This example shows a interesting unstable region.
The characteristic polynomial is given by:
his polynomial contains a bilinear term q1*q2, which can be handled by PARADISE.
Note: See Examples 1 + 2 for PARADISE usage hints.
1. Simulink model:
The Simulink model is as simple as it can be:
2. Start PARADISE and load the model into PARADISE:
Start PARADISE by typing paradise at the MATLAB prompt
and load the Simulink model into PARADISE.
We treat parameters q1 and q2 as varying. Parameter rsqr is fixed at 0.25.
3. Eigenvalue specifications:
We are interested in Hurwitz stability, i.e. all eigenvalues have to lie to the left of the imaginary axis.
Use Real part limitation as a boundary for the desired eigenvalue region.
4. Parameter Space:
After specifying the model and the eigenvalue specifications we can determine the stable regions in the q1-q2 plane.
Open the Parameter space window and use the Command: Run -> Execute grid to determine the stable regions.
As we can see from the following picture there is a single stable region, containing a circular unstable region.
5. Uncertainty in rsqr
So far we treated the parameter rsqr as fixed. Let's look how the stable region changes as we vary rsqr.
The parameter specifications are given as:
rsqr is varying in the range [.1; 1]. We use 3 grid points, i.e. PARADISE will determine the stability boundaries for
rsqr = [.1 .45 1].
Using the command: Run -> Execute grid we get the stability boundaries:
As we see the shape of the stable region does not really vary with parameter rsqr. But the radius of the circular unstable region changes with rsqr.
Well you might have noticed the area of the circle is proportional to rsqr.