Professor Keith Godfrey

Work in this area is focused on obtaining data-based models of processes using analysis in the frequency domain. The models may be non-parametric (frequency responses) or parametric (for linear systems, Laplace transfer functions or z-transfer functions). When working in the frequency domain, it is possible to design perturbation signals for particular purposes, for example, obtaining the best linear approximation to a nonlinear system, or characterising the nonlinearity itself; these have very different design requirements. For instance, to obtain a good linear approximation, it is very helpful to use a signal with harmonic multiples of 2 and 3 missing, while to characterise a nonlinearity, it is desirable that all harmonics are present; even then, some types of signal are better than others for this purpose.

We have available a comprehensive range of signal designs, both computer-optimised from the MATLAB Frequency Domain System Identification Toolbox, and binary and multilevel signals with fixed power spectra. Recent applications have been to a large-scale model of a zinc coating process at British Steel Strip Products at Port Talbot, and to the simulation of a process whose dynamics are different according to whether the output signal is increasing or decreasing - such departure from linearity occurs in many practical examples.

The work is also being applied to the design of autotune controllers. These are three-term (proportional + integral + derivative) controllers in which the parameters of the three terms are adjusted automatically. Most industrial autotune controllers make use of a relay to cause the loop to limit cycle; this interrupts normal control operation while the tuning update is done. Our objective is to perform the tuning update during normal operation, by adding a small amplitude perturbation signal and processing the system input and output signals in the frequency domain.

Funding for this work has been from EPSRC, and there has been considerable collaboration with research teams at the Multimedia University in Malaysia, the University of Wales Swansea, and the Vrije Universiteit, Brussels. Through the latter collaboration, we are members of ICCoS (Identification and Control of Complex Systems), a research programme between the Universities of Delft, Linkoping, Stanford, Warwick and five Belgian Universities.

Dr Ai Hui Tan did her Final Year Undergraduate Project at Warwick on the topic of Frequency Domain System Identification. She then stayed on to do a PhD under the supervision of Professor Keith Godfrey, in which she made use of many of the techniques in this area. She is now a Lecturer in the Faculty of Engineering of the Multimedia University, Cyberjaya, Malaysia, where she heads a research team working on system identification and control.

A binary signal of period N = 86 with no even harmonics, generated using the prs MATLAB package, together with its Discrete Fourier Transform and three periods of its power spectrum. The package, developed by Dr. Tan as part of her research, includes routines for generating many different classes of perturbation signals. It can be accessed (free of charge) at http://www.eng.warwick.ac.uk/eed/dsm/prs.htm