ABSTRACT
This chapter shows how the discrete models can be applied to sampled-data systems. It explains how open-and closed-loop transfer functions in z can be derived for digital control systems. The chapter explores the effect of changing gain and sampling rate on the closed-loop behaviour of simple digital control systems. It describes how the root-locus technique can be used in the z-plane. The chapter also explains the link between the s- and z-planes. The Laplace transform is first used to work out the (continuous) response of the plant to the rectangular pulse. Providing the plant can be modelled as a linear system, the hold, plant and output sampler can be characterized by a linear difference equation or a transfer function in z. Note that for one particular value of K, the closed-loop pulse transfer function consists of a single pole at the origin of the z-plane.
