Analysis of Non-linear Sampled-data Control Systems by a Method of Linear Response Correction†

Abstract

ABSTRACT The method of analysis outlined in this paper proceeds by developing an equivalent linear system having the same response to a given test input as would be obtained with the same input applied to the non-linear system. An analysis of the equivalent linear system then makes possible the evaluation of the system response The transformation from the non-linear system to its linear equivalent is made by forming a secondary input sequence, called a correction sequence, the response to which combines with the response to the test input to maintain the correct amplitude relationship between signals developed at the point of non-linearity In this paper the procedure is adapted to the Z-transform method of analysis and gives the exact response at sampling instants. No restriction is placed on the form of the non-linearity but the method is restricted in application to systems in which the non-linearity is directly associated with a data-hold circuit It is possible quickly to observe the effects of modification of the transfer characteristic of the non-linearity so that the method can form the basis of a procedure for developing improved systems by shaping of the non-linearity As a demonstration of the method, an example is given of the analysis of a particular problem.