Root Locus Problem

Root Locus Problem
Problem RLocus9
(Derived from Problem RLocus5)

Dr, Abner Mallity needs your help. He has been working on a system, and he got his two grad students - Willy Nilly and Millie Farad involved. Here is the transfer function of the system, and a block diagram for the system.

G(s) = 5(s - s_z)/[(s + 1)(s + 3)(s + 5)]

The system is being controlled in a feedback system as shown below.

Mallity's problem is that due to various things changing within the system there is a zero that can move and be anywhere on the negative real axis. His grad students say that can present problems. He doesn't see that. He claims the following is true.

No matter where the zero is, the real axis segments are always in the LHP.
Since there are three poles and one zero there are only two poles that go to infinity.

Since there are only two branches that go to infinity, they go at +90^o and -90^o.
Therefore - no problem.

Malllity is convinced that this system will never be unstable, and that it doesn't matter what gain value you have for K, or where the zero is. The trouble is, he can't prove it, and can't convince Willy and Millie that he is right. As a matter of fact, they claim that is not true and he is getting very angry about the whole deal.

Help Mallity out. His personal pride is at stake. Show that the system is always stable for any gain or zero position.