Ch. 8 Root Locus

Front 1

1. What is a root locus?

Back 1

1. The plot of a system's closed-loop poles as a function of gain

Front 2

2. Describe two ways of obtaining the root locus.

Back 2

2. (1) Finding the closed-loop transfer function, substituting a range of gains into the denominator, and
factoring the denominator for each value of gain. (2) Search on the s-plane for points that yield 180 degrees
when using the open-loop poles and zeros.

Front 3

3. If , for what value of gain is s a point on the root locus?

Back 3

3. K = 1/5

Front 4

4. Do the zeros of a system change with a change in gain?

Back 4

4. No

Front 5

5. Where are the zeros of the closed-loop transfer function?

Back 5

5. At the zeros of G(s) and the poles of H(s)

Front 6

6. What are two ways to find where the root locus crosses the imaginary axis?

Back 6

6. (1) Apply Routh-Hurwitz to the closed-loop transfer function's denominator. (2) Search along the
imaginary axis for 180 degrees.

Front 7

7. How can you tell from the root locus if a system is unstable?

Back 7

7. If any branch of the root locus is in the rhp, the system is unstable.

Front 8

8. How can you tell from the root locus if the settling time does not change over a region of gain?

Back 8

8.If the branch of the root locus is vertical, the settling time remains constant for that range of gain on the
vertical section.

Front 9

9. How can you tell from the root locus that the natural frequency does not change over a region of gain?

Back 9

9. If the root locus is circular with origin at the center

Front 10

10. How would you determine whether or not a root locus plot crossed the real axis?

Back 10

10. Determine if there are any break-in or breakaway points

Front 11

11. Describe the conditions that must exist for all closed-loop poles and zeros in order to make a second-order approximation.

Back 11

11. (1) Poles must be at least five times further from the imaginary axis than the dominant second order
pair, (2) Zeros must be nearly canceled by higher order poles.

Front 12

12. What rules for plotting the root locus are the same whether the system is a positive- or a negative-feedback system?

Back 12

12. Number of branches, symmetry, starting and ending points

Front 13

13. Briefly describe how the zeros of the open-loop system affect the root locus and the transient response.

Back 13

13. The zeros of the open loop system help determine the root locus. The root locus ends at the zeros.
Thus, the zeros are the closed-loop poles for high gain.