Question

Following the rules, sketch the root locus for K L(s)=K 1/s²+2s+10

Answer 1

To sketch the root locus for the given transfer function KL(s) = K/(s² + 2s + 10), follow the rules of locating the poles and zeros, drawing asymptotes, finding breakaway and reentry points, and sketching the root locus branches.

Step-by-step explanation:

The root locus is a graphical representation of the possible locations of the roots of a characteristic equation as a system parameter (in this case, K) varies. To sketch the root locus, we follow certain rules:

1. Locate the poles and zeros of the transfer function in the s-plane.
2. Draw the asymptotes, which are lines that approximate the behavior of the root locus at infinity.
3. Find the breakaway and reentry points, which are the values of K where the root locus starts and ends.
4. Sketch the root locus branches between the asymptotes, avoiding poles and zeros.

In this case, the transfer function is KL(s) = K/(s² + 2s + 10), where K is the system parameter. By following these rules, you can sketch the root locus for this transfer function.