A Rapid Synthesis Technique for the Duplicator Class of Feedback Control Systems

Abstract

A technique suitable for the rapid synthesis of the duplicator class of feedback control systems is developed. Simultaneous requirements of maximum percentage overshoot, bandwidth and velocity constant, such as commonly specified in instrument servomechanisms, are satisfied by the technique, which uniquely defines the compensation terms required to satisfy the specification. The techniques make use of the fact that many feedback control systems, irrespective of order, are dominated by a few system poles and zeros, and therefore places either one system zero, and two system poles, or an integrating dipole and two system poles in the dominant part of the s plane. Straight-line approximations to the Bode plot of amplitude ratio only are used in conjunction with a dummy transfer function, the coefficients of which are obtained directly from the performance specification by means of a universal chart. Digital computer results are given in verification of the accuracy of the technique.The approach is sufficient for the design of feedback control systems for which a linear or small perturbation model is adequate, provided the open loop dynamics can be approximated by the straight-line Bode plot. If the small perturbation model is inadequate, but a linear design approach is still chosen, the technique may be used to define trial systems for subsequent detailed nonlinear studies on the analogue computer.