Control System Synthesis by Root Locus Method

The root locus method determines all of the roots of the differential equation of a control system by a graphical plot which readily permits synthesis for desired transient response or frequency response. The base points for this plot On the complex plane are the zeros and poles of the open loop transfer function, which are readily available. The locus of roots is a plot of the values of s which make this transfer function equal to - 1 as loop gain is increased from zero to infinity. The plot can be established in approximate form by inspection and the significant parts of the locus calculated accurately and quickly by use of a simple device. For multiple loop systems, one solves the innermost loop first, which then permits the next loop to be solved by another root locus plot. The resultant plot gives a complete picture of the system, which is particularly valuable for unusual systems or those which have wide variations in parameters.