Differential Games Controllers That Confine a System to a Safe Region in the State Space, With Applications to Surge Tank Control

Surge tanks are units employed in chemical processing to regulate the flow of fluids between reactors. A notable feature of surge tank control is the need to constrain the magnitude of the Maximum Rate of Change (MROC) of the surge tank outflow, since excessive fluctuations in the rate of change of outflow can adversely affect down-stream processing (through disturbance of sediments, initiation of turbulence, etc.). Proportional + Integral controllers, traditionally employed in surge tank control, do not take direct account of the MROC. It is therefore of interest to explore alternative approaches. We show that the surge tank controller design problem naturally fits a differential games framework, proposed by Dupuis and McEneaney, for controlling a system to confine the state to a safe region of the state space. We show furthermore that the differential game arising in this way can be solved by decomposing it into a collection of (one player) optimal control problems. We discuss the implications of this decomposition technique, for the solution of other controller design problems possessing some features of the surge tank controller design problem

ALOHA With Collision Resolution(ALOHA-CR): Theory and Software Defined Radio Implementation

A cross-layer scheme, namely ALOHA With Collision Resolution (ALOHA-CR), is proposed for high throughput wireless communications in a cellular scenario. Transmissions occur in a time-slotted ALOHA-type fashion but with an important difference: simultaneous transmissions of two users can be successful. If more than two users transmit in the same slot the collision cannot be resolved and retransmission is required. If only one user transmits, the transmitted packet is recovered with some probability, depending on the state of the channel. If two users transmit the collision is resolved and the packets are recovered by first over-sampling the collision signal and then exploiting independent information about the two users that is contained in the signal polyphase components. The ALOHA-CR throughput is derived under the infinite backlog assumption and also under the assumption of finite backlog. The contention probability is determined under these two assumptions in order to maximize the network throughput and maintain stability. Queuing delay analysis for network users is also conducted. The performance of ALOHA-CR is demonstrated on the Wireless Open Access Research Platform (WARP) test-bed containing five software defined radio nodes. Analysis and test-bed results indicate that ALOHA-CR leads to significant increase in throughput and reduction of service delays

A New Gaussian Mixture Algorithm for GMTI Tracking Under a Minimum Detectable Velocity Constraint

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On the Semantic Approaches to Boolean Grammars

Boolean grammars extend context-free grammars by allowing conjunction and negation in rule bodies. This new formalism appears to be quite expressive and still efficient from a parsing point of view. Therefore, it seems reasonable to hope that boolean grammars can lead to more expressive tools that can facilitate the compilation process of modern programming languages. One important aspect concerning the theory of boolean grammars is their semantics. More specifically, the existence of negation makes it difficult to define a simple derivation-style semantics (such as for example in the case of context-free grammars). There have already been proposed a number of different semantic approaches in the literature. The purpose of this paper is to present the basic ideas behind each method and identify certain interesting problems that can be the object of further study in this area

Modelling of the liquid slag behaviour in the continuous casting mould

This work presents a fluid dynamics model of a continuous caster mould region, including the transient behaviour of the steel/slag interface. The research was carried out in collaboration with ArcelorMittal Research (AMR), based in Maizieres-les-Metz in France. The industrial objective of the thesis was to understand the factors affecting the transient behaviour of the liquid slag layer covering the steel and its interaction with the Submerged Entry Nozzle (SEN) jet supplying the steel from the tundish to the Continuous Casting (CC) mould. The study includes the very complex phenomenon of argon bubble transport which also affects the behaviour of the slag layer and SEN jet. The model developed in this study is based on the finite volume method with the liquid regions (steel, slag) solved in an Eulerian scheme on a fixed unstructured mesh. The interface behaviour is modelled using a number of VOF type schemes, including the time-efficient Counter Diffusion Method (CDM). A coupled Lagrangian particle tracking scheme is used to represent the presence of argon bubbles and their influence on the flowfield (mainly due to buoyancy) in conjunction with the fluctuating surface dynamics. The bulk of the research concerns comparisons against flowfield and interface data obtained from an experimental water/oil study of the process. However, the model is extended to include predictions of heat transfer and phase change in the steel and flux powder regions in an industrial CC unit and validation against available data. The three-phase model is developed making use of the unstructured mesh multi-physics finite volume code PHYSICA [1]. As stated, the main goal of this particular work has to do with the study of the dynamic behaviour of the steel/slag interface, including the effects of casting speed and injected gas. Because of the great difficulty in physical experiments with a real caster, the research is supported with water model experiments and mathematical simulation. Comparisons of observed interface profiles, measured and predicted mean and fluctuating velocities, gave an insight to the degree of coupling between interface behaviour and the fluid dynamics within the mould region. In particular, a spectral analysis of the dominant fluctuation frequencies in the water/oil experiment suggests a strong link between the upper and lower recirculation loops generated by the SEN jet as it splits after contact with the narrow face for the mould. The presence of gas bubbles alters the spectral picture, since the buoyancy induced in the flow affects the behaviour of the jet, leading to the one/two loop behaviour known from experiments. Good qualitative and quantitative agreement was achieved between the numerical results and water-model experimental data. The main observations drawn from the water model simulation and experiment are as follows: - An increase in casting speed, which is equivalent to an increase in SEN velocity leads to an increase in the amplitude of interfacial fluctuations. - At the highest SEN velocities, the oil layer is pushed away from the narrow ends of the mould, exposing the water surface to air. - When there is no oil on top of the water surface, the surface remains for all practical purpose flat. - Air entering through the SEN influences the flowfield in the mould and also disturbs the oil/water interface when it passes through it. - The ratio of water to air flow rate seems to be the most important parameter, with high air/water flow ratios leading to a change in flowfield at the top of the mould as the gas buoyancy lifts the SEN jet towards the surface. To achieve a good correlation between the experiments and the simulations a number of factors in the numerics were found to be important. These are: - The quality of the mesh used, especially in the complex transition from the SEN geometry – essentially a cylinder with two outlets set at a specific angle of 20o to the vertical, to the thin rectangular geometry of the mould which is designed to cast flat products. - The turbulence model, which was initially found to suppress interface oscillations whenever an oil layer was introduced. Various approaches were followed to overcome this problem, (a)removing the turbulence model from the oil layer, (b) using a low frequency filter to remove resolved turbulence kinetic energy from the k-ε model, (c)opting for the high order SMART numerical scheme in preference to the default Hybrid. - The interface tracking algorithm used as a default in the code PHYSICA is essentially a VOF technique with options for a Van-Leer (TVD) scheme [2] or alternative the popular Donor Acceptor scheme [3,4], both options work well but they are explicit and therefore extremely expensive computationally. Due to the size of the mesh and the CFL limit for stability, timesteps as small as 10-3s become necessary, meaning a 600s simulation could take up to 8 weeks! To overcome this, the implicit CDM scheme [5] was used, which allows the interface to spread by diffusion but then pushed back against the gradient to re-sharpen at the end of each timestep. With this scheme, timesteps up to 2 orders of magnitude larger become possible, the limit then governed by the frequency range to be resolved. A non-standard approach to the Lagrangian particle tracking scheme was adopted in the simulation with the following characteristics: - The amount of gas entering was divided into packets of equal bubble diameter and then each packet was further divided into individual tracks. The transport of 1000 and more particles tracks was used to ensure a realistic dispersion. - Tracks were updated at regular time intervals (but not necessarily at each Eulerian timestep) and then followed until they exited the calculation domain. - The residence time of particles in each cell provided information for the gas content of the cell and therefore its density. With this approach, the Navier-Stokes equations then solve for mixture (gas and liquid) and lighter cells are influenced by buoyancy. - The bubble tracks are affected by the mean velocity of the surrounding fluid and also by a stochastic component derived from the turbulence model. However, there is no direct feedback to fluid turbulence from the bubbles. To extend simulations to a real caster, heat transfer and phase change were introduced in the model, in addition to the property changes (water to steel, oil to slag, air to argon). Of importance here was the development of a solidified skin of steel on the water-cooled mould walls and also the melting of flux powder into a liquid layer on the top surface. This last component of the research was introduced to enable comparisons against plant data obtained by AMR. Of particular interest in this study was the transition from a double to a single roll recirculation in the top section of the mould, as a function of the relative quality of argon entering the SEN. The model was able to reproduce this behaviour for the cases studied. Although much has been done in developing this model of the continuous casting process it is evident that much more research is needed, especially in the case of a real caster. For example, the thermophysical property variations in the slag due to temperature, composition and mass transfer were ignored. A very simple approach was used for the phase change in steel and flux powder, although since the PHYSICA framework is modular, more sophisticated alternatives can be easily introduced. The boundary conditions for heat transfer remain uncertain and the values used in this study were obtained from the industrial partner from earlier experiments. In spite the aforementioned limitations, the model is very useful, especially in understanding the dynamic interactions between the SEN jets, and the slag/steel interface and in this respect in advance of other models used by industry

Driver Inattention During Vehicle Automation: How Does Driver Engagement Affect Resumption Of Control?

This driving simulator study, conducted as part of the EC-funded AdaptIVe project, investigated the effect of level of distraction during automation (Level 2 SAE) on drivers’ ability to assess automation uncertainty and react to a potential collision scenario. Drivers’ attention to the road was varied during automation in one of two driving screen manipulation conditions: occlusion by light fog and occlusion by heavy fog. Vehicle-based measures, drivers’ eye movements and response profiles to events after an automation uncertainty period were measured during a highly automated drive containing one of these manipulations, and compared to manual driving. In two of seven uncertainty events, a lead vehicle braked, causing a critical situation. Drivers' reactions to these critical events were compared in a between-subjects design, where the driving scene was manipulated for 1.5 minutes. Results showed that, during automation, drivers’ response profile to a potential collision scenario was less controlled and more aggressive immediately after the transition, compared to when they were in manual control. With respect to screen manipulation in particular, drivers in the heavy fog condition collided with the lead vehicle more often and also had a lower minimum headway compared to those in the light fog condition

Identifying cognitive distraction using steering wheel reversal rates

The influence of driver distraction on driving performance is not yet well understood, but it can have detrimental effects on road safety. In this study, we examined the effects of visual and non-visual distractions during driving, using a high-fidelity driving simulator. The visual task was presented either at an offset angle on an in-vehicle screen, or on the back of a moving lead vehicle. Similar to results from previous studies in this area, non-visual (cognitive) distraction resulted in improved lane keeping performance and increased gaze concentration towards the centre of the road, compared to baseline driving, and further examination of the steering control metrics indicated an increase in steering wheel reversal rates, steering wheel acceleration, and steering entropy. We show, for the first time, that when the visual task is presented centrally, drivers’ lane deviation reduces (similar to non-visual distraction), whilst measures of steering control, overall, indicated more steering activity, compared to baseline. When using a visual task that required the diversion of gaze to an in-vehicle display, but without a manual element, lane keeping performance was similar to baseline driving. Steering wheel reversal rates were found to adequately tease apart the effects of non-visual distraction (increase of 0.5 degree reversals) and visual distraction with offset gaze direction (increase of 2.5 degree reversals). These findings are discussed in terms of steering control during different types of in-vehicle distraction, and the possible role of manual interference by distracting secondary tasks

Cognitive Driver Distraction Improves Straight Lane Keeping: A Cybernetic Control Theoretic Explanation

Experimental data revealed that drivers performing a visual secondary task exhibited deteriorated lane keeping performance, but that the same drivers performing a cognitive secondary exhibited an improvement in lane keeping compared to baseline driving. In this paper we present a computational cybernetic driver model that characterizes the effect of difference in eye fixation durations between on and off road glances across the three task conditions on straight lane keeping performance. The model uses perceptual cues as control input, maintains internal representations of these cues across fixations through Bayesian updating, and each time a change in cue magnitude is perceived based on mechanisms akin to signal detection theory a change in control is applied. The model is shown to be able to capture the experimental results encouragingly well. The model also sheds light on the relative magnitude of lane keeping performance degradation caused by glancing away from the road and the fact that internal representations are degraded each time a saccade takes place. The adopted approach to modeling driver perception during and across fixations is expected to lead to new insights into the effects that various in-vehicle activities have on driving performance and risk

The need for speed: global optic flow speed influences steering

How do animals follow demarcated paths? Different species are sensitive to optic flow and one control solution is to maintain the balance of flow symmetry across visual fields; however, it is unclear whether animals are sensitive to changes in asymmetries when steering along curved paths. Flow asymmetries can alter the global properties of flow (i.e. flow speed) which may also influence steering control. We tested humans steering curved paths in a virtual environment. The scene was manipulated so that the ground plane to either side of the demarcated path produced larger or smaller asymmetries in optic flow. Independent of asymmetries and the locomotor speed, the scene properties were altered to produce either faster or slower globally averaged flow speeds. Results showed that rather than being influenced by changes in flow asymmetry, steering responded to global flow speed. We conclude that the human brain performs global averaging of flow speed from across the scene and uses this signal as an input for steering control. This finding is surprising since the demarcated path provided sufficient information to steer, whereas global flow speed (by itself) did not. To explain these findings, existing models of steering must be modified to include a new perceptual variable: namely global optic flow speed