Nonlinear Control Design for an Air-breathing Engine with State Estimation

A nonlinear control design approach is presented in this paper for a challenging application problem of ensuring robust performance of an air-breathing engine operating at supersonic speed. The primary objective of control design is to ensure that the engine produces the required thrust that tracks the commanded thrust as closely as possible by appropriate regulation of the fuel flow rate. However, since the engine operates in the supersonic range, an important secondary objective is to ensure an optimal location of the shock in the intake for maximum pressure recovery with a sufficient margin. This is manipulated by varying the throat area of the nozzle. The nonlinear dynamic inversion technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs have also been carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, an extended Kalman Filter based state estimation design has been carried out both to filter out the process and sensor noises as well as to make the control design operate based on output feedback. Promising simulation results indicate that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing system.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

The problem with teamwork: A discursive investigation

- Background Teamwork sits comfortably within the vocabularies of most physical education teachers. It is used to both describe and prescribe student behaviour in a variety of physical and sport-related activities. Yet while supporters of sport and PE have readily employed the term, remarkably few pedagogues have taken the time to consider what teamwork refers to, let alone what it means to teach it. - Focus of study In this paper, we examine practitioners' constructions of teamwork. - Participants and setting Data were generated with seven physical education teachers (four male and three female) at a state-funded secondary school near Brisbane, Australia. The teachers ranged in experience from three months to more than 30 years. - Research design The investigation was a case study of one physical education department at a secondary school. - Data collection Three interviews were conducted with each of the teachers. The first was biographical in nature and covered themes such as education and sporting experiences. During the second interviews, teachers produced examples and statements on the topic of teamwork as it occurs within their lessons. The material from the second set of interviews was explored in the final set where the teachers were invited to elaborate on and explain comments from their previous interviews. - Analysis Data were considered from a discursive-constructionist perspective and attention was given to linguistic and grammatical features of the teachers' commentary as well as the cultural relevance of the utterances. The notion of ‘interpretive repertoires’ – essentially cultural explanations bounded by particular socio-linguistic features – provided the central unit of analysis. - Findings The teachers in the project made use of an array of discursive resources to make sense of teamwork. These constructions often bore little resemblance to one another or to existing theories of teamwork. In some cases, the teachers offered vague descriptions or drew on alternative concepts to make sense of teamwork. - Conclusions Without a certain level of agreement in their everyday usage, teachers' constructions of teamwork fail to be convincing or useful. We maintain that a more substantive conceptualisation of teamwork is needed in the field of sport pedagogy and offer suggestions on how this might be accomplished.

Robust THP Transceiver Designs for Multiuser MIMO Downlink with Imperfect CSIT

We present robust joint nonlinear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for interuser interference precancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of CSIT errors. The first model is a stochastic error (SE) model, where the CSIT error is Gaussian-distributed. This model is applicable when the CSIT error is dominated by channel estimation error. In this case, the proposed robust transceiver design seeks to minimize a stochastic function of the sum mean square error (SMSE) under a constraint on the total BS transmit power. We propose an iterative algorithm to solve this problem. The other model we consider is a norm-bounded error (NBE) model, where the CSIT error can be specified by an uncertainty set. This model is applicable when the CSIT error is dominated by quantization errors. In this case, we consider a worst-case design. For this model, we consider robust (i) minimum SMSE, (ii) MSE-constrained, and (iii) MSE-balancing transceiver designs. We propose iterative algorithms to solve these problems, wherein each iteration involves a pair of semidefinite programs (SDPs). Further, we consider an extension of the proposed algorithm to the case with per-antenna power constraints. We evaluate the robustness of the proposed algorithms to imperfections in CSIT through simulation, and show that the proposed robust designs outperform nonrobust designs as well as robust linear transceiver designs reported in the recent literature.

A Combinatorial Optimization Problem for High Order PODs with Few Sensors

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

The Problem of Implementation and its Relation to the Philosophy of Cognitive Science

According to certain arguments, computation is observer-relative either in the sense that many physical systems implement many computations (Hilary Putnam), or in the sense that almost all physical systems implement all computations (John Searle). If sound, these arguments have a potentially devastating consequence for the computational theory of mind: if arbitrary physical systems can be seen to implement arbitrary computations, the notion of computation seems to lose all explanatory power as far as brains and minds are concerned. David Chalmers and B. Jack Copeland have attempted to counter these relativist arguments by placing certain constraints on the definition of implementation. In this thesis, I examine their proposals and find both wanting in some respects. During the course of this examination, I give a formal definition of the class of combinatorial-state automata , upon which Chalmers s account of implementation is based. I show that this definition implies two theorems (one an observation due to Curtis Brown) concerning the computational power of combinatorial-state automata, theorems which speak against founding the theory of implementation upon this formalism. Toward the end of the thesis, I sketch a definition of the implementation of Turing machines in dynamical systems, and offer this as an alternative to Chalmers s and Copeland s accounts of implementation. I demonstrate that the definition does not imply Searle s claim for the universal implementation of computations. However, the definition may support claims that are weaker than Searle s, yet still troubling to the computationalist. There remains a kernel of relativity in implementation at any rate, since the interpretation of physical systems seems itself to be an observer-relative matter, to some degree at least. This observation helps clarify the role the notion of computation can play in cognitive science. Specifically, I will argue that the notion should be conceived as an instrumental rather than as a fundamental or foundational one.

Global and EU governance for sustainable forest management with special reference to capacity building in Ethiopia and Southern Sudan

The purpose of this study was to produce information on and practical recommendations for informed decision-making on and capacity building for sustainable forest management (SFM) and good forest governance. This was done within the overall global framework for sustainable development with special emphasis on the EU and African frameworks and on Southern Sudan and Ethiopia in particular. The case studies on Southern Sudan and Ethiopia focused on local, national and regional issues. Moreover, this study attempted to provide both theoretical and practical new insight. The aim was to build an overall theoretical framework and to study its key contents and main implications for SFM and good forest governance at all administration levels, for providing new tools for capacity building in natural resources management. The theoretical framework and research approach were based on the original research problem and the general and specific aims of the study. The key elements of the framework encompass sustainable development, global and EU governance, sustainable forest management (SFM), good forest governance, as well as international and EU law. The selected research approach comprised matrix-based assessment of international, regional (EU and Africa) and national (Southern Sudan and Ethiopia) policy and legal documents. The specific case study on Southern Sudan also involved interviews and group discussions with local community members and government officials. As a whole, this study attempted to link the global, regional, national and local levels in forest-sector development and especially to analyse how the international policy development in environmental and forestry issues is reflected in field-level progress towards SFM and good forest governance, for the specific cases of Southern Sudan and Ethiopia. The results on Southern Sudan focused on the existing situation and perceived needs in capacity building for SFM and good forest governance at all administration levels. Specifically, the results of the case study on Southern Sudan presented the current situation in selected villages in the northern parts of Renk County in Upper Nile State, and the implications of Multilateral Environmental Agreements (MEAs) and of the new forest policy framework for capacity building actions. The results on Ethiopia focused on training, extension, research, education and new curriculum development within higher education institutions and particularly at the Wondo Genet College of Forestry and Natural Resources (WGCF-NR), which administratively lies under Hawassa University. The results suggest that, for both cases studies, informed decision-making on and capacity building for SFM and good forest governance require comprehensive, long-term, cross-sectoral, coherent and consistent approaches within the dynamic and evolving overall global framework, including its multiple inter-linked levels. The specific priority development and focus areas comprised the establishment of SFM and good forest governance in accordance with the overall sustainable development priorities and with more focus on the international trade in forest products that are derived from sustainable and legal sources with an emphasis on effective forest law enforcement and governance at all levels. In Upper Nile State in Southern Sudan there were positive development signals such as the will of the local people to plant more multipurpose trees on farmlands and range lands as well as the recognition of the importance of forests and trees for sustainable rural development where food security is a key element. In addition, it was evident that the local communities studied in Southern Sudan also wanted to establish good governance systems through partnerships with all actors and through increased local responsibilities. The results also suggest that the implementation of MEAs at the local level in Southern Sudan requires mutually supportive and coherent approaches within the agreements as well as significantly more resources and financial and technical assistance for capacity building, training and extension. Finally, the findings confirm the importance of full utilization of the existing local governance and management systems and their traditional and customary knowledge and practices, and of new development partnerships with full participation of all stakeholders. The planned new forest law for Southern Sudan, based on an already existing new forest policy, is expected to recognize the roles of local-level actors, and it would thus obviously facilitate the achieving of sustainable forest management.

Nonlinear Sliding Mode Control Design for an Air-breathing Engine with State Estimation

A modern system theory based nonlinear control design is discussed in this paper for successful operation of an air-breathing engine operating at supersonic speed. The primary objective of the control design of such an air-breathing engine is to ensure that the engine dynamically produces the thrust that tracks a commanded value of thrust as closely as possible by regulating the fuel flow to the combustion system. However, since the engine operates in the supersonic range, an important secondary objective is to manage the shock wave configuration in the intake section of the engine which is manipulated by varying the throat area of the nozzle. A nonlinear sliding mode control technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs are also carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, to filter out the sensor and process noises and to estimate the states for making the control design operate based on output feedback, an Extended Kalman Filter based state estimation design is also carried out. The promising simulation results suggest that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing engine.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the "sampling interval" used in the measurement for both "steady-state" and "finite" initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A "deterministic approximation" is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.

Joint Source-Channel Coding over a Fading Multiple Access Channel with Partial Channel State Information

In this paper we address the problem of transmission of correlated sources over a fast fading multiple access channel (MAC) with partial channel state information available at both the encoders and the decoder. We provide sufficient conditions for transmission with given distortions. Next these conditions are specialized to a Gaussian MAC (GMAC). We provide the optimal power allocation strategy and compare the strategy with various levels of channel state information.

Steady compressible flow of granular materials through a wedge-shaped hopper: The smooth wall, radial gravity problem

A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

Impedance parameters and the state-of-charge. III. Zinc-manganese dioxide and magnesium-manganese dioxide dry batteries

The problem of non-destructive determination of the state-of-charge of zinc- and magnesium-manganese dioxide dry batteries is examined experimentally from the viewpoint of internal impedance and open-circuit voltage at equilibrium. It is shown that the impedance is mainly charge-transfer controlled at relatively high states-of-charge and progressively changes over to diffusion control as the state-of-charge decreases in the case of zinc-manganese dioxide dry batteries. On the other hand, the impedance is mainly diffusion controlled for undischarged batteries but becomes charge-transfer controlled as soon as there is some discharge in the case of magnesium-manganese dioxide batteries. It is concluded that the determination of state-of-charge is not possible for both types of batteries by the measurement of impedance parameters due to film-induced fluctuations of these parameters. The measurement of open-circuit voltage at equilibrium can be used as a state-of-charge indicator for Zn-MnO2 batteries but not for Mg-MnO2 batteries.

Impedance parameters and the state-of charge. I. Nickel-cadmium battery

The problem of nondestructive determination of the state-of-charge of nickel-cadmium batteries has been examined experimentally as well as theoretically from the viewpoint of internal impedance. It is shown that the modulus of the impedance is mainly controlled by diffusion at all states of charge. Even so, a prediction of the state of charge is possible if the equivalent series/parallel capacitance or the alternating current phase shift is measured at a sufficiently low a.c. test frequency (5–30 Hz) which also avoids inductive effects. These results are explained on the basis of a uniform transmission-line analog equivalent circuit for the battery electrodes.