Digital control needs discrete time models, but conversion from continuous time, fed by a zero order hold, to discrete time introduces sampling zeros which are outside the unit circle, i.e. non-minimum phase (NMP) zeros, in the majority of the systems. Also, some systems are already NMP in continuous time. In both cases, the inverse problem to find the input required to maintain a desired output tracking, produces an unstable causal control action. The control action will grow exponentially every time step, and the error between time steps also grows exponentially. This prevents many control approaches from making use of inverse models. The problem statement for the existing stable inverse theorem is presented in this work, and it aims at finding a bounded nominal state-input trajectory by solving a two-point boundary value problem obtained by decomposing the internal dynamics of the system. This results in the causal part specified from the minus infinity time; and its non-causal part from the positive infinity time. By solving for the nominal bounded internal dynamics, the exact output tracking is achieved in the original finite time interval. The new stable inverses concepts presented and developed here address this instability problem in a different way based on the modified versions of problem states, and in a way that is more practical for implementation. The statements of how the different inverse problems are posed is presented, as well as the calculation and implementation. In order to produce zero tracking error at the addressed time steps, two modified statements are given as the initial delete and the skip step. The development presented here involves: (1) The detection of the signature of instability in both the nonhomogeneous difference equation and matrix form for finite time problems. (2) Create a new factorization of the system separating maximum part from minimum part in matrix form as analogous to transfer function format, and more generally, modeling the behavior of finite time zeros and poles. (3) Produce bounded stable inverse solutions evolving from the minimum Euclidean norm satisfying different optimization objective functions, to the solution having no projection on transient solutions terms excited by initial conditions. Iterative Learning Control (ILC) iterates with a real world control system repeatedly performing the same task. It adjusts the control action based on error history from the previous iteration, aiming to converge to zero tracking error. ILC has been widely used in various applications due to its high precision in trajectory tracking, e.g. semiconductor manufacturing sensors that repeatedly perform scanning maneuvers. Designing effective feedback controllers for non-minimum phase (NMP) systems can be challenging. Applying Iterative Learning Control (ILC) to NMP systems is particularly problematic. Incorporating the initial delete stable inverse thinkg into ILC, the control action obtained in the limit as the iterations tend to infinity, is a function of the tracking error produced by the command in the initial run. It is shown here that this dependence is very small, so that one can reasonably use any initial run. By picking an initial input that goes to zero approaching the final time step, the influence becomes particularly small. And by simply commanding zero in the first run, the resulting converged control minimizes the Euclidean norm of the underdetermined control history. Three main classes of ILC laws are examined, and it is shown that all ILC laws converge to the identical control history, as the converged result is not a function of the ILC law. All of these conclusions apply to ILC that aims to track a given finite time trajectory, and also apply to ILC that in addition aims to cancel the effect of a disturbance that repeats each run. Having these stable inverses opens up opportunities for many control design approaches. (1) ILC was the original motivation of the new stable inverses. Besides the scenario using the initial delete above, consider ILC to perform local learning in a trajectory, by using a quadratic cost control in general, but phasing into the skip step stable inverse for some portion of the trajectory that needs high precision tracking. (2) One step ahead control uses a model to compute the control action at the current time step to produce the output desired at the next time step. Before it can be useful, it must be phased in to honor actuator saturation limits, and being a true inverse it requires that the system have a stable inverse. One could generalize this to p-step ahead control, updating the control action every p steps instead of every one step. It determines how small p can be to give a stable implementation using skip step, and it can be quite small. So it only requires knowledge of future desired control for a few steps. (3) Note that the statement in (2) can be reformulated as Linear Model Predictive Control that updates every p steps instead of every step. This offers the ability to converge to zero tracking error at every time step of the skip step inverse, instead of the usual aim to converge to a quadratic cost solution. (4) Indirect discrete time adaptive control combines one step ahead control with the projection algorithm to perform real time identification updates. It has limited applications, because it requires a stable inverse.

Thesis (Ph.D.) -- Mississippi State University. Department of Industrial and Systems Engineering. / Title from title screen. Includes bibliographical references.

During development of a complex system, feasibility initially overshadows other concerns, in some cases leading to a design which may not be viable long-term. In particular for the case of Reusable Launch Vehicles, Operations&Maintenance comprises the majority of the vehicle's LCC, whose stochastic nature precludes direct analysis. Through the use of simulation, probabilistic methods can however provide estimates on the economic behavior of such a system as it evolves over time. Here the problem of operations optimization is examined through the use of discrete event simulation. The resulting tool built from the lessons learned in the literature review simulates a RLV or fleet of vehicles undergoing maintenance and the maintenance sites it/they visit as the campaign evolves over a period of time. The goal of this work is to develop a method for uncovering an optimal operations scheme by investigating the effect of maintenance technician skillset distributions on important metrics such as the achievable annual flight rate and maintenance man hours spent on each vehicle per flight. Using these metrics, the availability of technicians for each subsystem is optimized to levels which produce the greatest revenue from flights and minimum expenditure from maintenance.

The present work introduces a methodology to obtain a discrete time state space representation of an electrical network using the nodal [G] matrix of the Electromagnetic Transients Program (EMTP) solution. This is the first time the connection between the EMTP nodal analysis solution and a corresponding state-space formulation is presented. Compared to conventional state space solutions, the nodal EMTP solution is computationally much more efficient. Compared to the phasor solutions used in transient stability analysis, the proposed approach captures a much wider range of eigenvalues and system operating states. A fundamental advantage of extracting the system eigenvalues directly from the EMTP solution is the ability of the EMTP to follow the characteristics of nonlinearities. The system's trajectory can be accurately traced and the calculated eigenvalues and eigenvectors correctly represent the system's instantaneous dynamics. In addition, the algorithm can be used as a tool to identify network partitioning subsystems suitable for real-time hybrid power system simulator environments, including the implementation of multi-time scale solutions. The proposed technique can be implemented as an extension to any EMTP-based simulator. Within our UBC research group, it is aimed at extending the capabilities of our real-time PC-cluster Object Virtual Network Integrator (OVNI) simulator.

This dissertation comprises three essays in public finance. The first essay is a research of a theory of trading of club goods and its application to jurisdiction. The essay establishes a model of trading of club goods among clubs, and illustrates its effects on the process and outcome of club formation. Cost function as well as disutility of crowdedness is emphasized and integrated into the process of club formation, after allowing for exchanging club good among clubs. In the process, the essay develops a market for club goods. Then the model is revised and applied to the formation of jurisdictions. The second essay comes out of an interest regarding household demand, poverty and public goods in developing countries. The essay explores household food consumption in Jamaica and estimates the effects of related variables. With Jamaica Survey of Living Conditions 2001 data, the essay estimates an Engel curve which reflects the relation between household food consumption and related variables. What’s more, to investigate the possible neighborhood effect on food consumption, the essay tests and estimates the spatial correlation among neighborhood food consumption. The estimated results can be applied to poverty reduction policy. The third essay extends the theme of poverty, consumption, and government programs by analyzing one other public program—education. Education is closely linked to poverty alleviation. Determining the demand for education and the return to education will help government focus programs aimed at reducing drop-out rates and in the long run, poverty in the country. The essay applies discrete time survival analysis techniques to analyze education duration in Jamaica. Based on Jamaica Survey of Living Conditions 2002, the essay estimates the effects of household, individual and other related covariates on dropout risks of students. The essay compares discrete time Cox model and discrete time logit model and concludes that the two estimations are consistent. The estimation results could be used to predict the effects of changes in the covariates, or be used to predict the dropout risks of particular students in each grade, both of which could provide useful policy implications to improve education in Jamaica.

The purpose of this dissertation is threefold: to determine the differences in apparent prevalence and the antimicrobial susceptibility of Campylobacter spp. between antimicrobial-free and conventional swine farms; secondly, to introduce an appropriate statistical model to compare the minimum inhibitory concentration distributions of Escherichia coli and Campylobacter spp. isolated from both farm types; and thirdly, to examine the potential herd level risk factors that may be associated with antimicrobial resistance of Campylobacter spp. and E. coli isolates from finishers on antimicrobial-free and conventional farming systems. In addition, a critical review of studies that have compared the levels and patterns of antimicrobial resistance among animals from antimicrobial-free and conventional farming practices was performed. Fecal samples from 15 pigs were collected from each of 35 antimicrobial-free and 60 conventional farms in the Midwestern U.S. Campylobacter spp. was isolated from 464 of 1,422 fecal samples, and each isolate was tested for susceptibility to 6 antimicrobials. The apparent prevalence of Campylobacter spp. isolates was approximately 33 percent on both conventional and antimicrobial-free farms. The proportion of antimicrobial resistance among Campylobacter was higher for three antimicrobials within conventional compared to antimicrobial-free farms. The susceptibilities of populations of bacteria to antimicrobial drugs were summarized as minimum inhibitory concentration (MIC) frequency distributions. The use of MIC values removed the subjectivity associated with the choice of breakpoints which define an isolate as susceptible or resistant. A discrete-time survival analysis model was introduced as the recommended statistical model when MICs are the outcome. A questionnaire was completed by each farm manager on biosecurity, preventive medication, vaccines, disease history, and production management. Multivariable population-averaged statistical models were used to determine the relationships among antimicrobial susceptibility patterns and potential herd-level risk factors. Controlling for herd type (antimicrobial-free versus conventional), each antimicrobial-bacterial species combination yielded unique combinations of risk factors; however, housing type, history of rhinitis, farm ventilation, and history of swine flu were significant in more than one model. A variety of herd-level practices were associated with the prevalence of antimicrobial resistance on swine farms. Further studies are encouraged when considering interventions for antimicrobial resistance on both antimicrobial-free and conventional farms.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

Modern control design is sometimes accompanied by the challenge of dealing with nonlinear systems or plants. In some situations, due to the complexity of the plant and the unavailability of suitable models, the controls engineer opts for developing control schemes based on look-up tables. These tables, typically populated with the steady state inverse input-output characteristics of the plant, are used to compensate the plant via open-loop or closed-loop to solve the control problem. In an effort to present a new alternative, a general theoretical framework for online auto-calibration and control of general nonlinear systems is developed in this dissertation. This technique simultaneously learns the inverse input-state mapping (i.e. the calibration mapping) of the plant while forcing its state to follow a prescribed desired trajectory. The main requirements for the successful application of the novel control law are knowledge of the order of the plant and some generic data to initialize the inverse mapping. This last requirement can be easily fulfilled by using steady-state data or the equilibrium points of the plant. In this approach, the inverse mapping is learned from the current and past states. The learning is accomplished in a composite manner by employing input and state errors. The map is used simultaneously in the feedforward path to control the plant. The performance of the plant subject to this novel controller is validated through simulations and experimental data. The new control method is applied to a novel Electro-Hydraulic Poppet Valve (EHPV). These valves are used in a Wheatstone bridge arrangement for motion control of hydraulic actuators. This is preferred over the conventional use of spool valves due to the energy savings potential. It is shown in this dissertation that this method improves the value of using these types of valves for motion control in hydraulics. This is due to the combination of self-learning (auto-calibration) and better performance for a more efficient operation of hydraulic equipment. Additionally, it is shown that the auto-calibration of the valves can be used for health monitoring of the same, which consequently improves their reliability and expedites maintenance downtime.

Production lines with unreliable machines have received a great amount of attention in the literature. Especially, two-station systems have mostly been studied because such systems are easier to handle when compared to the longer lines. In literature, longer lines are usually evaluated by a decomposition algorithm, whereby the long line is partitioned into chunks of two-station lines. Decomposition algorithms require intermediate buffer storages of capacity at least two or three. The trends in modern manufacturing practices, on the other hand, such as the Toyota Production System, dictate that intermediate storages be eliminated. Our work studies multi-station lines with no intermediate storage. We develop software to automate the generation of transition probability matrices to allow the analysis of system behavior. The algorithm allows the use of software packages to handle computations and to solve for exact solutions. Long-run behavior is obtained via the algorithm developed in the computational environment MATLAB. The purpose is to analyze the system performance measures such as starvation and blockage times of stations, production rate and work-in-process. In addition, the production rate and the work-in-process measures over failure and repair probabilities are curve-fit to establish simple and useful empirical formulas for lines consisting three, four and five identical stations. Numerical analyses show that the proposed algorithm is effective for exact solutions and the suggested formulas are valid for approximate solutions.