Root locus of third order system

1. What is the root locus of a system?
2. What is third order transfer function?
3. How can you tell from the root locus of a system is unstable?

What is the root locus of a system?

Definition. The root locus of a feedback system is the graphical representation in the complex s-plane of the possible locations of its closed-loop poles for varying values of a certain system parameter. The points that are part of the root locus satisfy the angle condition.

What is third order transfer function?

Consider the third order differential transfer function: We start by multiplying by Z(s)/Z(s) and then solving for Y(s) and U(s) in terms of Z(s). We also convert back to a differential equation. We can now choose z and its first two derivatives as our state variables. Now we just need to form the output.

How can you tell from the root locus of a system is unstable?

The root locus procedure should produce a graph of where the poles of the system are for all values of gain K. When any or all of the roots of D are in the unstable region, the system is unstable. When any of the roots are in the marginally stable region, the system is marginally stable (oscillatory).