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7) and a rise time.

5 poles when K = 239. .

The damping ratio and natural frequency were found using the following equations which relate them to our maximum percent overshoot and settling time requirements: (2) (3).

Click Edit Æ Root Locus Æ Design Constraints then either New to add new constraints or Edit to edit existing constraints.

the. . .

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Printing/Saving the Figures. ωωn=2 rad/s Performance specification Damping ratio Damping ratio ζζ=0. Solution: The root locus may be obtained by the commands: >> den = conv([1 3 0],[1 6 64]) den = 1 9 82 192 0 >> num = [0 0 0 0 1]; >> >> % set the range of gains fine enough to figure out the right gain >> % to get 0.

6. Let’s understand with an example.

517 is represented by a radial line drawn on the s-plane at 121.

59.

The angle θ that a complex pole subtends to the origin of the s-plane. These quantities can be derived with the help of root locus method.

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In the root locus plot, MATLAB computes the percentage overshoot according to the lines of constant damping ratio (ζ).

5 Undamped natural freq.

7 are obtained by using the same MATLAB functions as those used in Example 8.

So if you want your damping ratio to be exactly \$ζ=0. . .

and the requirements are a damping ratio greater than 0. ωn=4 rad/s C(s) G(s) Controller Plant Re Im Desired pole CL pole with C(s)=1. . Damping ratio and pole location Recall 2nd—order underdamped sustem ω2 n s2 +2ζω ns + ω n2. If the above design problem had required finding closed loop poles with a particular damping ratio (or %OS), it would have been a bit more challenging to get the correct answer.

Perfoming these.

The following two equations will be used to find the damping ratio and the. Recall from the continuous Root-Locus Tutorial, we used the MATLAB function sgrid to find the root-locus region that gives an acceptable gain ().

At this point you can choose from settling time, percent overshoot, damping ratio, andal natur frequency constraints.

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

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0397 14.

I would like to automatically detect the intercept point (s) between the radial line which corresponds the damping ratio (i.