ABSTRACT
This chapter explores several methods of digital filter synthesis. These methods are all based on the assumption that the filter or compensator has been originally specified as a continuous-time filter or compensator either as an s-domain transfer function or the equivalent impulse response function or differential equation. The impulse invariant method revolves around the fact that a continuous time filter may be specified by its impulse response function h(t). The design of digital control systems is the process of choosing the difference equations or equivalent z-domain transfer functions for either cascade or feedback compensators, which will, when combined with the dynamics of the continuous-time plant, yield acceptable performance from the completed closed-loop system. The chapter discusses conversion of an s-domain transfer function H(s) into a discrete-time transfer function H(z) or an equivalent difference equation. It aims to derive the bilinear transformation or A. Tustin’s method from the point of view of numerical integration.
