Design of sampling servo systems in the z-plane

The paper summarizes the basic concepts of the sequence-transform theory, particularly emphasizing the non-physical form of samples assumed for mathematical convenience. In dealing with inverse transforms, it introduces some typical transient modes due to poles of the transform function Y(z). It is shown that the root-locus method is well suited to the design of sampling control systems; also that the passage of time can be described by a system of moving zeros in the complex z-plane. This provides a complete picture of the response of a system to a given input, both at the sampling instants and between them. Barker has suggested a particular form of stabilizing network which has the advantage of introducing a modifying function U(z) which is independent of the rest of the system. This work has been extended by showing the limitations of the method and by giving a table of the networks required to realize some functions U(z). Finally, two examples are worked out in some detail to illustrate the theory, and a brief description of an experimental unit is included for completeness.