A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems

This is an Author's Accepted Manuscript of an article published in Antonio González (2021) A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems, International Journal of Systems Science, 52:8, 1707-1718, DOI: 10.1080/00207721.2020.1869344, available online at: http://www.tandfonline.com/10.1080/00207721.2020.1869344[EN] This paper investigates the exponential stability of uncertain time delay systems using a novel descriptor redundancy approach based on delay partitioning. First, the original system is casted into an equivalent descriptor singular state¿space representation by introducing redundant state variables so that the resulting delay is progressively reduced. From the equivalent model and applying Lyapunov Functional method, a sufficient condition based on Linear Matrix Inequalities (LMIs) for exponential stability with guaranteed decay rate performance is obtained. As a result, the inherent conservatism of Lyapunov¿Krasovskii functional techniques can arbitrarily be reduced by increasing the number of delay partition intervals including decay rate performance and model uncertainties in polytopic form. Various benchmark examples are provided to validate the effectiveness of the proposed method, showing better trade-off between conservatism and performance in comparison to previous approaches.This work was supported by project PGC2018-098719-B-I00 (MCIU/AEI/FEDER,UE).González Sorribes, A. (2021). A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems. International Journal of Systems Science. 52(8):1707-1718. https://doi.org/10.1080/00207721.2020.18693441707171852

Robust Full-Order and Reduced- Order Observers for a Class of Uncertain Switched Systems

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system

Qualitative Studies of Nonlinear Hybrid Systems

A hybrid system is a dynamical system that exhibits both continuous and discrete dynamic behavior. Hybrid systems arise in a wide variety of important applications in diverse areas, ranging from biology to computer science to air traffic dynamics. The interaction of continuous- and discrete-time dynamics in a hybrid system often leads to very rich dynamical behavior and phenomena that are not encountered in purely continuous- or discrete-time systems. Investigating the dynamical behavior of hybrid systems is of great theoretical and practical importance. The objectives of this thesis are to develop the qualitative theory of nonlinear hybrid systems with impulses, time-delay, switching modes, and stochastic disturbances, to develop algorithms and perform analysis for hybrid systems with an emphasis on stability and control, and to apply the theory and methods to real-world application problems. Switched nonlinear systems are formulated as a family of nonlinear differential equations, called subsystems, together with a switching signal that selects the continuous dynamics among the subsystems. Uniform stability is studied emphasizing the situation where both stable and unstable subsystems are present. Uniformity of stability refers to both the initial time and a family of switching signals. Stabilization of nonlinear systems via state-dependent switching signal is investigated. Based on assumptions on a convex linear combination of the nonlinear vector fields, a generalized minimal rule is proposed to generate stabilizing switching signals that are well-defined and do not exhibit chattering or Zeno behavior. Impulsive switched systems are hybrid systems exhibiting both impulse and switching effects, and are mathematically formulated as a switched nonlinear system coupled with a sequence of nonlinear difference equations that act on the switched system at discrete times. Impulsive switching signals integrate both impulsive and switching laws that specify when and how impulses and switching occur. Invariance principles can be used to investigate asymptotic stability in the absence of a strict Lyapunov function. An invariance principle is established for impulsive switched systems under weak dwell-time signals. Applications of this invariance principle provide several asymptotic stability criteria. Input-to-state stability notions are formulated in terms of two different measures, which not only unify various stability notions under the stability theory in two measures, but also bridge this theory with the existent input/output theories for nonlinear systems. Input-to-state stability results are obtained for impulsive switched systems under generalized dwell-time signals. Hybrid time-delay systems are hybrid systems with dependence on the past states of the systems. Switched delay systems and impulsive switched systems are special classes of hybrid time-delay systems. Both invariance property and input-to-state stability are extended to cover hybrid time-delay systems. Stochastic hybrid systems are hybrid systems subject to random disturbances, and are formulated using stochastic differential equations. Focused on stochastic hybrid systems with time-delay, a fundamental theory regarding existence and uniqueness of solutions is established. Stabilization schemes for stochastic delay systems using state-dependent switching and stabilizing impulses are proposed, both emphasizing the situation where all the subsystems are unstable. Concerning general stochastic hybrid systems with time-delay, the Razumikhin technique and multiple Lyapunov functions are combined to obtain several Razumikhin-type theorems on both moment and almost sure stability of stochastic hybrid systems with time-delay. Consensus problems in networked multi-agent systems and global convergence of artificial neural networks are related to qualitative studies of hybrid systems in the sense that dynamic switching, impulsive effects, communication time-delays, and random disturbances are ubiquitous in networked systems. Consensus protocols are proposed for reaching consensus among networked agents despite switching network topologies, communication time-delays, and measurement noises. Focused on neural networks with discontinuous neuron activation functions and mixed time-delays, sufficient conditions for existence and uniqueness of equilibrium and global convergence and stability are derived using both linear matrix inequalities and M-matrix type conditions. Numerical examples and simulations are presented throughout this thesis to illustrate the theoretical results

Characterisation of ignition, combustion, and flame stabilisation for gasoline-like fuels under compression-ignition conditions

The gasoline compression-ignition (GCI) concept has been proposed in recent years to circumvent the typical diesel engine NOx and soot emissions trade-off, whilst maintaining high engine efficiency. The GCI concept is commonly realised in a conventional diesel engine with heated intake air, utilising a conventional injection system and a single low-reactivity gasoline-like fuel. Combustion phasing is controlled through the injection timing, while the fast and lean combustion enables very high brake efficiency in excess of 50% with low NOx/particulate emissions across a wide range of engine loads. Additionally, this combustion mode can utilise economical and potentially widely available low-grade gasoline fuels (naphtha) with octane numbers in the range of 70-80. Despite many advantages, the ignition timing and combustion rate of GCI are very sensitive to both fuel chemistry and engine operating conditions. The lack of a fundamental understanding of ignition and combustion behaviours limits the optimisation of GCI engines. The aim of this thesis was to advance the fundamental understanding of the GCI combustion process. Characteristics of fuel-oxidiser mixing, ignition and combustion processes for gasoline-like fuels with a range of octane rating at compression-ignition (CI) engine relevant conditions were investigated. Experiments were conducted in an optically accessible constant-volume combustion chamber (CVCC), featuring well-characterised quiescent charge throughout the injection and combustion events. A single-hole axial-drilled diesel injector mounted on the back wall of the CVCC was used for fuel injections. The first part aims to assess the combustion characteristics of iso-octane (a gasoline surrogate) at CI conditions. CVCC featured an ambient gas density of 22.8 kg/m3 and an O2 concentration of 21 vol.\%. Optical techniques including natural flame luminosity, OH* chemiluminescence and shadowgraph imaging were performed to compare the combustion characteristics over ambient gas temperatures from 1000 K to 1120 K Measurements were also performed for n-heptane (a diesel surrogate) for reference purposes. Formaldehyde (CH2O) planar laser-induced fluorescence (PLIF) imaging was performed to confirm the presence of low-temperature reactions across the jet head, prior to the high-temperature ignition of iso-octane. From the measurement results, the lift-off lengths (LOLs), ignition delays (IDs) and their corresponding uncertainties for both fuels are observed to increase with lowering ambient temperature conditions. The LOLs, IDs and their uncertainties for the iso-octane flames are also consistently measured to be higher than that of n-heptane, across the tested ambient temperature range. The results reveal that the highest variability detected for the flame stabilisation distance of the iso-octane flame at the lowest tested ambient temperature condition 1000 K is attributable to the long transient stabilisation phase that it exhibits after ignition. Additional tests performed using a single-injection test case with lower octane number fuel, as well as split-injection strategies with neat iso-octane as fuel, demonstrate their potential to reduce the transient stabilisation phase of the test flames when compared with single-injection test case with neat iso-octane as fuel. The second part aims to investigate the effect of laser-induced plasma ignition (LI) on combustion behaviours of iso-octane at compression-ignition conditions. A high-energy laser was used to force the fuel ignition at a quiescent-steady environment inside the CVCC with 900 K ambient gas temperature, 22.8 kg/m3 ambient gas density and 21 vol.% O2 concentration. The diesel surrogate (n-heptane) was tested at a lower charge temperature of 735 K to offset its higher fuel reactivity than the iso-octane, such that the flames of both fuels can have a similar lift-off length. Forced laser ignition was introduced either before or after the natural autoignition timing of the fuels. The laser was focused at the jet axis 15 mm and 30 mm from the nozzle. High-speed schlieren imaging, heat release analysis and flame luminosity measurement were applied to the flames. The high-speed schlieren imaging was used to monitor the flame structure evolution of the natural ignition and LI cases. Due to laser ignition, the flame lift-off lengths decrease, with which the uncertainties in the lift-off distances reduce by more than 80 %. The laser-affected flame bases return back to the natural flame base locations. The uncertainties in the lift-off lengths also increase, as the flame stabilisation locations approach the natural lift-off distances. Under the test conditions of this work, the rates at which the iso-octane flames shift downstream are slower than in the n-heptane cases. The heat release rate profiles show high heat release from the flames following the LI events, before transitioning to lower steady values. The flame luminosity measurements indicate a strong correlation between the LI affected lift-off length and increased soot formation. The luminosity levels decrease as the flame base shifts downstream over time. The third part aims to investigate the underlying processes governing ignition and flame stabilisation in CI engine-relevant conditions. Primary reference fuels (PRFs), including PRF100 (neat iso-octane), PRF80 (a blend of 80 vol.% iso-octane and 20 vol.% n-heptane) and PRF0 (neat n-heptane), were tested to simulate changes in fuel ignition quality inside a quiescent steady environment with an ambient density of 22.8 kg/m3 and an O2 concentration of 15 vol. %. The ambient gas temperatures were controlled at 1150 K (PRF100), 1120 K (PRF80) and 900 K (PRF0), in order to adapt to the fuel reactivity so that a constant ignition delay of 1.15 ms can be achieved for all blends. This approach was employed in order to substantially reduce the effect of fuel-oxidiser mixing prior to ignition while highlighting the effect of fuel chemistry on the ignition process and flame evolution. Under the test conditions of this study, optical imaging reveals that the blends with higher iso-octane content exhibit a faster spreading of combustion after ignition and establish a steady lifted flame that is closer to the nozzle. Imaging by CH2O-PLIF indicates that blends with higher iso-octane content produce CH2O that is distributed across larger portions of the jet at an earlier timing when compared to neat n-heptane that shows a propagating first-stage ignition through the fuel jet. Supporting unsteady flamelet calculations are presented to investigate the effect of chemistry and turbulent mixing. The flamelet calculations agree qualitatively in several respects to the experiments, especially in the spatial and temporal trends for CH2O production and consumption. Synthesis of the flamelet and experimental results suggests that for the iso-octane-containing fuels, CH2O is formed via single-stage ignition reactions rather than exhibiting the typical two-stage ignition behaviour which is found in the pure n-heptane fuel case. Furthermore, the flamelet calculations suggest high-temperature ignition occurs first in lean mixtures in the iso-octane-containing fuel cases, but in rich mixtures for the PRF0 case. If autoignition is the mode of flame stabilisation, this provides an explanation for why the PRF100 and PRF80 cases stabilise further upstream, since lean mixtures have longer residence times, experience lower scalar dissipation rate, and maybe more likely to be exposed to a supporting peripheral reservoir of hot products, should one exist. Overall, this study provides insights into the roles of fuel chemistry and turbulent mixing on the ignition and combustion behaviour of PRFs under engine-relevant conditions

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau

Spray Processes in Optical Diesel Engines - Air-Entrainement and Emissions

Internal combustion engines have been an important technological field for more than a century. It has had an important impact on society through improved transportation and industrial applications. However, concerns about environmental effects of exhaust gases and utilization of oil resources have pushed development of combustion engines towards cleaner combustion and higher efficiencies. The diesel engine is today an interesting solution in terms of fuel economy. However, emissions of pollutants such as soot particles are still a major concern for diesel engines. The combustion process in diesel engines is far from fully understood and there are many to questions to be answered about emissions formation and oxidation within the combustion chamber. The objective of this work is it to gain knowledge on in-cylinder processes related to engine-out emissions. More specifically, the focus is set on understanding the connections between spray processes and the formation of pollutants such as soot particles and unburned hydrocarbons by using optical diagnostics. Engines modified for optical studies allowing optical access inside the combustion chamber have been used in the different investigations presented in this thesis. The types of engines concerned here are four-stroke heavy- and light-duty diesel engines. Even though engines are complex systems with interacting sub-systems, such as turbochargers and after-treatment devices, the focus of this work is solely on the in-cylinder processes. The focus of this thesis is fuel-jet mechanisms related to air-entrainment and emission formations. The different investigations conducted in this work can be divided in two main categories. First, air-entrainment in fuel jets and its coupling to emissions formation were studied in different optical engines. Previous results in the field, often obtained in constant volume combustion vessels, were used for prediction calculations and comparison between free jets and jets in engine environment. Second, multiple injection strategies were investigated to reduce engine-out emissions of soot and unburned hydrocarbons and also to stabilize combustion in cold conditions. The results presented in this thesis can be divided in two main categories; air entrainment in fuel jets and multiple injection strategies. The first part regards air entrainment both upstream the lift-off length and in the interaction between adjacent jets. The second part presents multiple injections strategies as a tool for combustion stabilization in cold conditions and emissions reductio

Delayed failure of software components using stochastic testing

The present research investigates the delayed failure of software components and addresses the problem that the conventional approach to software testing is unlikely to reveal this type of failure. Delayed failure is defined as a failure that occurs some time after the condition that causes the failure, and is a consequence of long-latency error propagation. This research seeks to close a perceived gap between academic research into software testing and industrial software testing practice by showing that stochastic testing can reveal delayed failure, and supporting this conclusion by a model of error propagation and failure that has been validated by experiment. The focus of the present research is on software components described by a request-response model. Within this conceptual framework, a Markov chain model of error propagation and failure is used to derive the expected delayed failure behaviour of software components. Results from an experimental study of delayed failure of DBMS software components MySQL and Oracle XE using stochastic testing with random generation of SQL are consistent with expected behaviour based on the Markov chain model. Metrics for failure delay and reliability are shown to depend on the characteristics of the chosen experimental profile. SQL mutation is used to generate negative as well as positive test profiles. There appear to be few systematic studies of delayed failure in the software engineering literature, and no studies of stochastic testing related to delayed failure of software components, or specifically to delayed failure of DBMS. Stochastic testing is shown to be an effective technique for revealing delayed failure of software components, as well as a suitable technique for reliability and robustness testing of software components. These results provide a deeper insight into the testing technique and should lead to further research. Stochastic testing could provide a dependability benchmark for component-based software engineering

New optical sensing system applied to taut wire based straightness measurement

In modern manufacturing industry, precision components are typically produced on Computer Numerical Controlled (CNC) machine tools which translate their accuracy onto machined parts. This accuracy is affected by a set of different motion errors caused by inherent imperfections in the design and build of the machine, variations in the local environment such as temperature, the cutting process itself and human factors. The reduction of these effects is achieved primarily through design improvements and error compensation techniques. The latter requires detailed knowledge about the existing errors in order to deal with them effectively. This thesis describes a novel sensor system for measurement of errors caused by deviation in the straightness of Cartesian axes present in the structural loop of most machine tools. Currently there are very few methods available to measure straightness directly, each having advantages and disadvantages when considering simplicity, accuracy and affordability. The proposed system uses a taut wire reference with a novel sensor, a two-point technique for reference error cancellation and software to enable fast and accurate measurement of straightness between any two points of the measured machine’s working volume. The standout features of the sensing system include ultra-low cost and high performance when compared with existing state-of-the-art systems. It is capable of measuring a straightness error as low as 3μm and takes only 2s of dwell time between readings, while laser interferometer requires 4s to perform averaging when measuring the same error. Existing taut wire microscopy is limited by 10-20μm of measured error depending on optics quality and manual reading takes at least 5s to minimise the human error. Setup time is also different – the new system saves 15 minutes time on 2m axis and more on longer lengths compared the laser due to simpler reference alignment procedure. Theoretical analysis and practical implementation are followed by detailed performance evaluation experiments carried out under typical manufacturing conditions comprising different machine tools, different axes, measured errors, environmental effects and alternative measuring equipment. Tests cover aspects of accuracy, repeatability and overall system stability providing a complete picture of the system’s capability and the method’s potential which is also supported by uncertainty analysis. In addition to defining setup and measuring procedures, a user-friendly software interface is described and its main units are explained with respect to overall measurement efficiency and setup fault detection