Use of a coordinate transformation in the incremental phase plane

A coordinate transformation in the incremental phase plane is introduced which facilitates the design of sampled-data control systems in which there is a simple non-linearity. Use of these coordinates permits the slope of a boundary specified by the nonlinearity to be directly related to a simple gain term in the transformed system. A realizable form of compensation is shown to evolve in terms of the system variables. By using the transformed coordinates, it is possible to identify intersample oscillations which are undetectable in the original coordinate system. Examples are presented to illustrate the method.