Control system optimization studies. Volume 2: High frequency cutoff filter analysis

Abstract

The problem of digital implementation of a cutoff filter is approached with consideration to word length, sampling rate, accuracy requirements, computing time and hardware restrictions. Computing time and hardware requirements for four possible programming forms for the linear portions of the filter are determined. Upper bounds for the steady state system output error due to quantization for digital control systems containing a digital network programmed both in the direct form and in the canonical form are derived. This is accomplished by defining a set of error equations in the z domain and then applying the final value theorem to the solution. Quantization error was found to depend upon the digital word length, sampling rate, and system time constants. The error bound developed may be used to estimate the digital word length and sampling rate required to achieve a given system specification. From the quantization error accumulation, computing time and hardware point of view, and the fact that complex poles and zeros must be realized, the canonical form of programming seems preferable.