Singular Perturbations and Order Reduction in Control Theory - An Overview

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-72-C-0259U.S. Air Force / AFOSR 73-257

Stabilising falling liquid film flows using feedback control

Falling liquid films become unstable due to inertial effects when the fluid layer is sufficiently thick or the slope sufficiently steep. This free surface flow of a single fluid layer has industrial applications including coating and heat transfer, which benefit from smooth and wavy interfaces, respectively. Here, we discuss how the dynamics of the system are altered by feedback controls based on observations of the interface height, and supplied to the system via the perpendicular injection and suction of fluid through the wall. In this study, we model the system using both Benney and weighted-residual models that account for the fluid injection through the wall. We find that feedback using injection and suction is a remarkably effective control mechanism: the controls can be used to drive the system towards arbitrary steady states and travelling waves, and the qualitative effects are independent of the details of the flow modelling. Furthermore, we show that the system can still be successfully controlled when the feedback is applied via a set of localised actuators and only a small number of system observations are available, and that this is possible using both static (where the controls are based on only the most recent set of observations) and dynamic (where the controls are based on an approximation of the system which evolves over time) control schemes. This study thus provides a solid theoretical foundation for future experimental realisations of the active feedback control of falling liquid films

Microbiological, pathological and histological findings in four Danish pig herds affected by a new neonatal diarrhoea syndrome

BACKGROUND: Neonatal diarrhoea is a frequent clinical condition in commercial swine herds, previously regarded to be uncomplicated to treat. However, since 2008 it seems that a new neonatal diarrhoeic syndrome unresponsive to antibiotics and common management practices has emerged. Routine laboratory examinations have not detected any pathogen related to this syndrome. The primary purpose of this study was to evaluate if well-known enteric pathogens could be associated with outbreaks of neonatal diarrhoea, thus question the hypotheses of a new syndrome. Furthermore, we wanted to evaluate macroscopic and microscopic findings associated with these outbreaks and if possible propose a preliminary piglet-level case-definition on syndrome New Neonatal Porcine Diarrhoea syndrome (NNPDS). RESULTS: Four well-managed herds experiencing neonatal diarrhoea with no previously established laboratory conclusion and suspected to suffer from New Neonatal Porcine Diarrhoea Syndrome, were selected. Within these herds, 51 diarrhoeic and 50 non-diarrhoeic piglets at the age of three to seven days were necropsied and subjected to histological and microbiological examination. Faeces were non-haemorrhagic. Neither enterotoxigenic E. coli, Clostridium perfringens type A or C, Clostridium difficile, rotavirus, coronavirus, Cryptosporidium spp, Giardia spp, Cystoisospora suis nor Strongyloides ransomi were associated with diarrhoea in the investigated outbreaks. Macroscopically, the diarrhoeic piglets were characterized by filled stomachs and flaccid intestines without mucosal changes. The predominant histological lesions were villous atrophy in jejunum and ileum. Epithelial lesions in colon were seen in one third of the case piglets. CONCLUSIONS: The results of the study supported the hypothesis that a new neonatal porcine diarrhoea was present in the investigated herds, since no known pathogen(s) or management factors could explain the diarrhoeal outbreaks. Based on the findings in the four herds the following case-definition of NNPDS was suggested: Non-haemorrhagic diarrhoea during the first week of life, without detection of known infectious pathogens, characterized by milk-filled stomachs and flaccid intestines at necropsy

Disturbance Observer

Disturbance observer is an inner-loop output-feedback controller whose role is to reject external disturbances and to make the outer-loop baseline controller robust against plant's uncertainties. Therefore, the closed-loop system with the DOB approximates the nominal closed-loop by the baseline controller and the nominal plant model with no disturbances. This article presents how the disturbance observer works under what conditions, and how one can design a disturbance observer to guarantee robust stability and to recover the nominal performance not only in the steady-state but also for the transient response under large uncertainty and disturbance

Multimodeling, Singular Perturbations and Chained Aggregation of Large Scale Systems

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryDepartment of Energy / US ERDA EX-76-C-01-208

Global stabilization of the oscillating eccentric rotor

The oscillating eccentric rotor has been widely studied to model resonance capture phenomena occurring in dual-spin spacecraft and rotating machinery. This phenomenon arises during spin-up as a resonance condition is encountered. We consider the related problem of rotor despin. Specifically, we determine nonlinear feedback control laws that not only despin the rotor but also bring its translational motion to rest. These globally asymptotically stabilizing control laws are derived using partial feedback linearization and integrator backstepping schemes. For the case in which the oscillating eccentric rotor is excited by a translational sinusoidal forcing function, the control law is shown to attenuate the amplitude of the translational oscillation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43319/1/11071_2004_Article_BF00114798.pd

Methods of model reduction for large-scale biological systems: a survey of current methods and trends

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed