Extension of phase plane analysis to quantized systems

Abstract

The increasing applications of numerical control of processes have created a need for new methods of synthesis of control equipment. The method presented is applicable to systems commanded by discretely valued inputs, and processes whose outputs may be similarly quantized. Periodic sampling is not required. The most suitable sampling is by transmission of only significant data, as the new value obtained when the data are changed by a given increment. In certain cases, transmission of data by this means can be used to increase channel capacity. When the data are so quantized, the error signal is constrained to a finite number of discrete values, each of which may be associated with an area in the phase plane. Within each such area, the trajectories of any process subject to phase plane representation are a family of parallel curves. Thus, analytic synthesis may be simplified in the case of certain nonlinear processes. Graphical design is facilitated without requiring deduction of a mathematical representation of the process. The method is illustrated by synthesis of several systems involving a simple linear process.