Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Inner–Outer Factorization for Nonlinear Noninvertible Systems

This paper considers inner–outer factorization of asymptotically stable nonlinear state space systems in continuous time that are noninvertible. Our approach will be via a nonlinear analogue of spectral factorization which concentrates on first finding the outer factor instead of the inner factor. An application of the main result to control of nonminimum phase nonlinear systems is indicated.

Fault detection in nonlinear systems: an observer-based approach

An un-permitted deviation of at least one characteristic property or parameter of a system from standard condition is referred as a fault. Faults result in reduced efficiency of the system, reduced quality of the product, and sometimes complete breakdown of the process. This not only causes economic losses but may also result in fatalities. An early detection of faults can assist to avert these losses. Therefore, fault detection and process monitoring is becoming an essential part of modern control systems. Fault detection in linear dynamical systems has been extensively studied and well established techniques exist in the literature. However, fault detection for nonlinear dynamical systems is yet an active field of research. This work is motivated by the fact that most of real systems are nonlinear in nature and there is a need to develop fault detection techniques for nonlinear systems. Observer-based methods for fault detection have proven to be among the most capable approaches, therefore, this research is focused towards these methods. The first step in observer-based fault detection is to generate a symptom signal, called the residual signal, which carries the information of faults. This is done by comparing the measurements from the process to their estimates generated by an observer (filter). It is desired that the residual signal is sensitive to faults and robust against disturbances. This research presents new methods for designing observer (filter) to generate residual signal which is sensitive to faults and robust against disturbances. Three types of filters are proposed in this dissertation; these include a fault sensitive filter, disturbance attenuating filter, and a filter to achieve simultaneous attenuation of disturbances and amplification of faults. Despite the disturbance attenuation property of the proposed filters, the residual signal is not completely decoupled from the effect of disturbances and uncertainties. Therefore, a threshold is needed to care for the effect of disturbances and uncertainties. Selection of threshold plays an important role in the performance of the fault detection system. If it is selected too high, some faults will not be detected. Conversely, if it is selected too low, disturbances and uncertainties will result in false alarms. This research presents a new method to determine the threshold to avoid false-alarms and to minimize missed-detections. A threshold generator is proposed which is itself a dynamic system and produces a variable threshold. This threshold changes with the effects of uncertainties and disturbances and fits more tightly to the fault-free residual signal and, hence, the performance of fault detection system is improved. In addition to the residual generation stage, the efficiency of a fault detection system can also be optimized by post-filtering. A further contribution of this research is in proposing a post-filter which operates on the residual signal to generate a modified residual signal. This modified residual signal is simultaneously sensitive to faults and robust against disturbances. Together with this post-filter, a strategy is adopted to select a threshold which maximizes the fault detectability and minimizes the number of false-alarms