Abstract
An investigation of the characteristics of some commonly occuring frequency response loci is given and some errors in the existing literature of frequency response are exposed and corrected. A method for deriving transfer functions from restricted frequency response data is presented and shown to lead to satisfactory results for low order systems. A novel technique for the automatic display of frequency response loci using an analogue computer is then given. In particular the method enables pure time delay effects to he considered without the need for a pure time delay unit. Root locus properties are considered in relation to sensitivity and some contributions to root locus theory are made as a by-product of this work. Sensitivity effects are further considered for parameter changes related to pole and zero changes. This leads to the development of analogue computer circuits for sensitivity investigations. The work on polynomial formation for the automatic frequency response plotting indicated a more general approach, leading to the development of analogue computer circuits for the formation of orthonormal polynomials and related special functions, and circuit realisations are given for a number of important forms. It is then shown that a viable analogue computer method can be developed to enable Wiener's method of analysis and synthesis, based on orthornormal expansions, to be used. Finally an appendix is given which includes a study of the all-pass network compensation of third-order type 1 systems. This study was initiated by the work on frequency response loci which disclosed a number of design methods, the one included being selected for further discussion as it led to some original work on system compensation. Supporting publications are appended relating to developments of linear theory for frequency response and root locus methods and also to experimental methods of frequency response determination.