Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001
· Consider the basic transform tables. A superficial examination will show that the denominator (bottom terms) are the main factor in determining the final form of the solution. To explore this further, consider that the roots of the denominator directly impact the partial fraction expansion and the following inverse Laplace transfer.
· When designing a controller with variable parameters (typically variable gain), we need to determine if any of the adjustable gains will lead to an unstable system.
· Root locus plots allow us to determine instabilities (poles on the right hand side of the plane), overdamped systems (negative real roots) and oscillations (complex roots).
· Note: this procedure can take some time to do, but the results are very important when designing a control system.
· Consider the previous example, the transfer function for the whole system was found, but then only the denominator was used to determine stability. So in general we do not need to find the transfer function for the whole system.
