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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:55:26 +0000Conic Sector Analysis for Digital Control Systems with Structured Uncertainty
https://resolver.caltech.edu/CaltechETD:etd-03042008-093526
Authors: {'items': [{'id': 'Dailey-Russell-Lane', 'name': {'family': 'Dailey', 'given': 'Russell Lane'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/gz0q-x789
<p>This thesis presents a method which greatly reduces the conservativeness of conic sector analysis for sampled data feedback systems. The new method evaluates the stability and closed-loop performance of systems with structured uncertainty in the plant transfer function, including MIMO systems and those with multiple sampling rates. In contrast to most multirate analysis techniques, the sampling rates need not be related by rational numbers; this allows analysis when samplers are not strobed to a common clock.</p>
<p>The method is based on a theorem from P. M. Thompson which shows how to construct a conic sector containing a hybrid operator. Combining this theorem with the Structured Singular Value approach of J. C. Doyle, with its heavy use of diagonal scaling, provides an analysis framework for systems with multiple structured plant perturbations. Chapter 3 presents a theorem for the optimal conic sector radius in the SISO case; a MIMO extension of the the theorem completes the development of the new method. Chapter 5 gives three examples.</p>
<p>Chapter 6 presents a new method, based on the complex cepstrum, for synthesis of SISO rational functions to match given "target" transfer functions. The method offers complete control over stability and right half plane zeros. It solves directly for poles and zeros, avoiding the numerical sensitivity of methods which solve for polynomial coefficients. It can synthesize minimum phase functions to match a given magnitude or phase curve. In an example, it is used to synthesize a low- order digital replacement for an analog compensator which gives no degradation of stability margin or step response.</p>
<p>This thesis also presents a method for Kranc vector switch decomposition in state space; this is for stability analysis and input-output simulation of perturbed multirate systems. Moving the 30-year-old Kranc technique from the frequency domain to the state-space domain simplifies the analysis tremendously. Because the number of states is preserved, the dimensionality problems long associated with the Kranc method disappear. The new method is also useful for simulating intersample ripple behavior.</p>https://thesis.library.caltech.edu/id/eprint/869Modeling Requirements for Process Control
https://resolver.caltech.edu/CaltechETD:etd-05052006-140158
Authors: {'items': [{'email': 'daniel.rivera@asu.edu', 'id': 'Rivera-Daniel-Eduardo', 'name': {'family': 'Rivera', 'given': 'Daniel Eduardo'}, 'show_email': 'YES'}]}
Year: 1987
DOI: 10.7907/KS5Q-PJ57
<p>Modeling and control system design have traditionally been viewed as distinct, independent problems. Not all model characteristics, however, are relevant to the control system design problem. One can expect, then, that parsimonious, more effective controllers are possible if control considerations are incorporated in the modeling stage.</p>
<p>The synergism of dynamic modeling and process control, as pertaining to the fields of low-order controller design, model reduction, and model identification, is investigated in this thesis. The guiding theoretical framework is the robust control paradigm using the Structured Singular Value, which addresses controller design in the presence of model uncertainty.</p>
<p>The main contribution of this thesis is the development of a control-relevant model reduction methodology. The effectiveness of reduction is increased by incorporating the closed-loop performance/robustness specifications, plant uncertainties, and setpoint/disturbance characteristics explicitly as weights in the reduction procedure. The efficient computation of the control-relevant reduction problem is indicated and illustrated with examples taken from the control of a methanation reactor and a binary distillation column.</p>
<p>A low-order controller design methodology for single-input, single-output plants is also presented. The basis for this methodology is the combination of the control-relevant reduction problem with the Internal Model Control (IMC) design procedure. The relationship between low-order IMC controllers and classical feeback compensators is examined. It is shown that for many models common to the process industries, the controllers obtained from the low-order compensator design technique are of the PID type.</p>
<p>Finally, a model identification methodology is established using spectral time series analysis to obtain plant transfer function and uncertainty estimates directly from experiments. The control-relevant model reduction procedure can then be used to fit the "full-order" frequency response to a "reduced-order" parametric model. Model validation for control purposes is achieved by insuring that the robustness condition is satisfied.</p>
https://thesis.library.caltech.edu/id/eprint/1632Studies on Robust Control of Distillation Columns
https://resolver.caltech.edu/CaltechETD:etd-06142006-104731
Authors: {'items': [{'email': 'sigurd.skogestad@chemeng.ntnu.no', 'id': 'Skogestad-Sigurd', 'name': {'family': 'Skogestad', 'given': 'Sigurd'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/WS2X-Z786
<p>Distillation is undoubtedly the most important unit operation in chemical engineering. During design a significant effort is normally put into steady-state optimization of the column with respect to its size, feed location and reflux ratio. However, operating the column close to this optimal point requires reasonably tight control of the product compositions. This is usually not achieved in industrial practice due to stability problems. Improved strategies for distillation control offer a viable means for significant economic savings as compared to the existing ad hoc techniques. This thesis addresses robust control of distillation columns in the face of model-plant mismatch caused by model uncertainty, nonlinearity and changes in operating conditions. The robust control paradigm, introduced by Doyle and coworkers, is used as the basis for controller design and analysis. An important tool is the Structured Singular Value (SSV) which enables the evaluation of a plant's achievable control performance. This provides a consistent basis for comparing controllers and design alternatives. Achievable performance is also related to other commonly used measures such as the RGA and the condition number.</p>
<p>Physical insight is used to derive low-order column models which address the issues most important for feedback control. It is shown that the dynamic behavior can be explained in terms of the fundamental difference between external and internal flows. This difference manifests itself both at steady-state and in the dynamic response. Furthermore, the initial response, which is of principal importance for feedback control, is affected much less by changes in the operating conditions than is the steady-state response. The initial response is even less markedly affected when logarithmic compositions are used.</p>
<p>An important issue in distillation control is which two of the possible five manipulated inputs should be selected for composition control; each configuration may yield entirely different control performance. Issues which must be addressed include model uncertainty and dynamic response as well as rejection of flow disturbances by the level loops.</p>
<p>Finally, a design method for robust decentralized controllers, which generalizes the SSV-interaction measure of Grosdidier and Morari, is introduced. Each loop is designed independently such that robust performance of the overall system is guaranteed.</p>https://thesis.library.caltech.edu/id/eprint/2587Optical Computing for Adaptive Signal Processing and Associative Memories
https://resolver.caltech.edu/CaltechETD:etd-06142006-094757
Authors: {'items': [{'id': 'Hong-John-Hyunchul', 'name': {'family': 'Hong', 'given': 'John Hyunchul'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/3vpt-fn50
<p>Optical techniques for performing two computing tasks are investigated. First, acousto-optical systems that implement adaptive filtering structures are presented for operation in environments that are not well characterized <i>a priori</i> or are time-varying. Theoretical analyses along with experimental confirmations are given to identify the important system parameters that affect the performance. Extensions of the systems to the multidimensional domain of phased array signal processing are discussed as well as novel implementations that use photorefractive crystals as time-integrating elements.</p>
<p>Also investigated are various associative memory models. An acousto-optic implementation of the so-called Hopfield model is presented. The system's storage capacity and attraction radius are characterized experimentally and are shown to agree with computer simulations. Secondly, an upper bound is derived for the storage capacity of holographic associative memories that use planar holograms. It is shown that if the space bandwidth product of the hologram is N<sub>2</sub>, then the holographic memory can store at most N<sub>2</sub>/N<sub>3</sub> associations, where N<sub>3</sub> is the number of pixels in each output item. Finally, associative memories whose performance is invariant with respect to shifts in the input pattern position are considered. It is shown that nonlinear interconnections are required to achieve shift invariant operation, and optical implementations are discussed.</p>
https://thesis.library.caltech.edu/id/eprint/2583Control System Design for Robust Performance Despite Model Parameter Uncertainties: Application to Cross-Directional Response Control in Paper Manufacturing
https://resolver.caltech.edu/CaltechETD:etd-11212007-094804
Authors: {'items': [{'id': 'Laughlin-Daniel-Lee', 'name': {'family': 'Laughlin', 'given': 'Daniel Lee'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/cps9-m559
<p>The problem of robust performance analysis is solved for SISO control systems with uncorrelated model parameter uncertainties. The robust performance problem is formulated in a manner consistent with structured singular value µ-analysis - for SISO systems this means restricting the magnitude of a weighted closed-loop sensitivity function. The solution to the problem is graphical in nature and well suited to a computer-aided controller-design procedure. It utilizes region boundaries on the complex plane that contain specified sets of process models at each frequency. An algorithm is presented for locating the region boundaries corresponding to model transfer-functions with uncertain real coefficients and time-delay. Convergence and containment properties of the algorithm are proven.</p>
<p>The region-based analysis is combined with the Internal Model Control design procedure to form a controller synthesis method for robust performance. Tradeoffs between performance and robustness are transparent to the designer in the proposed synthesis method. Useful tables of controller parameters are presented in tabular form for a wide range of parameter uncertainty levels in a first-order-with-time-delay model. The controller resulting from the IMC design procedure is compared with the µ-optimal controller. Although the new synthesis procedure is generally applicable to SISO systems, it can be used to design decentralized controllers for MIMO systems with uncertain scalar dynamics and symmetric interactions. The particular application of cross-machine-direction basis-weight control in paper manufacturing is discussed in detail. Robust performance and robust failure tolerance of desirable decentralized controllers for this system are proven.</p>
https://thesis.library.caltech.edu/id/eprint/4630Synthesis of PWM and Quasi-Resonant DC-to-DC Power Converters
https://resolver.caltech.edu/CaltechETD:etd-02132007-105916
Authors: {'items': [{'email': 'maksimov@colorado.edu', 'id': 'Maksimović-Dragan', 'name': {'family': 'Maksimović', 'given': 'Dragan'}, 'orcid': '0000-0002-8867-0230', 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/B8XA-2R90
<p>Synthesis of DC-to-DC converter topologies in the two largest families - PWM and Quasi-Resonant (QR) - is completed in this thesis.</p>
<p>In a PWM converter, two linear time-invariant networks, consisting of only capacitors and inductors, source and load, are switched at constant frequency with duty ratio <i>D</i>. From defining assumptions, several general properties of PWM converter networks are derived. The established general properties interrelate the number of elements, attainable DC conversion ratio <i>M</i>(<i>D</i>), and features such as continuous terminal currents or possible coupling of inductors.</p>
<p>Based on matrix representation of the converter topology, the systematic synthesis procedure for generation of PWM converters with a given number of reactive elements is constructed. A prescribed set of requirements is the input for the procedure. The requirements may include desired DC conversion ratio, continuous terminal currents, possible coupling of inductors and a given number of switches. In particular, the number of switches implemented as transistors can be specified. Outputs of the procedure are complete classes of PWM converters that satisfy the input requirements. A number of useful PWM topologies, which have not been identified before, are uncovered. A comparison of members of the classes is included.</p>
<p>Several extensions of PWM converters are considered, including insertion of the isolation transformer and two discontinuous operating modes for which unified DC analyses are completed.</p>
<p>Quasi-Resonant converters are defined as two-switch PWM converter networks to which resonant elements are added. Synthesis of QR, converters is based on the recognition that there are only a finite number of topologically distinct positions for resonant elements within a two-switch PWM parent converter. If a single resonant inductor and a single resonant capacitor are added to a two-switch PWM topology, examination of all possible positions yields a total of six QR classes, which come in dual pairs. Two pairs are identified as known QR classes, namely, Zero-Current/Zero-Voltage (ZV/ZC) and Zero-Current/Zero-Voltage Quasi-Square-Wave (ZC-QSW/ZV-QSW). The remaining two classes, named Off-Resonant and On-Resonant Quasi-PWM (Q<sub>f</sub>-PWM/Q<sub>n</sub>-PWM), have not been recognized so far. The names originate from the fact that Q-PWM converters can be regarded as PWM converters operating in both discontinuous modes simultaneously. The synthesis procedure can be generalized to encompass additional resonant elements. As an example, classes of Zero-Current and Zero-Voltage Multi-Resonant (ZC-MR/ZV-MR) converters are formally defined.</p>
<p>In contrast to square-wave switch waveforms in PWM converters, all QR topologies exhibit smooth quasi-sinusoidal waveforms and therefore reduced switching losses. Of particular interest are operating modes in which all switching transitions are at zero current or at zero voltage.</p>
<p>A study of operating modes and a DC analysis unified with respect to all PWM parents and all topological variations are carried out for four selected classes of QR Converters - Q<sub>n</sub>-PWM, ZV, ZV-QSW, and ZV-MR. It is emphasized that for a QR converter, topology alone is not sufficient to derive DC conversion properties. Subject to different switch implementations and control timing, the emerging operating modes can result in vastly different behavior of the same converter topology.</p>
<p>Two switch implementations are considered - conventional, with one controllable switch and one diode, and the one that resembles the technique of synchronous rectification - with two controllable switches. In the first case, with the exception of converters in two Q-PWM classes, only variable-frequency control is applicable. However, if both switches are controllable, constant-frequency control is restored in all QR classes, and several novel operating modes of practical interest are uncovered.</p>
<p>Various QR classes and operating modes are compared with respect to sets of switching transitions, sensitivity to parasitic elements, available operating region, frequency range and stresses on switching devices. The role of free parameters in various design trade-offs is exposed, thus allowing a designer to select and realize the topology best suited for a particular application.</p>https://thesis.library.caltech.edu/id/eprint/626Robust Analysis of Feedback Systems with Parametric and Dynamic Structured Uncertainty
https://resolver.caltech.edu/CaltechETD:etd-02012005-084251
Authors: {'items': [{'email': 'ricardo@conae.gov.ar', 'id': 'Sánchez-Peña-Ricardo-Salvador', 'name': {'family': 'Sánchez Peña', 'given': 'Ricardo Salvador'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/MM2J-E556
<p>This thesis presents the first general program implementation of the algorithm by deGaston and its generalization by Sideris and deGaston to compute the Multivariable stability margin or Structured singular value of a feedback system under real (independent or related) parametric uncertainty. An improved implementation of the algorithm mentioned above is also considered, which simplifies significantly the code and increases the computational speed. The latter also allows a simple and fast analysis by just checking the extreme values of the set of parameters, with a high probability of achieving the actual stability margin; this being supported by an intense statistical analysis performed at the end of this thesis.</p>
<p>A great deal of work has recently been done related to this class of uncertain systems initiated by the well known theorem of Kharitonov. A connection is made in Chapter 4 between these procedures and the above ones in terms of generality of the class of uncertain polynomials considered. A theorem characterizing the set of polynomials whose robust stability can be determined by a finite number of tests is addressed. Sufficient conditions to determine when the latter conditions apply are also given, which in some cases can considerably simplify the analysis. In particular cases, polynomials with related uncertain parameters can be treated in the same way as independent parameters as shown in two examples.</p>
<p>The main part of this thesis is concerned with the analysis of more general type of uncertainties. In particular, the analysis of robust stability for the case when unstructured dynamic uncertainty is combined with real parametric uncertainty is treated in Chapter 5. This can also be applied in the analysis of robust performance for plants with parametric uncertainty. Chapter 6 generalizes the latter to the most general case in which structured dynamic and real parametric uncertainty appear simultaneously in the plant. A computational scheme is given in both cases which uses the algorithm mentioned in the first part and is applied to several examples.</p>
<p>At the end, an example of the robust analysis of an experimental aircraft demonstrates how a practical situation can be handled by this procedure.</p>https://thesis.library.caltech.edu/id/eprint/425Binary Correlators for Optical Computing and Pattern Recognition
https://resolver.caltech.edu/CaltechETD:etd-02082007-130728
Authors: {'items': [{'id': 'Mok-Fai-Ho', 'name': {'family': 'Mok', 'given': 'Fai Ho'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/dwpt-gn93
<p>The matrix-vector multiplier is an important building block in optical information processing architectures, examples of which are correlators for pattern recognition, associative memories, and neural networks. Such architectures are most suitable for implementation by optics due to the ease in realizing dense interconnections optically. The success of the implementation partially relies on the quality of the SLM used to record the information for processing. Limited dynamic range for the representation of the data recorded is a common drawback suffered by most commercially available devices. In this thesis, the importance of the dynamic range of the device on the performance of the implementation is investigated. The effect of limited dynamic range on the signal to noise ratio, probability of error, capacity, and training of various forms of matrix-vector multipliers are addressed. Through the use of theoretical analyses, computer simulations, and optical experiments, it will be shown that a large dynamic range is not essential in most applications. Specifically, it is shown that only one bit of dynamic range, i.e. two gray levels, for the representation of each data point, results in acceptable loss in performance.</p>https://thesis.library.caltech.edu/id/eprint/555Elementary solutions for the H infinity- general distance problem- equivalence of H2 and H infinity optimization problems
https://resolver.caltech.edu/CaltechETD:etd-05152007-142515
Authors: {'items': [{'id': 'Kavranoglu-D', 'name': {'family': 'Kavranoglu', 'given': 'Davut'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/y2q9-nq75
This thesis addresses the H[infinity] optimal control theory. It is shown that SISO H[infinity] optimal control problems are equivalent to weighted Wiener-Hopf optimization in the sense that there exists a weighting function such that the solution of the weighted H2 optimization problem also solves the given H[infinity] problem. The weight is identified as the maximum magnitude Hankel singular vector of a particular function in H[infinity] constructed from the data of the problem at hand, and thus a state-space expression for it is obtained. An interpretation of the weight as the worst-case disturbance in an optimal disturbance rejection problem is discussed.
A simple approach to obtain all solutions for the Nehari extension problem for a given performance level [gamma] is introduced. By a limit taking procedure we give a parameterization of all optimal solutions for the Nehari's problem.
Using an imbedding idea [12], it is proven that four-block general distance problem can be treated as a one-block problem. Using this result an elementary method is introduced to find a parameterization for all solutions to the four-block problem for a performance level [gamma].
The set of optimal solutions for the four-block GDP is obtained by treating the problem as a one-block problem. Several possible kinds of optimality are identified and their solutions are obtained.https://thesis.library.caltech.edu/id/eprint/1824Model Validation for Uncertain Systems
https://resolver.caltech.edu/CaltechETD:etd-10252002-162453
Authors: {'items': [{'email': 'roy@ece.ucsb.edu', 'id': 'Smith-Roy-S-R', 'name': {'family': 'Smith', 'given': 'Roy S.R.'}, 'show_email': 'YES'}]}
Year: 1990
DOI: 10.7907/7S0Z-ZY41
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Modern robust control synthesis techniques aim at providing robustness with respect to uncertainty in the form of both additive noise and plant perturbations. On the other hand, most popular system identification methods assume that all uncertainty is in the form of additive noise. This has hampered the application of robust control methods to practical problems. This thesis begins to address this disparity by considering the connection between uncertain models and data. The model validation problem addressed here is this: given experimental, data and a model with both additive noise and normbounded perturbations, is it possible that the model could produce the observed inputoutput data? This question is reformulated as an optimization problem: what is the minimum norm noise required to account for the data and meet the constraint imposed by the perturbation uncertainty? The assumptions typically used for robust control analysis are introduced and shown to lead to a constant matrix problem. This problem is studied in detail, and bounds on the size of the required noise are developed. The dimensionality issues that arise in the consideration of the structured singular value ([...]) also arise here.
A geometric framework is used to introduce a variation on [...]. This is extended to allow the consideration of robust control analysis problems that include input and output data. The more general problem is then used to illustrate the connection between [...] and the model validation theory.
The application of the theory is illustrated by a study of a laboratory process control experiment. Typical steps in the identification of a robust control model for a physical system are discussed. It is shown, by example, how the model validation theory can be used to provide insight into the limitations of uncertain models in describing physical systems.https://thesis.library.caltech.edu/id/eprint/4244Studies in Robust Control of Systems Subject to Constraints
https://resolver.caltech.edu/CaltechETD:etd-10252002-161632
Authors: {'items': [{'id': 'Campo-Peter-John', 'name': {'family': 'Campo', 'given': 'Peter John'}}]}
Year: 1990
DOI: 10.7907/4w3h-b335
<p>Two approaches to control system design for constrained systems are studied. The first involves theoretical investigations of constrained model predictive control algorithms. The second involves extensions of robust linear control theory to handle the nonlinear control schemes commonly used in practice for constrained systems.</p>
<p>A novel model predictive control algorithm, with attractive functional and numerical characteristics is developed. This algorithm minimizes peak excursions in the controlled outputs and is particularly suited to regulatory control problems common in continuous process systems.</p>
<p>Model predictive control concepts are extended to uncertain linear systems. An on-line optimizing control scheme (RMPC) is developed which has as its objective the minimization of worst-case tracking error for an entire family of linear plants. For model uncertainty descriptions which provide plant impulse response coefficients as affine functions of uncertain parameters, it is shown that the required minimax optimization problem can be recast as a single linear program.</p>
<p>The discrete time optimal averaging level control problem is formulated and solved. A finite horizon approximation to the problem is introduced and analytical solutions are obtained in important special cases. A model predictive control formulation is introduced which provides optimal flow filtering and integral action. Analysis tools are provided to characterize the trade-off between flow filtering and rapid integral action.</p>
<p>A complete theory is developed for the multivariable anti-windup, bumpless transfer (AWBT) problem. The theoretical framework allows the consideration of any linear time invariant (LTI) control system subject to plant input limitations and substitutions. A general AWBT compensation scheme, applicable to multivariable controllers of arbitrary structure and order, is developed. Conditions are derived under which this general AWBT method reduces to any one of several well-known heuristics for AWBT (e.g., PI anti-reset windup and IMC). The design issues which affect AWBT performance are identified and quantitative analysis methods are developed. Sufficient conditions for nonlinear stability of the AWBT compensated system are provided. These results are a generalization of, and are less conservative than, those available in the AWBT literature. The definition of AWBT performance objectives which are independent of controller structure allows the formulation of a general AWBT synthesis problem. This formal synthesiproblem addresses each of the identified performance objectives in a quantitative manner. The synthesis problem is shown to be a special case of a constrained structure controller synthesis (CSCS) problem. A solution method via reduction to static output feedback is presented and the engineering trade-offs available in the AWBT design are discussed.</p>https://thesis.library.caltech.edu/id/eprint/4243Multirate adaptive filtering algorithms : analysis and applications
https://resolver.caltech.edu/CaltechETD:etd-07122007-103754
Authors: {'items': [{'id': 'Sathe-V-P', 'name': {'family': 'Sathe', 'given': 'Vinay Padmakar'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/ec5w-7460
In this thesis, we discuss the application of multirate signal processing concepts to adaptive filtering to achieve low computational complexity and speed. To be able to analyze systems involving multirate building blocks, we have studied effects of multirate filters on the statistics of random inputs. As an example of the multirate adaptive filtering concepts, we study the problem of adaptive identification of an unknown bandlimited channel. We show that the bandlimited property can be very efficiently exploited to reduce both the speed and number of computations. The new method embeds an adaptive filter into multirate filters to reduce complexity and speed of computation.
We have applied the theoretical results obtained for the effects of multirate building blocks on stationary inputs to the adaptive identification scheme above and shown that the optimal filter is a matrix filter. We have shown through simulations that for a practical setup, a scalar adaptive filter performs almost as well if the fixed filters in the scheme are designed to have good stopband attenuation.
In a practical implementation of adaptive algorithms, computational noise is of concern. Most of the current analysis focuses on deriving the worst case upper bound on the roundoff errors. We analyze some basic signal processing steps by introducing a statistical flavor to it. This analysis answers questions such as "what is a typical value of the roundoff error?" In particular, for the case of dot product computation, we obtain expressions for the roundoff noise variance for the floating point case, and compare the results with the fixed point noise roundoff noise analysis. We also perform error variance analysis of Givens rotation and Householder transformation. These two algorithms are used in the upper triangularization of matrices. We have compared the results obtained for these cases and shown that error variance for the Householder case is lower, meaning that the Householder transformation adds lower roundoff error "on an average".
We also address the problem of bandlimited extrapolation of discrete-time signals. We have explained why the term "best solution" does not have a unique answer. Several new techniques for bandlimited extrapolation of discrete-time segments are explored. These methods apply to a wide range of situations (including multiple-burst interpolation of multiband signals). A closed form expression for the optimal solution (for a given value of the energy of extrapolated sequence) has been obtained and evaluated for various values of the final energy. The various methods are compared on the basis of out-of-band energy of the extrapolated signal, total energy of the extrapolated signal (in relation to that of the given segment), and numerical robustness.https://thesis.library.caltech.edu/id/eprint/2860Robustness properties of nonlinear process control and implications for the design and control of a packed bed reactor
https://resolver.caltech.edu/CaltechETD:etd-07112007-084012
Authors: {'items': [{'id': 'Doyle-Francis-Joseph-III', 'name': {'family': 'Doyle', 'given': 'Francis Joseph, III'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/3n52-hk32
The robustness properties of nonlinear process control are studied with particular emphasis on applications to the design and control of a catalytic fixed bed reactor.
Analysis tools are developed to determine the stability and performance of nonlinear dynamical systems. The results are based upon new extensions of the structured singular value to a class of nonlinear and time-varying systems. Conic sectors are utilized in approximating the static nonlinearities present and an algorithm is developed for optimal conic sector calculation.
The synthesis tools of differential geometry are studied with respect to their closed loop robust performance properties. New results in approximate linearization are contrasted with exact linearization and linear control. It is shown that the approximate linearization technique is superior with respect to disturbance handling, optimization of the resultant transformations, and range of applicability.
Nonlinear approaches for the control of a packed bed reactor are investigated. In particular, the differential geometric technique of input-output linearization is found to yield superior closed-loop performance over regions of open-loop parametric sensitivity. The synthesis of a linearizing controller for this nonlinear distributed parameter system involves a two-tier approach. In the first stage, a low order nonlinear model is developed for the reactor. This is accomplished by treating the active transport mechanisms in the bed as a nonlinear wave which propagates through the bed in response to changes in the operating conditions. The resultant lumped parameter model facilitates the design of the input-output linearizing controller in the second tier of this scheme. The implementational hurdles for this approach are identified and comparisons are drawn on the strengths of this approach over robust linear control for the reactor.
Practical guidelines are developed for the design of packed bed reactors. The criteria result from requirements on the radial temperature profile, temperature sensitivity, and acceptable pressure drop. The stabilizing effects of feedback control for industrial fixed bed catalytic reactors are addressed. Simulations support the result that violation of the proposed criteria leads to unacceptable closed-loop performance.
In conclusion, general guidelines are constructed from a series of case studies on the proper selection of linear versus "linearizing" control. The relative performance is measured by the region of attraction, magnitude of manipulated variable action, and sensitivity to input disturbances. The work represents the first objective evaluation of the strengths and limitations of input-output linearization compared to linear control.https://thesis.library.caltech.edu/id/eprint/2853Robust Inferential Control: A Methodology for Control Structure Selection and Inferential Control System Design in the Presence of Model/Plant Mismatch
https://resolver.caltech.edu/CaltechETD:etd-11162005-134952
Authors: {'items': [{'id': 'Lee-Jay-Hyung', 'name': {'family': 'Lee', 'given': 'Jay Hyung'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/3dp3-ba80
<p>Two major tasks that are required to obtain a control system utilizing secondary measurements are measurement selection and inferential control system design. The first involves choosing an appropriate subset of the available measurements and the second involves designing a feedback controller based on the chosen measurements. The important issues to be addressed are not only the theoretical performance of the closed-loop system, but also the effects arising from the factors prevalent in practical environments such as model/plant mismatch, constraints, and failures of actuators and sensors.</p>
<p>General measurement selection methodology is developed accounting for all the factors that can affect the measurement selection in signifcant ways. These factors include model uncertainty, signal-to-noise ratios, and measurement dynamics. The underlying philosophy is to reduce the number of candidates to a sufficiently low level before going onto detailed analysis by eliminating those candidates for which there does not exist a linear time-invariant controller meeting the required level of robust performance. Based on this philosophy and using the Structured Singular Value theory as a vehicle, a number of numerically efficient screening tools are developed. Conditions are derived under which some of the new criteria reduce to previously published measurement selection criteria. The proposed tools are applied to the measurement selection problems in a multi-component distillation column and a high-purity distillation column.</p>
<p>Two different approaches are considered for inferential control system design: an output estimation based design approach and a state estimation based design approach. The former approach involves independent design of an output estimator and a feedback controller while the latter involves direct one step design although the design can be actually separated into those of a state estimator and of a feedback regulator using the separation principle argument.</p>
<p>For the former approach, design of the output estimator was examined for two different cases: the case where a full dynamic model is available and the case where only the time records of the primary and secondary measurements are available either from simulations or from process measurements. For the former case, multi-rate Kalman filter design and μ-Synthesis design are discussed. For the latter case, the estimator design problem is formulated as a regression problem and various regression techniques are evaluated in terms of their suitability to the output estimator design problem. For design of the feedback controller, traditional techniques such as LQG, IMC, and MPC were combined into a control technique that has nice algorithmic properties as well as many operational merits such as straightforward constraint handling and simple, intuitive on-line tuning. A heavy-oil fractionator was used as an example application.</p>
<p>For the latter approach, general state estimation techniques (e.g., multi-rate Kalman filtering) used in LQG and finite receding horizon control used in traditional MPC were integrated into a control technique that can incorporate general disturbances and multi-rate sampled measurements and has desirable operational characteristics. The concept of classical IMC was extended to equip the control system with on-line tuning parameters that have direct connections with the speed of the closed-loop responses. Application to a high purity distillation column demonstrates the effectiveness of the control technique in terms of closed-loop performance and operational flexibility.</p>https://thesis.library.caltech.edu/id/eprint/4589Towards a simple and fast learning and classification system
https://resolver.caltech.edu/CaltechETD:etd-10172006-104502
Authors: {'items': [{'id': 'Wong-Yiu-fai-Isaac', 'name': {'family': 'Wong', 'given': 'Yiu-fai Isaac'}, 'show_email': 'NO'}]}
Year: 1992
DOI: 10.7907/531t-v696
This work consists of two parts which can be read independently.
The first part contains a novel proof of the learning convergence in the Cerebral Model Articulation Controller (CMAC) proposed by Albus in 1976. That CMAC can learn any discrete input-output mapping was not known. Our work presents two ways of looking at the learning algorithm in CMAC. The learning algorithm is formulated as a matrix iteration scheme, the convergence of which can be proved by a) standard matrix theory and b) Fourier analysis. Each approach offers unique insights about the nature of the learning mechanism in CMAC. The analysis provides mathematical rigor and structure for a neural network learning model with simple and intuitive mechanisms.
The second part presents a new clustering algorithm derived from an interdisciplinary approach. The original motivation came from studies in Part I. The new algorithm departs from traditional approaches in many ways. It is the only algorithm which incorporates scale, though scale has been recognized by other researchers. It also introduces a new concept into clustering: cluster independence, which proves essential. The new framework allows us to derive a formulation based on information theory and statistical mechanics. The cluster centers correspond to the local minima of the thermodynamical free energy, which are identified as the fixed points of a one-parameter nonlinear map. Bifurcation techniques are used to obtain a complete picture of the dynamics of the map. A new clustering algorithm based on the melting process is obtained, which is hierarchical and unsupervised. Melting produces a tree of clusters in the scale space, analogous to a dendrogram. A characterization of "cluster" is given. Robustness considerations in scale space lead to a natural way of determining the optimal number of clusters. The algorithm is also insensitive to variability in cluster densities, cluster sizes and ellipsoidal shapes and orientations. We tested the algorithm successfully on both simulated data and a multi-dimensional Synthetic Aperture Radar image of an agricultural site for crop identification, and found that it beat the competition. Our clustering algorithm may also provide new and important insights for neural network research and optimization theory.https://thesis.library.caltech.edu/id/eprint/4133Robust adaptive control of manipulators with application to joint flexibility
https://resolver.caltech.edu/CaltechETD:etd-08072007-073507
Authors: {'items': [{'id': 'Lee-H-H', 'name': {'family': 'Lee', 'given': 'Ho-Hoon'}, 'show_email': 'NO'}]}
Year: 1992
DOI: 10.7907/ks5z-8e20
This thesis discusses the model-based adaptive trajectory control of commercial manipulators whose dynamics are well known with uncertainties confined to parameters.
This thesis emphasizes the importance of the transient behavior as well as robust stability of a system and takes it into account in the design of adaptive control laws. The basic idea is to search for compensators in the direction of minimizing a quadratic performance index, and then analyze the stability and robustness of the selected compensators in the presence of bounded disturbances, sensor noises, and unmodelled dynamics. With this idea, centralized and decentralized adaptive control schemes are proposed for rigid-joint manipulators. Stability bounds for disturbances, control and adaptation gains, and desired trajectories and their time-derivatives are derived for the proposed schemes. These bounds are sufficient conditions for robust stability of the proposed schemes in the presence of unmodelled dynamics such as feedback delays in the digital control systems and the coupled dynamics in the decentralized scheme.
A flexibility compensator is designed to treat the problem of joint flexibility. With the flexibility compensator, a manipulator having flexible joints is transformed to that having rigid joints with high-frequency dynamics of joint couplings representing unmodelled dynamics. In this way, control of flexible-joint manipulators is converted to that of the corresponding rigid-joint manipulators. Accordingly, the robust adaptive control schemes proposed for rigid-joint manipulators are applied. Then, through stability analysis, stability bounds for disturbances, control and adaptation gains, and desired trajectories and their time-derivatives are derived for the scheme with the flexibility compensator, in the presence of the unmodelled dynamics. Under the constraint of these bounds, the proposed adaptive scheme is not only almost independent of the gear-reduction ratios, flexibilities of joint couplings, and characteristics of actuators, but also free from the requirements of measuring angular accelerations and jerks of links.https://thesis.library.caltech.edu/id/eprint/3035Neural network control and an optoelectronic implementation of a multilayer feedforward neural network
https://resolver.caltech.edu/CaltechETD:etd-08202007-091426
Authors: {'items': [{'id': 'Yamamura-Alan-Akihiro', 'name': {'family': 'Yamamura', 'given': 'Alan Akihiro'}, 'show_email': 'NO'}]}
Year: 1992
DOI: 10.7907/4dbn-z991
Artificial neural networks are a computational paradigm inspired by biological neural systems. By modeling neural networks to a certain degree after their counterparts in nature, it is hoped that they can capture those aspects of biological neural systems that allow them to outperform more conventional processing systems in tasks such as motor control and pattern recognition. A brief overview of neural networks is provided in Item 1, concentrating on those aspects pertinent to the remainder of this thesis.
The application of neural networks to control is examined in Item 2. A general control system can be divided into feedforward and feedback components. Specifically, the use of neural networks in learning to generate the feedforward control signal for unknown, potentially nonlinear, plants is examined. A class of learning algorithms applicable to feedforward networks is developed, and their use in learning to control a simulated two-link robotic manipulator is studied.
An optoelectronic implementation of a multilayer feedforward neural network, with binary weights and connections, is described in the final part of this thesis. The neurons and connections are implemented electronically on a custom VLSI chip. The pattern and strength of the connections is controlled, through photodetectors placed in the connections, by a pattern of light illuminating the chip. This pattern is read out, in parallel, from an optical disk. Issues concerning parallel readout of information from optical disks are discussed in Item 3, while Item 4 contains a descriptionn of both the design of the Optoelectronic Neural Network Chip (ONNC) and experiments involving the optical disk and neural network chip.
https://thesis.library.caltech.edu/id/eprint/3173Constrained H[infinity]-optimization for discrete-time control systems
https://resolver.caltech.edu/CaltechETD:etd-11282007-130457
Authors: {'items': [{'id': 'Rotstein-H-P', 'name': {'family': 'Rotstein', 'given': 'Hector P.'}, 'show_email': 'NO'}]}
Year: 1993
DOI: 10.7907/51VE-9H34
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In order to formulate a problem in the [...]-optimal control framework, all specifications have to be combined in a single [...]-norm objective, by an appropriate selection of weighting functions. If some of the specifications have the form of hard time domain constraints, the task of finding weighting functions that achieve a satisfactory design can become arduous. In this thesis, a theory for constrained [...]-control is presented, that can deal with the standard [...] objective and time domain constraints. Specifically, the following time domain constrained problem is solved: given a number [...], and a set of fixed inputs [...], find a controller such that the closed loop transfer matrix has an [...]-norm less than [...], and the time response [...] to the signal [...] belongs to some pre-specified set [...] for each [...]. Constraints are only imposed over a finite horizon, and this allows the formulation of a two step procedure. In the first step, the optimal way of clearing the constraints is found by computing a solution to a convex non differentiable problem. In the second, a standard unconstrained [...]-problem is solved. The final controller results from putting together the solution to both subproblems.
The objective function for the minimization, and the solution to the whole problem are constructed using state-space formulas. The ellipsoid algorithm is argued to be a convenient procedure for performing the optimization since, if carefully implemented, it can deal with the two main characteristics of the problem, i.e., nondifferentiability and large-scale. The validity of assuming constraints over a finite horizon is justified by presenting a procedure for computing a solution that gives an overall satisfactory behavior. For clarity of exposition, this thesis starts by discussing a very special instance of the problem, and then proceeds to give the solution to the general case. Also, a benchmark problem for robust control is solved to illustrate the applicability of the theory.
https://thesis.library.caltech.edu/id/eprint/4676Robust control of systems subject to constraints
https://resolver.caltech.edu/CaltechETD:etd-10232007-141113
Authors: {'items': [{'id': 'Zheng-Z-Q-A', 'name': {'family': 'Zheng', 'given': 'Zhi Qiang (Alex)'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/q8vt-s855
Most practical control problems are dominated by constraints. Although a rich theory has been developed for the robust control of linear systems, very little is known about the robust control of linear systems with constraints. Over the years various model-based algorithms (given a generic term Model Predictive Control) have been used in industry to control complex multivariable systems with operating constraints. The design and tuning of these controllers is difficult for two reasons:
1. Process models are always inaccurate which implies that the controllers must be robust.
2. Even in the simplest case where process models are linear, the overall systems are nonlinear because of the constraints.
Despite Model Predictive Control's considerable practical importance, there is very little theory to guide the design and tuning of these controllers for stability and robustness. It is the goal of this thesis to develop such a theory. Specifically, a general framework based on Model Predictive Control is developed to synthesize controllers for discrete-time linear systems subject to constraints with robust stability and performance guarantees.https://thesis.library.caltech.edu/id/eprint/4224