Question

For a system with three poles and two finite zeros: (a) 1 branch goes to infinity (b) 2 branches go to infinity (c) 3 branches go to infinity (d) 4 branches go to infinity

   For a system with three poles and two finite zeros:
(a) 1 branch goes to infinity
(b) 2 branches go to infinity
(c) 3 branches go to infinity
(d) 4 branches go to infinity

Control Engineering: An Introductory Course

Control Engineering: An Introductory Course

Jacqueline Wilkie,… 1st Edition

Chapter 13, Problem 5

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The root locus shows how the poles of a closed-loop system move as a parameter (typically the gain K) varies from 0 to infinity. Show more…

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For a system with three poles and two finite zeros: (a) 1 branch goes to infinity (b) 2 branches go to infinity (c) 3 branches go to infinity (d) 4 branches go to infinity

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Key Concepts

Asymptotes in Root Locus

When there are more poles than zeros, some branches of the root locus do not converge to finite zeros but instead tend to infinity. The number of these asymptotes is equal to the difference between the number of poles and finite zeros, indicating the directions along which the infinite branches leave the finite region in the s-plane.

Root Locus Analysis

Root locus is a graphical method used to study how the roots of a system’s characteristic equation (poles) change as a system parameter, typically gain, is varied. This analysis helps in understanding stability and transient behavior by showing the trajectories of the poles in the s-plane.

Poles and Zeros

In control theory, poles and zeros represent the roots of the denominator and numerator of a system’s transfer function, respectively. They are fundamental in understanding the system's response characteristics, with poles typically related to the natural frequencies and stability, and zeros affecting the amplitude and phase of the output.

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