Sarah Spurgeon heads an established research team of international repute. Work is largely concerned with the development of practically realisable nonlinear control strategies which yield robust performance in the presence of uncertainty, and the design of robust condition monitoring schemes. The theoretical tools use unique properties of differential equations with discontinuous right-hand sides which provide total robustness to a substantial class of parameter changes and external disturbance signals. Essentially, the output response of the differential equation is invariant despite the presence of uncertain parameters and external disturbance signals. Dynamic performance requirements are met by prescribing an appropriate manifold and ensuring the trajectories of the system of interest are constrained to lie on the manifold by selection of an appropriate discontinuous injection signal.
Many control problems are solved with the assumption that full state information is available to the control law. This is often a limiting assumption in practice as some physical quantities will be difficult or expensive to measure. In this situation it is common to employ an observer to estimate unmeasurable states from a subset of measured state information and input information. The team has been at the forefront of developments in the area of sliding mode observers. Here, the manifold is a function of the error between the measured and estimated states and a discontinuous injection signal is used to force the error to zero. This ensures the generation of a set of estimated states for use by the control law which exactly correlate with the measured signals obtained from the plant.
The robustness of such sliding mode controller and observers is achieved because the applied discontinuous injection signal causes the plant, or observer, to experience 'on average' a signal which exactly cancels the effects of any unmodelled parameter variations or external disturbance signals. This injection signal is thus a potentially useful source of information. For example, if the model used to define the observer represents nominal, healthy operation of a plant or process, any deviation in the average value of the applied discontinuous injection signal from zero can be interpreted as an indication of 'abnormal' operating conditions. Further, appropriate analysis of the applied injection signal can enable precise information concerning the nature of the fault or parameter variation to be ascertained.
From the springboard of such successful fundamental research has developed an exciting and continuing programme of experimental research that is currently receiving a great deal of industrial interest and support. Current key research themes include:
- Output feedback control of time delay systems
- Application of output sampling and the development of controllers with memory for discrete sliding mode control and reconfiguration
- Condition monitoring for robust dynamic reconfiguration of engineering systems
- Development of control and estimation strategies for bioprocesses and the food and drink industry
- Application of modelling and simulation tools from engineering to the analysis of pathalogical gait
- Development of controller and observer strategies for nonminimum phase systems
- Advanced control of fusion plasma
- Output feedback control for uncertain variable structure systems with resets
- Development of robust control and estimation paradigms for networked control systems
Additional mathematical modelling, based on the numerical solution of differential equations, has been developed to study biological systems. A coarse-grain model of the red blood cell membrane, based on molecular dynamics, has been implemented which is able to reproduce membrane thermal fluctuations. As part of this work a theoretical method to quantify elastic moduli of 2- dimensional membrane embedded in the 3-dimensional space and in contact with a thermal reservoir has been proposed for the first time. The combination of experiments, molecular dynamics model and elastic theory enables the derivation of elastic moduli of red blood cells; the technique is currently used to identify differences between normal and diseased cells and to explain microcirculatory changes in some blood diseases in patients with sepsis.
Furthermore, a reaction-diffusion model, based on the solution of diffusion equations, has been implemented to study cell signalling in the ovary and in the intestine. This work proposes a novel approach for the spatial analysis of cell signalling to identify likely sources of regulatory molecules. This approach has wide applicability within many branches of cell biology for studying spatial signalling within tissues and cells. For example, findings from this work have been used to target the identification of bone-morphogenetic protein antagonists in the ovary. Moreover, the approach, combining experiment and mathematical modelling, allowed measuring the extracellular serotonin concentration in the intestine, and allowed the characterisation of transmission properties of different intestine tissues and the efficacy of pharmacological agents.