Formularization Method for Calculating the Breakaway and Break-in Points and the Corresponding Gain of Root Locus Graphs

Break points, break-away and break-in points, are an essential part in root locus technique for single input single output linear invariant control systems. The importance of Break points comes from the fact that at the Break points at least two roots of the characteristic equation of the closed loop control system change their type from real to a complex at the break away point, and from complex to real at break-in point. This change affects the response of the system which can be crucial for some of systems’ applications. The conditions for being a Break point are analysed and a new formulated systematic method for finding the Break points and their corresponding gains is presented. An efficient algorithm was developed and can be solved analytically. There is no mathematical differentiation during calculation, and the algorithm can be programmed easily. The developed algorithm is applicable for any order of transfer function of a linear invariant control system. This method is compared with other common methods to show its merits and effectiveness.