Calculating Root Locus Gain

        These problems are intended to increase you skill at computing root locus gain.

Problem 1.

        Determine the root locus gain at the points indicated on the plot below.

After you have calculated the gain at the three points indicated, answer these questions.

A.  What is the gain at point 1 - the green point?

B.  What is the gain at point 2 - the blue point?

C.  What is the gain at point 3 - the purple point?

D.  Do your calculations support the root locus rule that says that closed loop poles start at open loop poles for low gain and move away from the open loop poles along the root locus as the gain increases?  Explain why your data does or does not support that conclusion.


Problem 2

         Determine the root locus gain at the points indicated on the plot below.

After you have calculated the gain at the three points indicated, answer these questions.

A.  What is the gain at point 1 - the green point?

B.  What is the gain at point 2 - the blue point?

C.  What is the gain at point 3 - the purple point?

D.  Do your calculations support the root locus rule that says that closed loop poles start at open loop poles for low gain and move away from the open loop poles along the root locus as the gain increases?  Explain why your data does or does not support that conclusion.

E.  Determine the root locus gain at the point on the locus which has the smallest damping ratio.

F.  For the point at s = -4, there is another closed loop pole somewhere on the root locus.  Estimate where that pole is and explain your reasoning for your conclusion.

Problem 3

         Determine the root locus gain at the points indicated on the plot below.

After you have calculated the gain at the three points indicated, answer these questions.

A.  What is the gain at point 1 - the green point?

B.  What is the gain at point 2 - the blue point?

C.  What is the gain at point 3 - the purple point?

D. Determine the root locus gain at the point on the locus which has the largest damping ratio.