Describing-function expressions for sine-type functional non-linearity in feedback control systems

The paper derives describing-function expressions for a sine-type functional non-linearity. In feedback control systems non-linearities of this type are encountered where synchros are used as error-sensing devices and the controlled variable undergoes large-angle variations. The characteristic curve of the non-linearity is approximated by straight-line segments over the entire angular range from ¿¿ to +¿ radians; the slopes and break-points are obtained by minimizing the mean square error between the exact and approximate characteristics. The describing-function expressions are useful for studying sustained oscillatory states of feedback systems comprising such elements. An example is given to illustrate this point.