| Using the SISO Design Tool and the LTI Viewer | |
Design Constraints for the Root Locus
For the root locus, you have the following constraint types:
Use the Constraint Type menu to select a design constraint. In each case, to specify the constraint, enter the value in the Constraint Parameters panel. You can select any or all of them, or have more than one of each.
If you specify a settling time in the continuous-time root locus, a vertical line appears on the root locus plot at the pole locations associated with the value provided (using a first-order approximation). In the discrete-time case, the constraint is a curved line.
Specifying percent overshoot in the continuous-time root locus causes two rays, starting at the root locus origin, to appear. These rays are the locus of poles associated with the percent value (using a second-order approximation). In the discrete-time case, In the discrete-time case, the constraint appears as two curves originating at (1,0) and meeting on the real axis in the left-hand plane.
Note that the percent overshoot (p.o.) constraint can be expressed in terms of the damping ratio, as in this equation.
Specifying a damping ratio in the continuous-time root locus causes two rays, starting at the root locus origin, to appear. These rays are the locus of poles associated with the damping ratio. In the discrete-time case, the constraint appears as curved lines originating at (1,0) and meeting on the real axis in the left-hand plane.
If you specify a natural frequency, a semicircle centered around the root locus origin appears. The radius equals the natural frequency.
Region Constraint
Specifying a region of the complex plane causes a line to appear between the two specified points, with a shaded region below the line.
| | Creating and Editing Design Constraints | Example: Adding Damping Ratio Constraints | |
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is the damping ratio.