New class of discrete-time models for continuous-time systems

Abstract

Digital computing in estimation, control or signal processing for continuous-time systems requires the use of discrete-time models. While conventional difference equation or z-transfer function models are widely popular, a class of methods exists that uses discrete approximations of continuous signals and operators, retaining the continuous-time parameters. Some important advantages of this class have been demonstrated in the contexts of parameter estimation, adaptive control and controller design. This paper proposes a new class of discrete-time models that originates from the z transfer function but which is close to continuous-time models in structure and parameters, thereby retaining its advantageous features. The recently proposed ‘delta’ model is seen to be a member of this class. The interrelations among various digital model types are brought out. Better sensitivity properties over z transfer function models are established. Finite word length properties of these models vis-à-vis the z-transfer functions are explored. This, it is hoped, would help motivate the use of continuous-time or similar model structures in design and implementation of digital estimators, controllers and filters for handling continuous-time systems.