An approach to the estimation of errors in linear transfer functions

Abstract

Of increasing interest is the investigation of the effects of parameter variations on the response of control systems. Whereas much of the work in the analysis of errors may be accomplished by large scale computers, the need exists for a fairly simple scheme of estimating errors resulting from variations in the internal elements of a system. The information provided would find application both in determining the desirability of using a computer and in checking the results of computer solutions. A method is presented for estimating the errors in the frequency response of control systems caused by large as well as by small variations in the component parts. Also presented is a method by which these errors in response may be determined exactly. The results obtained will be correct within the limits possible in the graphical techniques required by the method. Incremental sensitivity, which serves to measure the effect of a large change in a parameter, is defined in terms of the general problems of error analysis. Examples are given to illustrate the method of approximating errors in open loop and in closed loop systems.