.

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. . .

.

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.

0034. .

**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. **