Analysis of Sampled-Data Systems Using the w-Transform and the Modified w-Transform

Abstract

The w-transform method and the modified w-transform method are developed in this paper. The w-transform can be applied to sampled-data systems which have all samplers followed by zeroorder hold devices. The w-transform is developed utilizing the change of variable, w^-n=(e^-nsT-e^-(n+1)sT)/s, where T is the sampling period and s is the Laplace transform variable.
The w-transform is defined as W[e(t)]=E(w)=∞∑n=0e(nT)w^-n.
As the w-transform and the z-transform are the special forms of the Laplace transform, there is no great difference between them. However. the physical meaning of the sampling process using the w-transform method is clearer than that of the z-transform method.
Using the modified w-transform, we can obtain the output response at all times.
An extensive table of Gp(w)and G (w, μ)is presented in the Appendix.