Digital Control Law Synthesis in the w' Domain

Utility of w' transform domain analysis/synthesis procedures for linear, constant, single-rate sampled-data systems is explored. Basic properties of the wf domain are reviewed and compared with corresponding Z-,H>-, and s-domain properties. The main contribution of the paper is recognition that sampling and data-hold operations are modeled exactly in the w' domain, regardless of the sampling rate employed, and that the w' variable is analogous to the s variable in the sense that all familiar frequency domain design concepts, procedures, and interpretations can be carried over directly. Moreover, the imaginary part of w' approximates angular frequency to for Ico 1 < ir/lT, which further facilitates interpretation. Two example applications illustrate the procedure and make clear (by means of transfer functions and Bode plots) the nonminimum phase effects of sampling and data-hold operations and of sampling rate. It is demonstrated that acceptable closed-loop performance can be achieved at sampling rates that are an order of magnitude less than those employed when an emulation design approach is used.