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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 08 Dec 2023 13:57:41 +0000An Operator Theory Approach to Nonlinear Controller Design
https://resolver.caltech.edu/CaltechETD:etd-03192008-083200
Authors: Economou, Constantin George
Year: 1986
DOI: 10.7907/2ewe-dp19
<p>Strong similarities between control theory and the theory on the solution of operator equations have been observed and basic results in control theory have been derived from operator theory arguments. The purpose of this work is to investigate the theory of controller design as an application of basic operator theory principles and to establish a unified framework in which control theory can benefit from a "rich" operator theory. The major impact is anticipated in nonlinear feedback control theory: controller design can be formulated as selection of an iterative algorithm to solve a nonlinear operator equation corresponding to the control objective. As an example, controllers induced by the method of successive substitution and the Newton method are introduced and the corresponding analysis and synthesis issues are studied. Applied to linear systems, the proposed concepts have a straightforward interpretation in terms of familiar notions in linear controller design theory. Applications are presented and extensions of the current results are suggested to conclude the thesis.</p>https://thesis.library.caltech.edu/id/eprint/1009Interaction Measures for Systems Under Decentralized Control
https://resolver.caltech.edu/CaltechETD:etd-03192008-093230
Authors: Grosdidier, Pierre
Year: 1986
DOI: 10.7907/xhj6-3x76
<p>Multivariable controllers are often avoided in the chemical process industries in favor of simpler diagonal or block-diagonal controllers. Such "decentralized" controllers are desirable because they result in control systems with fewer tuning parameters and greater failure tolerance. However, the ensuing simplicity in controller design must be weighted against the interactions which result from ignoring the off-diagonal system blocks. These can lead to performance deterioration and even instability. The purpose of an Interaction Measure (IM) is to indicate under what conditions the stability of the diagonal loops/blocks will guarantee that of the complete system.</p>
<p>One such measure, the Relative Gain Array (RGA), has found widespread acceptance both in industry and academia despite its empirical basis. This measure, in fact, has sound theoretical justifications. Rigorous relationships are derived in this study linking the RGA to closed-loop stability and robustness with respect to model uncertainty.</p>
<p>Using the notion of Structured Singular Value, a new dynamic IM is also defined for multi-variable systems under feedback with diagonal or block-diagonal controllers. This measure, the µ IM, can be used to select the "best" variable pairings for the controller as well as predict the stability of the decentralized control system. Its steady-state value also provides a sufficient condition for achieving offset-free performance with the closed-loop system. The relationship of this new IM with Rijnsdorp' IM and Rosenbrock's Direct Nyquist Array is clarified.</p>
<p>Finally, it is shown how the µ IM, in conjunction with the RGA, can form the basis of a novel and useful methodology for the design of decentralized controllers.</p>https://thesis.library.caltech.edu/id/eprint/1014Modeling Requirements for Process Control
https://resolver.caltech.edu/CaltechETD:etd-05052006-140158
Authors: Rivera, Daniel Eduardo
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/1632A Methodology for the Synthesis of Robust Control Systems for Multivariable Sampled-Data Processes
https://resolver.caltech.edu/CaltechETD:etd-05052006-140832
Authors: Zafiriou, Evanghelos
Year: 1987
DOI: 10.7907/m08p-9102
<p>The problem of the synthesis of multivariable controllers which are robust with respect to model-plant mismatch is addressed. A two-step design procedure based on the Internal Model Control (IMC) structure is used. In the first step the IMC controller is designed assuming no modeling error, and in the second step the IMC filter is designed to preserve the closed-loop characteristics in spite of model-plant mismatch.</p>
<p>Two alternatives are provided for the first step. One of them allows the designer to satisfy structural performance specifications, in terms of the structure of the closed-loop interactions, their magnitude and duration. The closed-loop transfer function matrix is directly designed. The method requires only standard linear algebra operations and includes the construction of the IMC or the feedback controller in state-space. The second approach involves the minimization of the appropriately weighted H<sub>2</sub>-norm of the sensitivity transfer function matrix, that relates the errors to the external inputs (setpoints or disturbances). A method is given for the meaningful selection of a full matrix weight so that the H<sub>2</sub>-error is minimized for a set of external input directions and their linear combinations. The procedure is extended to open-loop unstable systems. In both approaches, special care is taken to avoid intersample rippling.</p>
<p>The design of the filter in the second step is formulated as an optimization problem over the filter parameters. The objective function is constructed by using the Structured Singular Value theory so that the maximum singular value of the sensitivity transfer function remains bounded in spite of modeling error. The selection of the frequency bound is based on the properties of the design that was obtained in the first step. Analytic gradient expressions have been developed for the objective function. The optimization problem is an unconstrained one, solved with standard gradient search techniques. An iterative method for the selection of the appropriate sampling time is proposed, which explicitly takes into account model uncertainty information and performance specifications.</p>
https://thesis.library.caltech.edu/id/eprint/1633Studies on Robust Control of Distillation Columns
https://resolver.caltech.edu/CaltechETD:etd-06142006-104731
Authors: Skogestad, Sigurd
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/2587Control 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: Laughlin, Daniel Lee
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/4630Area, Cost and Resilience Targets for Heat Exchanger Networks
https://resolver.caltech.edu/CaltechETD:etd-02062007-104756
Authors: Colberg, Richard Dale
Year: 1989
DOI: 10.7907/pndd-bc72
<p>This thesis presents improved area and capital cost targets for synthesis of heat exchanger networks (HEN) for fixed operating conditions, and a new resilience target for synthesis of HENs for changing, uncertain operating conditions. In addition, methods are presented to predict, before synthesis, the trade-off between cost and resilience.</p>
<p>A pair of "transshipment" nonlinear programs (NLP) is formulated to calculate the area and capital cost targets for HEN synthesis with unequal heat transfer coefficients and different capital cost laws (for different materials of construction, pressure ratings, etc.) when there are constraints on the number of matches, forbidden matches, and required matches with specified areas (for revamp synthesis). With these NLPs, the trade-off between area and number of units can be evaluated before synthesis. In addition to the targets themselves, solution of the NLPs yields "ideal" temperature profiles (much like the composite curves) for a HEN achieving the targets, and a selection of stream matches and their heat loads which provide an excellent starting point for synthesis of HENs achieving (within a few percent) the area and capital cost targets.</p>
<p>For changing or uncertain operating conditions, a Class 1 resilience target is presented which predicts, given the nominal operating conditions, the largest uncertainty range for which a "practical" HEN (with few more units and stream splits than that required for nominal conditions) can be synthesized. This resilience target also predicts whether trade-offs (in utilities, number of units, or size of uncertainty range) must be made to achieve resilience, and the operating condition and constraint most likely to limit resilience.</p>
<p>A nonlinear program is formulated to calculate the Class 1 HEN resilience target. Trade-offs with minimum approach temperature, utility consumption, and nominal network area are presented. The use of the Class 1 resilience target as a synthesis tool is discussed.</p>
<p>Finally, a simple procedure to predict the trade-off between cost and resilience is introduced so that a process engineer can design for an economically "optimal" amount of resilience.</p>https://thesis.library.caltech.edu/id/eprint/520Robust Control Strategies for a Fixed Bed Chemical Reactor
https://resolver.caltech.edu/CaltechETD:etd-11132007-110352
Authors: Webb, Christopher John
Year: 1990
DOI: 10.7907/h2d4-tq78
<p>This thesis addresses the practical application of robust control design to an experimental fixed bed reactor. Controllers are designed using robust control theory, specifically, Structured Singular Value analysis and Internal Model Control theory. These controllers are guaranteed to be stable and have good performance even when there is plant-model mismatch. To understand the sources of model mismatch and how model mismatch affects a fixed bed reactor's control design, an experimental methanation reactor was constructed.</p>
<p>The reactor is non-adiabatic with a constant wall temperature. A series of thermo couples located inside an axial thermowell are used to measure bed temperatures, and a gas chromatograph is used to measure gas concentrations. The pilot plant includes a feed-effluent heat exchanger and a product recycle line for positive feedback of both mass and energy.</p>
<p>A mathematical model of the reactor is developed from first principles. This dynamic model is a three dimensional heterogenous model. It consists of four non-linear coupled partial differential equations. Finite difference methods are used to approximate these equations with a series of ordinary differential equations. The temperature profiles simulated using the model compare favorably with the profiles obtained from the experimental reactor.</p>
<p>Two control configurations are studied: the control of the hot spot temperature using the flow rate of an inert gas, and the control of the outlet concentration and temperature by manipulating the recycle flow rate and power supplied to an inlet heater. For both of these experiments, the control objective is to maintain stability and acceptable performance for a variety of operating conditions. Bounds of the amount of model uncertainty are explicitly incorporated in the controller design.</p>
<p>A new methodology for computing frequency domain uncertainty bounds for single-input single-output systems is presented. This new methodology uses spectral analysis to identify a series of non-parametric frequency domain models and a "regions-mapping" technique to bound the frequency by frequency description of these models in the complex plane. The methodology is compared to existing non-parametric techniques and shown to be superior for identifying the uncertainty bound associated with a nonlinear system. This methodology is then applied to the hot spot temperature identification problem of the fixed bed reactor. A robust controller with a single adjustable parameter is designed for the reactor using Internal Model Control (IMC) theory. The computed uncertainty bounds are experimentally validated using the IMC controller.</p>
<p>A simple procedure is presented for designing a robust controller when one or more of the control variables must be inferred from other process measurements. As part of this procedure, a robust measurement selection scheme determines which process measurements should be used for inference. The measurement selection scheme is based on Structured Singular Value analysis. This procedure is successfully applied to the outlet concentration control for the experimental methanation reactor.</p>https://thesis.library.caltech.edu/id/eprint/4542Studies in Robust Control of Systems Subject to Constraints
https://resolver.caltech.edu/CaltechETD:etd-10252002-161632
Authors: Campo, 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/4243Robustness 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: Doyle, Francis Joseph, III
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: Lee, Jay Hyung
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/4589Homogeneous Azeotropic Distillation: Entrainer Selection
https://resolver.caltech.edu/CaltechETD:etd-11162005-143300
Authors: Laroche, Lionel
Year: 1991
DOI: 10.7907/V760-0555
<p>We examine the simplest homogeneous azeotropic distillation sequence of industrial relevance, where we add an entrainer to a binary azeotrope in order to recover both azeotropic constituents as pure products. Despite its apparent simplicity, such distillation columns can exhibit an unusual behavior not observed in zeotropic distillation:<br />
- For some mixtures, separation as a function of reflux goes through a maximum. At infinite reflux, no separation is achieved.<br />
- In some cases, achieving the same specifications with a larger number of trays requires a larger reflux.<br />
- In some cases the only feasible separation yields the intermediate component as a pure distillate while the bottom product contains the light and heavy components.<br />
- In some cases the only feasible separation yields the intermediate component as a pure bottom product while the distillate contains the light and Hay components.</p>
<p>While these unusual features can be regarded as curiosities, they are essential for proper entrainer selection and design. When designing a homogeneous azeotropic sequence which separates a binary azeotrope into two pure products, we must first choose the entrainer. Currently available entrainer selection criteria, are inadequate: They contradict one another and often lead to incorrect conclusions. Indeed, for a minimum boiling azeotrope, the existing entrainer selection rules state that, one should use a high boiling component that introduces no additional azeotrope (Benedict & Rubin 1945), an intermediate boiling component that introduces no additional azeotrope (Hoffman 1964), a component which introduces no distillation boundary between the azeotropic constituents (Doherty & Caldarola 1985), and either a low boiling component that introduces no additional azeotrope or a component that introduces new minimum boiling azeotropes (Stichlmair, Fair & Bravo 1989). By taking advantage of the curious aforementioned features, we have been able to understand when these criteria, are correct, or incorrect.</p>
<p>In the case of homogeneous azeotropic distillation, separability at finite reflex and at infinite reflux are not equivalent and must be examined separately. By analyzing in detail the profiles of columns operated at infinite reflux, we have:<br />
- shown that a binary azeotrope can be separated with only one distillation column. We present a necessary and sufficient condition that identifies such situations;<br />
- found a necessary and sufficient condition for separability in a two-column sequence. When separation is feasible, this condition indicates the flowsheet of the corresponding separation sequence;<br />
- shown that separation is very often feasible in a three-column separation if the two azeotropic constituents are located in adjacent distillation regions.</p><br />
<p>Then, we examine two situations where separation is feasible at finite reflux but not at infinite reflex.</p>
<p>Finally, we present practical solutions (in the case of entrainers that add no azeotropes to two problems of industrial relevance: Given a binary azeotrope that we want to separate into pure components, and a set of candidate entrainers, how do we determine which one is the best? Also, for each of these entrainers, what is the flowsheet of the feasible separation sequence(s)? We obtain these solutions by analyzing in detail the mechanisms by which heavy, intermediate and light entrainers make separation feasible, using the new notions of equivolatility curves, of isovolatility curves and of local volatility order. We show that the second question finds an easy solution from the volatility order diagram.</p>
<p>This analysis shows that a good entrainer is a component that "breaks" the azeotrope easily (i.e., even when its concentration is small) and yields high relative volatilities between the two azeotropic consituents. Because these attributes can be easily identified in an entrainer from the equivolatility curve diagram of the ternary mixture azeotropic component #1 - azeotropic component #2 - entrainer, we can easily compare entrainers by examining the corresponding equivolatility curve diagrams. We also demonstrate the validity and limits of this method with numerous examples.</p>
https://thesis.library.caltech.edu/id/eprint/4590Robust Loopshaping for Process Control
https://resolver.caltech.edu/CaltechETD:etd-08222007-105213
Authors: Braatz, Richard Dean
Year: 1993
DOI: 10.7907/vqmv-kw76
<p>Strong trends in chemical engineering and plant operation have made the control of processes increasingly difficult and have driven the process industry's demand for improved control techniques. Improved control leads to savings in resources, smaller downtimes, improved safety, and reduced pollution.</p>
<p>Though the need for improved process control is clear, advanced control methodologies have had only limited acceptance and application in industrial practice. The reason for this gap between control theory and practice is that existing control methodologies do not adequately address all of the following control system requirements and problems associated with control design:
<ul>
<li>The controller must be insensitive to plant/model mismatch, and perform well under unmeasured or poorly modeled disturbances.</li>
<li>The controlled system must perform well under state or actuator constraints.</li>
<li>The controlled system must be safe, reliable, and easy to maintain.</li>
<li>Controllers are commonly required to be decentralized.</li>
<li>Actuators and sensors must be selected before the controller can be designed.</li>
<li>Inputs and outputs must be paired before the design of a decentralized controller. </li>
</ul></p>
<p>A framework is presented to address these control requirements/problems in a general, unified manner. The approach will be demonstrated on adhesive coating processes and distillation columns.</p>https://thesis.library.caltech.edu/id/eprint/3199Multiple steady states in distillation
https://resolver.caltech.edu/CaltechETD:etd-09122007-075846
Authors: Bekiaris, Nikolaos
Year: 1995
DOI: 10.7907/S6MC-5V73
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
We study multiple steady states in distillation. We first analyze the simplest case of ternary homogeneous azeotropic mixtures. We show that in the case of infinite reflux and an infinite number of trays ([...] case) one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. We also locate in the composition triangle the feed compositions that lead to these multiple steady states.
We further note that most of these results are independent of the thermodynamic model used. We show that the prediction of the existence of multiple steady states in the [...] case has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows. Nevertheless, the [...] multiplicities do exist for columns at realistic operating conditions. We comment on the effect of multiplicities on column design and operation for some specific examples.
We then extend the homogeneous mixture results to ternary heterogeneous mixtures. We study the [...] case in much more depth and detail by demonstrating how the [...] analysis can be applied to different column designs. More specifically, we show how the feasible distillate and bottom product paths can be located for tray or packed columns, with or without decanter and with different types of condenser and reboiler. We derive the fully detailed, necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the product paths. Simulation results for finite columns show that the predictions carry over to the finite case.
The complete list of the [...] case predictions is presented. The implications of these multiplicities for column design, synthesis and simulation are demonstrated. More specifically, we show how the [...] predictions can be useful for the selection of the entrainer, the equipment and the separation scheme. We show that, in some cases, the column operation at an unstable steady state may have some advantages. The important issue of the effect of the thermodynamic phase equilibrium on the existence of multiplicities is discussed. Using the [...] analysis, we identify entire mixture classes for which multiplicities are inherent and robust. Mixtures with ambiguous VLE data are studied; we show that in some cases a slight VLE difference between models and/or experimental data may affect the existence of multiplicities while other, major VLE discrepancies do not. Finally, we identify the key issues and the pitfalls one should be cautious about when designing or computing the composition profile of an azeotropic distillation column with a commercial simulator.
https://thesis.library.caltech.edu/id/eprint/3503Robust control of systems subject to constraints
https://resolver.caltech.edu/CaltechETD:etd-10232007-141113
Authors: Zheng, Zhi Qiang (Alex)
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/4224Model Predictive Control (MPC) for Constrained Nonlinear Systems
https://resolver.caltech.edu/CaltechETD:etd-12192007-112031
Authors: De Oliveira, Simone Loureiro
Year: 1996
DOI: 10.7907/MXYW-TB71
<p>This thesis addresses the development of stabilizing model predictive control algorithms for nonlinear systems subject to input and state constraints and in the presence of parametric and/or structural uncertainty, disturbances and measurement noise.</p>
<p>Our basic model predictive control (MPC) scheme consists of a finite horizon MPC technique with the introduction of an additional state constraint which we have denoted contractive constraint. This is a Lyapunov-based approach in which a Lyapunov function chosen a priori is decreased, not continuously, but discretely; it is allowed to increase at other times (between prediction horizons). We will show
in this work that the implementation of this additional constraint into the on-line optimization makes it possible to prove rather strong stability properties of the closed-loop system. In the nominal case and in the absence of disturbances, it is possible to show that the presence of the contractive constraint renders the closed-loop system exponentially stable. We will also examine how the stability properties weaken as structural and/or parametric model/plant mismatch, disturbances and measurement noise are considered.</p>
<p>Another important aspect considered in this work is the computational efficiency and implement ability of the algorithms proposed. The MPC schemes previously proposed in the literature which are able to guarantee stability of the closed-loop system involve the solution of a nonlinear programming problem at each time step in order to find the optimal (or, at least, feasible) control sequence. Nonlinear programming is the general case in which both the objective and constraint functions may be non-linear, and is the most difficult of the smooth optimization problems.</p>
<p>Due to the difficulties inherent to solving nonlinear programming problems and since MPC requires the optimal (or feasible) solution to be computed on-line, it is important that an alternative implementation be found which guarantees that the problem can be solved in a finite number of steps. It is well-known that both linear and quadratic programming (QP) problems satisfy this requirement.</p>
<p>If a standard quadratic objective function is used and the input/state constraints are linear in the decision variables, then the contractive constraint (which is originally a quadratic constraint) can be implemented in such a way that the optimization problem to be solved in the prediction step of the MPC algorithm is reduced to a QP. Having linear input/state constraints means that a linear approximation of the original nonlinear system has to be used in the prediction as well as in the computation of the contractive constraint. Thus, in order to make the algorithm more easily implementable we introduce the difficulty of having to handle the mismatch between the real nonlinear system and its linear approximation which is used for prediction. In other words, we now have a robust MPC control problem at hand. In this case, it is the contractive constraint which comes to the rescue and allows the MPC controller to stabilize the closed-loop system spite of the linear/nonlinear mismatch, for certain choices of the contractive parameter (the parameter which defines how much "shrinkage" of the states is required during one prediction horizon).</p>
<p>In summary, this thesis is an application of contractive principles to model predictive control and it is dedicated to robust stability analysis, design and implementation of state and output feedback "contractive" MPC schemes.</p>
https://thesis.library.caltech.edu/id/eprint/5069Control of Systems Subject to Constraints
https://resolver.caltech.edu/CaltechETD:etd-01162008-153136
Authors: Kothare, Mayuresh V.
Year: 1997
DOI: 10.7907/anhq-xj51
<p>Every operating control system must deal with constraints. On the one hand, the range and rate of change of the input or manipulated variable is limited by the physical nature of the actuator (saturation limits). On the other hand, process state variables or outputs (pressures, temperatures, voltages) may not be allowed to exceed certain bounds arising from equipment limitation, safety considerations, or environmental regulations.</p>
<p>A rich theory exists for designing controllers - both linear (H<sub>2</sub>/H<sub>∞</sub>, LQG, LTR, pole-placement) and nonlinear (nonlinear H<sub>∞</sub>, control, feedback linearization, sliding mode control, gain scheduling). However, none of these popular and fashionable controller design techniques account for the presence of input or output constraints. Although occasionally these constraints may be neglected, in general, they lead to design and operating problems unless they are accounted for properly.</p>
<p>In traditional control practice, overrides or mode selection schemes are used to deal with output constraints: they switch between a "bank" of controllers, each of which is designed to achieve a specific objective. In both cases (saturation limit and mode selection), a control input nonlinearity is introduced into the operating system.</p>
<p>Despite its significance, the study of the constrained control problem has received far less attention than the traditional unconstrained (linear and nonlinear) control theory. With few exceptions, most of the controller design techniques for constrained systems are by-and-large ad-hoc, with very little guarantees of stability, performance and robustness to plant model uncertainty.</p>
<p>The objective of this thesis is to take a broad approach towards the constrained control problem. One part of the thesis is devoted to the development of a systematic and unifying theory for studying the so-called Anti-Windup Bumpless Transfer (AWBT) problem. The other part aims towards the development of a general novel approach for the synthesis of a robust model predictive control (MPC) algorithm.</p>
https://thesis.library.caltech.edu/id/eprint/207Nonlinear modeling and identification for process control
https://resolver.caltech.edu/CaltechETD:etd-02042008-082018
Authors: Rhodes, Carl
Year: 1998
DOI: 10.7907/96TN-SN45
Ideally, processes to be controlled would behave in a linear manner so that well-developed methods of linear control could be applied directly. However, environmental regulations and increased competition are forcing these processes to operate in regions where the assumptions of linearity tend to break down. There has been a great deal of recent academic interest in the control of nonlinear systems, but there are relatively few applications of these methods in industry. One major reason may be the lack of tools for developing models suitable for nonlinear control schemes.
A number of tools that can be used in the modeling of nonlinear systems for process control are presented in this thesis. In the first section, the problem of determining the proper regression vector size for black-box modeling is examined. The false nearest neighbors algorithm (FNN) is suggested as a solution for this problem. Extensions, analysis, and numerous applications of the FNN algorithm are given and the algorithm is seen to be a useful tool in the identification of nonlinear models.
In the second section of the thesis, the problem of nonlinear model reduction for systems exhibiting large time-scale separations is examined. A method of determining the reduced order manifold of slow dynamics is outlined and it is proved that this algorithm identifies the proper manifold. Some thoughts on how the results of the algorithm can be used for developing reduced models are presented.
In the third section, the concept of data-based control is introduced. This method of control attempts to utilize process data directly through local modeling techniques. Some preliminary work in this area is given for trajectory tracking and computing controllable sets and data-based control is successfully applied to an experimental electrical circuit. Finally, some thoughts on possible future work in this field are presented.
https://thesis.library.caltech.edu/id/eprint/493Design and control studies on the fluid catalytic cracking process
https://resolver.caltech.edu/CaltechETD:etd-02012008-111240
Authors: Huq, Iftikhar
Year: 1998
DOI: 10.7907/7SWK-0M04
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Fluid Catalytic Cracking (FCC) units are widely used in the oil refining industry to crack low value hydrocarbons into a range of higher value hydrocarbons including gasoline. Because of its feed processing flexibility, the FCC process is considered a primary conversion unit in an integrated refinery and optimal FCC operation can have a significant impact on the refinery profitability. Because of its important role in the refinery, the FCC process has recently attracted renewed interest both from academia and industry, with the main emphasis on better understanding and operating the process. In general, several possible alternatives can usually be postulated or envisioned to realize operational improvements, and the critical task is then to rank order these alternatives. Rank ordering the available alternatives requires the utilization of suitable:
1. process models describing each alternative,
2. tools to quantitatively assess the operational performance achievable with each alternative. "Operational performance" here refers to the quality of closed loop process response.
The different alternatives have often been analyzed and compared through extensive simulations. However, because of stringent environmental and economic requirements, most industrial plants, including the FCC process have evolved into highly complex and integrated processes and ranking through simulation might be infeasible. In ranking design alternatives through simulation, two crucial factors must be considered if the conclusions drawn from such studies are to be reasonably reliable:
• Detailed case studies need to be conducted for all the alternatives. These case studies typically require considering the effect of a wide range of disturbances, inputs, operating conditions, model structures and parameters, control structures and parameters. It might be necessary to examine many hundreds if not thousands of possible alternatives. Moreover, the effect of many other aspects of practical operation such as plant/model mismatch, process constraints, sensor/actuator failures, etc. on the operational performance must also be considered for each case, and makes the assessment significantly more involved.
• While qualitative "good/bad" indicators might have been sufficient in the past, it is becoming more important to quantitatively rank order the available alternatives in todays highly competitive environment. Indeed, choosing a "slightly better" alternative over a "good" alternative can have a significant impact on the sustained profitability of the process.
Because of the large number of possible cases that must be considered, contradictory conclusions can often be drawn when using such an approach to rank the available alternatives. Such a simulation approach is therefore infeasible except possibly for the simplest of cases. This suggests the utilization of more efficient screening tools to effectively assess the many design alternatives possible for improved process operation while accounting for the practical considerations just discussed. With respect to the requirements (1) and (2) above for ranking the possible alternatives, we note that:
1. FCC models: The renewed interest in improved FCC operation is partially reflected by the recent publication in the open literature of two first principles models claiming to describe the essential features of the FCC process dynamics (Arbel, Huang, Rinard, Shinnar and Sapre 1995, McFarlane, Reineman, Bartee and Georgakis 1993).
2. Tools for operational performance assessment: The structured singular value (SSV) framework introduced by Doyle (1982) provides a quantitative measure of the achievable operational performance, explicitly accounts for plant/model mismatch, and also permits the approximate incorporation of many of the practical requirements indicated above into the analysis.
Utilizing the two first principles FCC models and the structured singular value framework, several aspects of the design and control of FCC processes have been addressed in this thesis, with special emphasis on quantitatively ranking possible design/control options from an operational performance improvement viewpoint:
1. Model IV FCC units differ from other cracking units in that model IV FCC units do not have slide valves in the catalyst circulation lines to enable direct control of catalyst circulation rate through the unit. Reducing fluctuations in catalyst circulation rate is found to significantly improve closed loop performance of this FCC unit. Based on this process insight: (1) an operational modification: operating the regenerator with the catalyst overflow weir always flooded, and (2) a design modification: installing slide valves in the catalyst circulation U- tubes are studied and shown to reduce catalyst flow fluctuations and improve the operational performance of the FCC unit. It is interesting to note that essentially all new FCC units and revamped older FCC units typically include both the above two modifications. To reflect this current FCC operation it is assumed for all the subsequent analysis in this thesis that the above two modifications are already incorporated into the FCC design.
2. A quantitative rank ordering of possible control structures for FCC operation in both partial combustion (PC) mode and complete combustion (CC) mode operation is undertaken. It is argued that intentional transitions between the PC and CC modes is rare. For FCC units operated within design specifications, 2 x 2 control structures are found to be sufficient for effective regulatory control. In particular, it is found that high coking feeds cannot be processed in CC mode operation as the safe upper limit on regenerator temperature can be violated. For PC mode regulation, riser temperature [...] and regenerator dense bed temperature [...] are the most suitable choice for controlled variables. For CC mode regulation, [...] are the most suitable choice for controlled variables, where [...] is the flue gas [...] molar concentration. If higher coking feeds are to be processed, the FCC would need to be refitted with additional process units, as discussed in Point 4 below. For both PC and CC modes, using feed temperature [...] and combustion air rate [...] as manipulated variables is found to provide operational performance levels comparable to those achieved with more conventional control structures typically used in industry (using catalyst circulation rate [...] and combustion air rate). That feed temperature can be an effective manipulated variable can have significant implications for the improved operation of older FCCs (e.g. the Model IV) where catalyst circulation rate cannot be directly manipulated.
3. Decentralized regulatory control of the FCC unit operating in PC mode is examined in detail. Decentralized PI controllers are considered, as they are most often used in the industrial setting. It is found that (1) Decentralized PI controllers can provide satisfactory regulation over the normal FCC operating range. (2) A common regulatory control strategy for PC mode operation is to use decentralized PI controllers for the pairing [...](notation in Point 2). It is shown that "tightening" the two PI controllers in fact reduces the process interactions and improves operational performance. This is counterintuitive - typically, detuning the controllers is expected to reduce process interactions and improve performance. (3) Certain FCC operating points are unstable. In the absence of control action, the FCC process would either drift to a stable operating point at a higher regenerator temperature or wind down to the cold state (negligible regenerator combustion and reactor cracking). It is shown that reasonable transitions to unstable operating points can be effectively handled with an appropriately tuned decentralized PI controller. (4) A theoretical development that provides insight into possible changes in the sign of the steady—state and infinite frequency relative gain array (RGA) elements is also presented. It is found to be related to the non—minimal phase behavior of one or more of the following (a) the overall plant, (b) the individual loop transfer functions, (c) the remaining system if some controlled variable and the associated manipulated variable is removed. Stable plants for which pairing for performance can correspond to negative steady—state RGA pairings are thus identified.
4. There is a growing need in the oil refining industry to process higher coking feeds in FCC units. However, FCC units operated in the CC mode might not be able to process sufficiently high coking feeds (as discussed in Point 2 above), and would have to be refitted to accommodate this greater feed processing flexibility. The most significant operating limitation is found to be the upper limit on regenerator temperature. The two possible refitting options considered here to alleviate the impact of this constraint are: (1) converting to partial combustion mode (PC mode) operation by installing a CO boiler and (2) extending complete combustion mode (CCE mode) operation by installing a catalyst cooler. The main objective is to compare the steady—state and dynamic characteristics of these two refitting options. From a steady state viewpoint, it is found that installing the catalyst cooler has a distinct advantage over installing the CO boiler when processing high coking feeds - because the regenerated catalyst is always clean burned. In particular, the product yields as well as overall conversions are typically higher. A comparison of dynamic characteristics suggests that while a simple decentralized control strategy provides satisfactory performance over a wide operating regime in PC mode, a more sophisticated control strategy might be required to achieve tight control over a comparable operating range in CCE mode with the catalyst cooler.https://thesis.library.caltech.edu/id/eprint/446