A method of analysing the effect of certain kinds of non-linearity in closed-cycle control systems

A method is described by which the characteristic effects of the inclusion of certain non-linear relationships in an otherwise linear system may be determined. It is further shown how, by the choice of suitable parameters for recording the results of such calculations, considerable generality may be given to such results. The possibilities are illustrated by discussion of the following topics:- (a) The effect of a non-linear multiplier in the main sequence, the particular example being taken of saturation at various stages of the main sequence, producing the phenomenon of "repeated overshoot" and a prolonged "settling-down time." (b) The effect of a non-linear multiplier in a feedback sequence, the particular example being taken of speed-dependent friction acting on a load, producing the phenomenon of jerky motion at low speeds. (c) The effect of non-linearities of more complicated kinds than simple non-linear multipliers, the particular example being taken of backlash in gearing, producing sustained oscillation. The method of calculation of time functions of response which is described is one in which equally spaced ordinates of the time functions are calculated in succession, a relationship being established by which the value of each successive ordinate depends upon a group of immediately preceding ordinates.