Task: Determine all parameters of a oscillator which lead to stability.
The transfer function is given as:
We would like to now all parameter q1 and q2 for which the system is stable.
If you don't know yet q1 and q2 have to be both positive.
But we are using this simple example to introduce you to PARADISE.
1. As a first step we create a Simulink model:
Note: If you don't have Simulink you can use a text file to specify your model,
see the manual for more information on how to specify a model.
The Block parameters of the transfer function are entered as text:
2. Start PARADISE and load the model into PARADISE:
Typing paradise at the MATLAB prompt opens the PARADISE main window.
Now load the model:
Select the just created SIMULINK model:
3. Now let's specify the closed loop eigenvalue specifications:
Open the Gamma-Editor:
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:
Open the Parameter space window:
And select the Command: Run -> Execute grid from the menu.
PARADISE determines the boundaries my mapping the eigenvalue specifications. Use the Options->Check Stability command to check each region. In this example a simple check in the first quadrant yields the stable region (shown by a little green star, as expected).