Example: Adding Damping Ratio Constraints :: SISO Design Tool (Using the SISO Design Tool and the LTI Viewer)

Using the SISO Design Tool and the LTI Viewer

Example: Adding Damping Ratio Constraints

This example add a damping ratio of 0.707 inequality constraint. First, type

```
load ltiexamples
sisotool(sys_dc)
```

at the MATLAB prompt. This opens the SISO Design Tool with the DC motor example imported.

From the root locus right-click menu, select Design Constraints and then New to open the New Constraint window. To add the constraint, select Damping Ratio as the constraint type. The default damping ratio is 0.707. The SISO Design Tool should now look similar to this figure.

Damping Ratio Constraints in the Root Locus

The two rays centered at (0,0) represent the damping ratio constraint. The dark edge is the region boundary, and the shaded area outlines the exclusion region. This figure explains what this means for this constraint.

You can, for example, use this design constraint to ensure that the closed-loop poles, represented by the red squares, have some minimum damping. Try adjusting the gain until the damping ratio of the closed-loop poles is 0.7.

Design Constraints for the Root Locus Design Constraints for Open-Loop and Prefilter Bode Diagrams