2 - Z Transforms

Abstract

This chapter discusses the z transform along with its advantages and limitations. The z transform is a powerful method for solving linear, shift invariant difference equations. For many systems that can be adequately modeled by such difference equations, the z transform is an invaluable tool for control system design. When dealing with control systems, a distinction needs to be drawn between a real physical phenomenon and the signal that represents it in a control system model. The chapter lists some of the important properties of the z transform—namely, delay, linearity, first difference, summation, final value theorem, and initial value theorem. The z transform is a fine tool for analyzing general system behavior, specifically for predicting how a system will respond to inputs in general. The chapter also briefly describes frequency response analysis and its use in bringing measured system response data into the realm of z-domain analysis, without actually needing to have a z-domain model of the system.