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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:58:54 +0000μ-sensitivities as an aid for robust identification
https://resolver.caltech.edu/CaltechAUTHORS:20170620-161438264
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'R. D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'M.'}}]}
Year: 1991
Identification for a model for robust control design is more complicated than for the standard linear system transfer function model-the structure of the uncertainty as well as bounds on its size must be determined. It is especially unclear as to which parts of the system should be better modeled to improve robust performance. This paper addresses this question through some new tools, the μ-sensitivities.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g3hwd-54d75Avery Final Report: Identification and Cross-Directional Control of Coating Processes
https://resolver.caltech.edu/CaltechCDSTR:1992.004
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'Matthew L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
Coating refers to the covering of a solid with a uniform layer of liquid. Of special industrial interest is the cross-directional control of coating processes, where the cross-direction refers to the direction perpendicular to the substrate movement. The objective of the controller is to maintain a uniform coating under unmeasured process disturbances.
Assumptions that are relevant to coating processes found in industry are used to develop a model for control design. We show how to identify the model from input-output data. This model is used to derive a model predictive controller to maintain flat profiles of coating across the substrate by varying the liquid flows along the cross direction.
The model predictive controller computes the control action which minimizes the predicted deviation in cross-directional uniformity. The predictor combines the estimate obtained from the model with the measurement of the cross-directional uniformity to obtain a prediction for the next time step. A filter is used to obtain robustness to model error and insensitivity to measurement noise. The tuning of the noise filter and different methods for handling actuator constraints are studied in detail. The three different constraint-handling methods studied are: the weighting of actuator movements in the objective function, explicitly adding constraints to the control algorithm, i.e. constrained model predictive control, and scaling infeasible control actions calculated from an unconstrained control law to be feasible.
Actuator constraints, measurement noise, model uncertainty, and the plant condition number are investigated to determine which of these limit the achievable closed loop performance. From knowledge of how these limitations affect the performance we find how the plant could be modified to improve the process uniformity. Also, because identification of model parameters is time-consuming and costly, we study how accurate the identification must be to achieve a given level of performance.
The theory developed throughout the paper is rigorously verified though simulations and experiments on a pilot plant. The effect of interactions on the closed loop performance is shown to be negligible for this pilot plant. The measurement noise and the actuator constraints are shown to have the largest effect on closed loop performance.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/94qmz-vz212Robust Control for a Noncolocated Spring-Mass System
https://resolver.caltech.edu/CaltechAUTHORS:20170613-173733581
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1992
Robust control laws are presented for an undamped pair of coupled manes with a noncolocated sensor and actuator. This simple problem captures many of the features of more complex aircraft and space structure vibration control problems. The control problem is formulated in the structured singular value framework, which addresses the stability robustness to parameter variations directly. Controllers are designed by D-K iteration (commonly called μ-synthesis), and the resulting high-order controllers are reduced using Hankel model reduction. Design specifications such as settling time, actuator constraints insensitivity to measurement noise, and parameter uncertainty are achieved by the resulting controllers. Design Problems #1 and #2 were considered in [2]. Design Problem #4 in [11] will be considered in this paper.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/w10fj-kcd72Identification and Cross-Directional Control of Coating Processes: Theory and Experiments
https://resolver.caltech.edu/CaltechAUTHORS:20170613-172633659
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Tyler-M-L', 'name': {'family': 'Tyler', 'given': 'Matthew L.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Pranckh-F-R', 'name': {'family': 'Pranckh', 'given': 'Ferdinand R.'}}, {'id': 'Sartor-L', 'name': {'family': 'Sartor', 'given': 'Luigi'}}]}
Year: 1992
Of special industrial interest is the cross-directional control of continuous coating processes, where the cross-direction refers to the direction perpendicular to the substrate movement. The objective of the controller is to maintain a uniform coating under unmeasured process disturbances based on assumptions relevant to coating processes found in industry. A model for control design is developed. This model is used to derive a model predictive controller with the objective of maintaining flat profiles of coating across the substrate by varying the liquid flows along the cross direction. Actuator constraints, measurement noise, and model uncertainty are investigated to determine which of these limit the achivable closed loop performance. From a knowledge of the effect of these limitations on performance we determine how the plant could be modified to improve the coating uniformity. The theory developed throughout the paper is rigorously verified though experiments on an industrial pilot plant.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/djmrf-r3693Computational Complexity of μ Calculation
https://resolver.caltech.edu/CaltechCDSTR:1993.005
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Young-P-M', 'name': {'family': 'Young', 'given': 'Peter M.'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/yy8es-83493Computational complexity of μ calculation
https://resolver.caltech.edu/CaltechAUTHORS:20190320-132001216
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Young-P-M', 'name': {'family': 'Young', 'given': 'Peter M.'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
DOI: 10.23919/ACC.1993.4793162
The structured singular value μ measures the robustness of uncertain Systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/r3w7x-hye17Stability and Performance Analysis of Systems Under Constraints
https://resolver.caltech.edu/CaltechCDSTR:1993.009
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1993
All real world control systems must deal with actuator and state constraints. Standard conic sector bounded nonlinearity stability theory provides methods for analyzing the stability and performance of systems under constraints, but it is well-known that these conditions can be very conservative. A method is developed to reduce conservatism in the analysis of constraints by representing them as nonlinear real parametric uncertainty.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2zdma-ddb77Robust Loopshaping for Process Control
https://resolver.caltech.edu/CaltechCDSTR:1993.010
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard Dean'}}]}
Year: 1993
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. 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:
* The controller must be insensitive to plant/model mismatch, and perform well under unmeasured or poorly modeled disturbances.
* The controlled system must perform well under state or actuator constraints.
* The controlled system must be safe, reliable, and easy to maintain.
* Controllers are commonly required to be decentralized.
* Actuators and sensors must be selected before the controller can be designed.
* Inputs and outputs must be paired before the design of a decentralized controller.
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.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/mexyy-rcd09Robust Control Structure Selection
https://resolver.caltech.edu/CaltechCDSTR:1993.012
Authors: {'items': [{'id': 'Lee-J-H', 'name': {'family': 'Lee', 'given': 'Jay H.'}}, {'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}, {'id': 'Packard-A', 'name': {'family': 'Packard', 'given': 'Andrew'}}]}
Year: 1993
Screening tools for control structure selection in the presence of model/plant mismatch are developed in the context of the Structured Singular Value (μ) theory. The developed screening tools are designed to aid engineers in the elimination of undesirable control structure candidates for which a robustly performing controller does not exist. Through application on a multicomponent distillation column, it is demonstrated that the developed screening tools can be effective in choosing an appropriate control structure while previously existing methods such as the Condition Number Criterion can lead to erroneous results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8qa3g-ndw41Minimizing the Euclidean Condition Number
https://resolver.caltech.edu/CaltechAUTHORS:20120229-153642155
Authors: {'items': [{'id': 'Braatz-R-D', 'name': {'family': 'Braatz', 'given': 'Richard D.'}}, {'id': 'Morari-M', 'name': {'family': 'Morari', 'given': 'Manfred'}}]}
Year: 1994
DOI: 10.1137/S0363012992238680
This paper considers the problem of determining the row and/or column scaling of a matrix A that minimizes the condition number of the scaled matrix. This problem has been studied by many authors. For the cases of the ∞-norm and the 1-norm, the scaling problem was completely solved in the 1960s. It is the Euclidean norm case that has widespread application in robust control analyses. For example, it is used for integral controllability tests based on steady-state information, for the selection of sensors and actuators based on dynamic information, and for studying the sensitivity of stability to uncertainty in control systems.
Minimizing the scaled Euclidean condition number has been an open question—researchers proposed approaches to solving the problem numerically, but none of the proposed numerical approaches guaranteed convergence to the true minimum. This paper provides a convex optimization procedure to determine the scalings that minimize the Euclidean condition number. This optimization can be solved in polynomial-time with off-the-shelf software.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/77k80-98q27