Modeling and Reduction with Applications to Semiconductor Processing

This thesis consists of several somewhat distinct but connected parts, withan underlying motivation in problems pertaining to control and optimizationof semiconductor processing. The first part (Chapters 3 and 4) addressesproblems in model reduction for nonlinear state-space control systems. In1993, Scherpen generalized the balanced truncation method to the nonlinearsetting. However, the Scherpen procedure is not easily computable and hasnot yet been applied in practice. We offer a method for computing a workingapproximation to the controllability energy function, one of the mainobjects involved in the method. Moreover, we show that for a class ofsecond-order mechanical systems with dissipation, under certain conditionsrelated to the dissipation, an exact formula for the controllabilityfunction can be derived. We then present an algorithm for a numericalimplementation of the Morse-Palais lemma, which produces a local coordinatetransformation under which a real-valued function with a non-degeneratecritical point is quadratic on a neighborhood of the critical point.Application of the algorithm to the controllabilty function plays a key rolein computing the balanced representation. We then apply our methods andalgorithms to derive balanced realizations for nonlinear state-space modelsof two example mechanical systems: a simple pendulum and a double pendulum. The second part (Chapter 5) deals with modeling of rapid thermal chemicalvapor deposition (RTCVD) for growth of silicon thin films, viafirst-principles and empirical analysis. We develop detailedprocess-equipment models and study the factors that influence depositionuniformity, such as temperature, pressure, and precursor gas flow rates,through analysis of experimental and simulation results. We demonstratethat temperature uniformity does not guarantee deposition thicknessuniformity in a particular commercial RTCVD reactor of interest. In thethird part (Chapter 6) we continue the modeling effort, specializing to acontrol system for RTCVD heat transfer. We then develop and apply ad-hocversions of prominent model reduction approaches to derive reduced modelsand perform a comparative study

Realization of multi-input/multi-output switched linear systems from Markov parameters

This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the submodels have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, zero sets of LTV Hankel matrices where the realized system has a linear time-invariant (LTI) pulse response matching that of the original SLS are exploited to extract the submodels, up to arbitrary similarity transformations, by a clustering algorithm using a statistics that is invariant to similarity transformations. Recovery is shown to be complete if the dwell times are sufficiently long and some mild identifiability conditions are met. In the third stage, the switching sequence is estimated by three schemes. The first scheme is based on forward/backward corrections and works on the short segments. The second scheme matches Markov parameter estimates to the true parameters for LTV systems and works on the medium-to-long segments. The third scheme also matches Markov parameters, but for LTI systems only and works on the very short segments. In the fourth stage, the submodels estimated in Stage~2 are brought to a common basis by applying a novel basis transformation method which is necessary before performing output predictions to given inputs. A numerical example illustrates the properties of the realization algorithm. A key role in this algorithm is played by time-dependent switching sequences that partition the state-space according to time, unlike many other works in the literature in which partitioning is state and/or input dependent

Communication-constrained feedback stability and Multi-agent System consensusability in Networked Control Systems

With the advances in wireless communication, the topic of Networked Control Systems (NCSs) has become an interesting research subject. Moreover, the advantages they offer convinced companies to implement and use data networks for remote industrial control and process automation. Data networks prove to be very efficient for controlling distributed systems, which would otherwise require complex wiring connections on large or inaccessible areas. In addition, they are easier to maintain and more cost efficient. Unfortunately, stability and performance control is always going to be affected by network and communication issues, such as band-limited channels, quantization errors, sampling, delays, packet dropouts or system architecture. The first part of this research aims to study the effects of both input and output quantization on an NCS. Both input and output quantization errors are going to be modeled as sector bounded multiplicative uncertainties, the main goal being the minimization of the quantization density, while maintaining feedback stability. Modeling quantization errors as uncertainties allows for robust optimal control strategies to be applied in order to study the accepted uncertainty levels, which are directly related to the quantization levels. A new feedback law is proposed that will improve closed-loop system stability by increasing the upper bound of allowed uncertainty, and thus allowing the use of a coarser quantizer. Another aspect of NCS deals with coordination of the independent agents within a Multi-agent System (MAS). This research addresses the consensus problem for a set of discrete-time agents communicating through a network with directed information flow. It examines the combined effect of agent dynamics and network topology on agents\u27 consensusability. Given a particular consensus protocol, a sufficient condition is given for agents to be consensusable. This condition requires the eigenvalues of the digraph modeling the network topology to be outer bounded by a fan-shaped area determined by the Mahler measure of the agents\u27 dynamics matrix

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

A Methodology For Measuring Resilience in a Satellite-Based Communication Network

According to Presidential Policy Directive 21, increasing resilience of critical infrastructures is not only desired, but United States policy. Communications infrastructures are one such critical infrastructure. The purpose of this research is to develop a methodology for measuring resilience in satellite communication systems for use as a key criterion in the selection and acquisition of new satellite architectures, in accordance with the National Security Space Strategy. The base methodology utilized in this thesis is Extreme Event Modeling implemented through the use of Bi-Level Programming with monotonically nonlinear continuous and mixed integer variables. This model differs from previous efforts applied to other critical infrastructures in that it captures the temporal component associated with multiple events, as well as the repairs, or reconstitution, of infrastructure components. Furthermore, a heuristic based upon a ratio of impact to cost and local searches is developed to solve the resulting continuous bi-level problem

Model-Based Life Extending Control for Rotorcraft

Rotorcraft are subjected to fatigue loads that not only limit the fatigue life of components but also add to their cost. Most of the fatigue-critical rotorcraft components are located in the rotor system, creating challenges for real-time load and structural health monitoring of such components. Furthermore, in forward flight, as the helicopter's main rotor rotates and simultaneously advances, a very complex aerodynamic environment dominated by large dynamic loads is created. Because of the asymmetric air flow past the main rotor, the lift forces each blade generates vary depending on its location. This creates cyclic loading that occurs at the main rotor frequency of rotation (1/rev) and at higher harmonic frequencies (n/rev, n = 2, 3 ,4, etc.) which become important for vibration, fatigue, and forward flight performance. Hence, many components in the rotor system are highly loaded with cyclic loads at multiples of the rotor frequency. In addition, during aggressive maneuvers, the low-duration high magnitude cyclic loads may lead to small amounts of localized damage, for example, localized plasticity, at stress concentration regions. Therefore, it is crucial to develop control strategies that can guard against premature fatigue failure of critical helicopter components to enable component life extension. This research aims at developing real-time algorithms that estimate component level dynamic loads in order to enable real-time load monitoring of critical rotor components and control strategies which alleviate or limit fatigue damage. A nonlinear helicopter model with 33-inflow states and elastic blade representation is modeled in FLIGHTLAB. The developed nonlinear model gives a suitable representation of the dynamic loads that the rotor system experiences. From the nonlinear model, a first order Linear Time Periodic (LTP) model of coupled body-rotor-inflow dynamics is extracted by performing a linearization about a periodic equilibrium. The LTP model is transformed into a Linear Time Invariant (LTI) model using harmonic decomposition methodology. The obtained LTI model which has 1513 states is used to develop novel schemes for online estimation of rotor component loads. The fidelity of the 1513-state LTI model is assessed in the frequency domain via comparison with flight test data. A model order reduction approach based on singular perturbation theory is used to reduce the 1513-state LTI model to a 10^{th} order LTI model. The 10^{th} order LTI model retains the physical meaning of relevant states and the fidelity of the dynamic load prediction of the 1513-state LTI model. Using the reduced order LTI model, two component load limiting strategies to limit fatigue damage are pursued. The first one is based on a receding horizon model predictive control (i.e., Load Limiting Control (LLC) scheme) while the second one is based on active rotor control (i.e., Load Alleviation Control (LAC) via IBC scheme). In both approaches, component life extension is achieved by directly limiting fatigue life usage associated with harmonic loads. In the receding horizon model predictive control formulation, an optimal control problem is formulated where given a desired user-defined maximum harmonic load limit, an estimate of the control margin associated with the component load limit is found and used in the form of pilot cueing/automatic limiting to prevent the component harmonic load from exceeding the maximum limit. In this approach, the use of the reduced order LTI model is twofold. The component harmonic load estimate generated by the reduced order LTI model is used in the detection of limit violation. Furthermore, the reduced order LTI model is used to generate a mapping between the limit and control margins. To assess the effectiveness of this scheme, its integration with a visual cueing system is performed. Subsequently, the resulting architecture is implemented within the Georgia Tech Re-configurable Rotorcraft Flight Simulator to perform real-time piloted flight simulation experiments. The component load limiting scheme based on active rotor control uses the 10^{th} order LTI model in the synthesis of a higher harmonic individual blade controller (i.e, IBC controller). The IBC controller uses load predictions from the 10^{th} order LTI model to compute optimal higher harmonic individual blade pitch inputs to reduce specific harmonic loads. It is found that the proposed component load limiting scheme via IBC is effective in reducing desired harmonic components of pitch link load at trim but also during maneuvering flight with no impact on the maneuver performance and vibratory hub loads. Furthermore, using the handling quality requirement for small amplitude pitch changes in forward flight, it is shown that the proposed scheme does not cause handling qualities degradation.Ph.D