Strategies for non-uniform rate sampling in digital control theory

This thesis is about digital control theory and presents an account of methods for enabling and analysing intentional non-uniform sampling in discrete compensators. Most conventional control algorithms cause numerical problems where data is collected at sampling rates that are substantially higher than the dynamics of the equivalent continuous-time operation that is being implemented. This is of relevant interest in applications of digital control, in which high sample rates are routinely dictated by the system stability requirements rather than the signal processing needs. Considerable recent progress in reducing the sample frequency requirements has been made through the use of non-uniform sampling schemes, so called ‘alias-free’ signal processing. The approach prompts the simplification of complex systems and consequently enhances the numerical conditioning of the implementation algorithms that otherwise, would require very high uniform sample rates. Such means of signal representation and analysis presents a variety of options and thus is being researched and practiced in a number of areas in communications. However, the control communities have not yet investigated the use of intentional non-uniform sampling, and hence the ethos of this research project is to investigate the effectiveness of such sampling regimes, in the context of exploiting the benefits. Digital control systems exhibit bandwidth limitations enforced by their closed-loop frequency requirements, the calculation delays in the control algorithm and the interfacing conversion times. These limitations pave the way