Application of the Continuation Method to Root Locus. A Natural Homotopy System

The homotopy continuation method has been employed to solve many chemical engineering problems involving nonlinear equations. It has not been employed to draw root locus in process control. The application of the continuation method makes it possible to draw root locus more accurately and more efficiently, particularly for control systems with a time delay. For such systems, two problems related to the starting points and the crossings must be solved first. Methods to locate the starting points and to handle crossings are also discussed.