Additions to sample data theory

Abstract

"In the current literature, two different approaches to sampled-data theory prevail. One approach emphasizes the z-transformation methods for design and synthesis. The other approach emphasizes the Laplace transformation methods and studies stability problems through the frequency response of the system in conjunction with the Nyquist diagram. In this paper the basic equations for the two different approaches are examined and it is shown that the forms of these equations that are accepted in the literature as being equivalent give identical results only under special conditions. The equation based on the frequency response approach is corrected in order that the two equations are equivalent. An open loop example is presented showing that the corrected equation gives the proper results. A closed-loop example is considered in conjunction with the Nyquist diagram in the complex plane and the maximum velocity constant for absolute stability is derived. This result is checked by a similar development based on z-transformation methods to show that it is correct and that the result found by methods accepted in the literature is incorrect."--Page 1.