[ { "id": "authors:r3w7x-hye17", "collection": "authors", "collection_id": "r3w7x-hye17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190320-132001216", "type": "book_section", "title": "Computational complexity of \u03bc calculation", "book_title": "1993 American Control Conference", "author": [ { "family_name": "Braatz", "given_name": "Richard D.", "clpid": "Braatz-R-D" }, { "family_name": "Young", "given_name": "Peter M.", "clpid": "Young-P-M" }, { "family_name": "Doyle", "given_name": "John C.", "orcid": "0000-0002-1828-2486", "clpid": "Doyle-J-C" }, { "family_name": "Morari", "given_name": "Manfred", "clpid": "Morari-M" } ], "abstract": "The structured singular value \u03bc measures the robustness of uncertain Systems. Numerous researchers over the last decade have worked on developing efficient methods for computing \u03bc. This paper considers the complexity of calculating \u03bc with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the \u03bc 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 \u03bc of general systems with pure real or mixed uncertainty for other than small problems.", "doi": "10.23919/ACC.1993.4793162", "isbn": "0-7803-0860-3", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1993-06", "pages": "1682-1683" }, { "id": "authors:djmrf-r3693", "collection": "authors", "collection_id": "djmrf-r3693", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170613-172633659", "type": "book_section", "title": "Identification and Cross-Directional Control of Coating Processes: Theory and Experiments", "book_title": "1992 American Control Conference", "author": [ { "family_name": "Braatz", "given_name": "Richard D.", "clpid": "Braatz-R-D" }, { "family_name": "Tyler", "given_name": "Matthew L.", "clpid": "Tyler-M-L" }, { "family_name": "Morari", "given_name": "Manfred", "clpid": "Morari-M" }, { "family_name": "Pranckh", "given_name": "Ferdinand R.", "clpid": "Pranckh-F-R" }, { "family_name": "Sartor", "given_name": "Luigi", "clpid": "Sartor-L" } ], "abstract": "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.", "isbn": "0-7803-0210-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1992-06", "pages": "1556-1561" }, { "id": "authors:w10fj-kcd72", "collection": "authors", "collection_id": "w10fj-kcd72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170613-173733581", "type": "book_section", "title": "Robust Control for a Noncolocated Spring-Mass System", "book_title": "1992 American Control Conference", "author": [ { "family_name": "Braatz", "given_name": "Richard D.", "clpid": "Braatz-R-D" }, { "family_name": "Morari", "given_name": "Manfred", "clpid": "Morari-M" } ], "abstract": "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 \u03bc-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.", "isbn": "0-7803-0210-9", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1992-06", "pages": "2061-2062" }, { "id": "authors:g3hwd-54d75", "collection": "authors", "collection_id": "g3hwd-54d75", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170620-161438264", "type": "book_section", "title": "\u03bc-sensitivities as an aid for robust identification", "book_title": "1991 American Control Conference", "author": [ { "family_name": "Braatz", "given_name": "R. D.", "clpid": "Braatz-R-D" }, { "family_name": "Morari", "given_name": "M.", "clpid": "Morari-M" } ], "abstract": "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 \u03bc-sensitivities.", "isbn": "0-87942-565-2", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "1991-06", "pages": "231-236" } ]