Extensions to the Root Locus Method.

Analytical conditions are derived which enable the root locus shapes of many simple systems to be obtained directly from the relative positions of their open loop poles and zeros. It is also shown that the pole-zero patterns of these systems can often be normalised in order to display all possible forms of their root loci on a single map. Many previously unknown locus shapes are given and these are considered in relation to the corresponding new forms of closed loop response. A computer program is developed which enables root loci to be plotted for systems which include pure time delay or distributed lag. This extension to the method makes it possible to predict the closed loop responses of pure time delay systems directly from their root loci. It also enables these systems to be designed to achieve specified closed loop performance and provides a method of obtaining their open loop dynamics from measurements of closed loop response. The speed of the new computer algorithm makes it feasible to use root locus methods for the design of high order multiloop systems. This improved capability is illustrated for aircraft control systems. A general pole-zero method is developed which enables control laws to be chosen for a desired aircraft response throughout the complete flight envelope. The pure time delay capability of the program is then used to determine human pilot transfer functions from flight records of the pilot-aircraft response. Finally the results of this analysis are used to design improved forms of manual aircraft control systems