School of Electronic, Electrical and Systems Engineering

Most conventional control algorithms often fail in situations where data is collected at sampling rates that are higher than the dynamics of the underlying continuous-time process. This is of particular 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. 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 practised 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 its natural frequency, the calculation delays in the control algorithm and the interfacing conversion times. These limitations pave the way for additional phase lags within the control loop that demand very high sample rates. Since non-uniform sampling is propitious in reducing the sample frequency requirements of digital processing, it proffers the prospects of being utilised in achieving a higher control bandwidth without opting for very high uniform sample rates.

The concept, to the author's knowledge, has not formally been studied and very few definite answers exist in control literature regarding its analysis techniques. The findings adduced here begin by establishing a brief historical perspective on the use of non-uniform sampling in numerical analysis and its role for digital processing. The abstract is then applied to the problem of digital control design, and applications are further discoursed. This is followed by the implementation aspects on standard hardware.

Keywords: Digital control, non-uniform sampling, delta transform, real-time signal processing, Fourier analysis.

References (or Publications)

1. M.S.Khan, R.Goodall,R.Dixon: IMPLEMENTATION OF NON-UNIFORM SAMPLING FOR 'ALIAS-FREE PROCESSING IN DIGITAL CONTROL, UKACC, Manchester, 2008.