Curve of the gain margin and phase margin [control system analysis]

The root-locus method is a graphical procedure for finding the roots of the characteristic equation 1+G(s)H(s)=0 as one of the parameters of G(s)H(s) varies continuously. At first the parameter which will be varied is the gain K of the controller. The significance of this method is that it graphically shows the system's variation which allows the user to select the most appropriate value for the system's function. The aim of this investigation is to develop an analysis technique of control systems in the frequency domain. The analysis is done by obtaining and using the curve of the gain margin and phase margin (analogous to the root-locus method, but in the frequency domain and with another kind of applications). Then it is possible to determine the system's behaviour for gain variations, when these variations occur within an infinite range of values in terms of gain margins and phase margins.