Poles and Zeroes

Further information: Wikibooks, MIT Poles Zeros

The Root Locus plot indicates the areas where our system is unstable, marginally stable and fully stable:

Poles = frequencies where denominator becomes zero

Zeros = frequencies where numerator becomes zero

The values of poles and zeros of a system determine its stability.

For physically realizable control systems: number of poles (denominator) >= number of zeros (numerator).

Addition of poles to the transfer function has the effect of pulling the root locus to the right, making the system less stable. Addition of zeros to the transfer function has the effect of pulling the root locus to the left, making the system more stable.

all poles of the system must have negative real parts, and therefore they must all have the form (s + l) for the system to be stable.

Example: