Question

Sketch the root locus for variations in the value of K, for a unity feedback system that has the following forward transfer function K/(s+1)(s+2). Find the range for which the system is stable and the value at break points?

Answer 1

To sketch the root locus for the given unity feedback system, we can follow a step-by-step process to identify the open-loop transfer function and determine the poles and zeros. By analyzing the angles and magnitudes of the branches, we can sketch the root locus and find the range of K values for system stability. Additionally, we can identify the breakaway and break-in points on the root locus plot.

Step-by-step explanation:

Solution:

The root locus plot provides a graphical representation of how the poles of a system vary as the gain parameter, K, is varied. To sketch the root locus for the given transfer function, K/(s+1)(s+2), we can follow these steps:

1. Identify the open-loop transfer function by removing the feedback loop.
2. Find the poles and zeros of the transfer function.
3. Determine the angles and magnitudes of the branches of the root locus using the angle and magnitude criteria.
4. Sketch the root locus based on the determined branches, taking into account the real and complex poles and zeros.
5. Identify the range of K values for which the system is stable by analyzing the root locus plot.
6. Find the breakaway and break-in points on the root locus plot, which indicate the values of K where the poles come together and split apart.

By following these steps, you can sketch the root locus, determine the stability range, and find the break points for the given unity feedback system.