Analogue to digital transformation.
Abstract:ESDU 92044 examines the replacement of an analogue controller element by an equivalent digital controller element while retaining for the new hybrid system performance characteristics that are acceptably similar to those of the original continuous system. The main features are described of a system containing both analogue and digital elements within the same loop, and analogue-to-digital and digital-to-analogue components that are then necessarily a part of the system. The frequency response characteristics of transformation are discussed, introducing the problem of aliasing whereby a digital output can be matched by continuous sine waves of different frequencies that are then indistinguishable to the digital sampler. The need to avoid aliasing is considered and the concept of a folding frequency introduced below which aliasing is impossible. Two transformation methods for designing digital filters equivalent to analogue filters are discussed: the impulse invariance and bilinear transformations. They are compared by examining digital equivalents of such analogue filters as simple and compound first-order lag and lead filters, second-order lag filters and first-order notch filters. The methods are compared for two sampling rates using Bode plots illustrating the gain and phase variation with frequency. An example based on an electromechanical instrument servo illustrates the transformation of an analogue lag-lead controller using the bilinear transformation.
- Analogue-To-Digital Transformation
- Bode Diagram
- Control Systems
- Frequency Response
|Data Item ESDU 92044|