figure 48: Increasing the time step