Theory and application of error analysis for improving the performance of practical digital controllers
thesisposted on 19.12.2013, 11:22 by Michael A. Oliver
The thesis begins with an overview of the four types of error that are generated in digital filters which arise from two sources. The first source is the quantisation of time through the sampling process which gives rise to the first error type - algorithmic error. The second source of error is the quantisation of amplitude due to finite wordlength effects. Coefficient representation error (coefficient error), ADC quantisation error (ADC error) and multiple-word truncation error (truncation error) are all effects of amplitude quantisation. The shift operator commonly used in digital filters is prone to sensitivity problems especially at high sampling rates. Alternative filter operators are reviewed and advantages and disadvantages of their use are identified in enhancing the performance of digital filters. The measurement of algorithmic error and coefficient error can be carried out deterrninistically whilst ADC error and truncation error need to be treated stochastically. The thesis presents a technique to separate the deterministic error and the stochastic error in a composite output signal from a digital filter that is implemented using a high-Ievellangnage with floating-point arithmetic. This technique represents a method for validating the error analysis techniques. The error analyses presented in the thesis are used as tools to improve the performance of emulated digital filters. Each different error form varies in an individual manner with respect to changes in the sampling period. By careful selection of a sampling rate the filter performance can be improved by ensuring that the magnitudes of all the error forms are consistent with each other. Similar techniques can be used to improve the performance of digital compensators in c1osedloop control systems. Careful consideration of the duration of the sampling interval needs to be observed to ensure that the stability of the closed-loop system is adequate. This method of determining the controller parameters is used to exploit the digital control hardware to its fullest potential, and is automated in software; details are described in the thesis.
- Mechanical, Electrical and Manufacturing Engineering