Question

For the system given in fig. 5.49, plot the root locus of the characteristic equation as the parameter k1 is varied from 0 to [infinity] with λ = 2. Give the corresponding l(s), a(s), and b(s).

Answer 1

Plotting a root locus involves sketching how the poles of a transfer function move on the complex plane as parameter k1 varies from 0 to infinity, based on the characteristic equation 1 + K G(s)H(s) = 0. The exact construction depends on the poles and zeros of the system's open-loop transfer function and applying root locus rules.

Step-by-step explanation:

To plot the root locus of a system as the parameter k1 varies from 0 to infinity, we need to observe how the poles of the transfer function of the system move on the complex plane. The characteristic equation determines the poles of the system. For a typical control system, the characteristic equation can be represented as 1 + K G(s)H(s) = 0, where K is the gain and G(s)H(s) is the open-loop transfer function of the system.

The procedure generally involves determining the location of the poles and zeroes of the open-loop transfer function and then applying the rules of root locus construction to sketch how the poles migrate with changes in K. The terms l(s), a(s), and b(s) likely refer to parts of the characteristic equation or transfer function, but without the specific context or system diagrams, providing details on these terms is challenging.

To complete the root locus plot, one would look for all values of s that satisfy the magnitude and angle criteria given by the root locus rules. These rules take into account the number of poles versus zeros and their location relative to each other on the complex plane.