Probabilistic Robust Control: Theory and Applications

<p>In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input un...

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Main Author: May, Bennett Scott
Format: Others
Language:en
Published: 1998
Online Access:https://thesis.library.caltech.edu/8102/1/may_bs_1998.pdf
May, Bennett Scott (1998) Probabilistic Robust Control: Theory and Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/19jn-c337. https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011 <https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011>
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spelling ndltd-CALTECH-oai-thesis.library.caltech.edu-81022021-08-24T05:01:32Z https://thesis.library.caltech.edu/8102/ Probabilistic Robust Control: Theory and Applications May, Bennett Scott <p>In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input uncertainty for the system may be described most appropriately using probabilistic or "soft" bounds on the model and input sets. The probabilistic robust control methodology contrasts with existing H∞/μ robust control methodologies that do not use probability information for the model and input uncertainty sets, yielding only the guaranteed (i.e., "worst-case") system performance, and no information about the system's probable performance which would be of interest to civil engineers.</p> <p>The design objective for the probabilistic robust controller is to maximize the reliability of the uncertain structure/controller system for a probabilistically-described uncertain excitation. The robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model by the probability of that model, then integrating over the set of possible models. This integration is accomplished efficiently using an asymptotic approximation. The probable performance can be optimized numerically over the class of allowable controllers to find the optimal controller. Also, if structural response data becomes available from a controlled structure, its probable performance can easily be updated using Bayes's Theorem to update the probability distribution over the set of possible models. An updated optimal controller can then be produced, if desired, by following the original procedure. Thus, the probabilistic framework integrates system identification and robust control in a natural manner.</p> <p>The probabilistic robust control methodology is applied to two systems in this thesis. The first is a high-fidelity computer model of a benchmark structural control laboratory experiment. For this application, uncertainty in the input model only is considered. The probabilistic control design minimizes the failure probability of the benchmark system while remaining robust with respect to the input model uncertainty. The performance of an optimal low-order controller compares favorably with higher-order controllers for the same benchmark system which are based on other approaches. The second application is to the Caltech Flexible Structure, which is a light-weight aluminum truss structure actuated by three voice coil actuators. A controller is designed to minimize the failure probability for a nominal model of this system. Furthermore, the method for updating the model-based performance calculation given new response data from the system is illustrated.</p> 1998 Thesis NonPeerReviewed application/pdf en other https://thesis.library.caltech.edu/8102/1/may_bs_1998.pdf May, Bennett Scott (1998) Probabilistic Robust Control: Theory and Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/19jn-c337. https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011 <https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011> https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011 CaltechTHESIS:03042014-093439011 10.7907/19jn-c337
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language en
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description <p>In this work, the development of a probabilistic approach to robust control is motivated by structural control applications in civil engineering. Often in civil structural applications, a system's performance is specified in terms of its reliability. In addition, the model and input uncertainty for the system may be described most appropriately using probabilistic or "soft" bounds on the model and input sets. The probabilistic robust control methodology contrasts with existing H∞/μ robust control methodologies that do not use probability information for the model and input uncertainty sets, yielding only the guaranteed (i.e., "worst-case") system performance, and no information about the system's probable performance which would be of interest to civil engineers.</p> <p>The design objective for the probabilistic robust controller is to maximize the reliability of the uncertain structure/controller system for a probabilistically-described uncertain excitation. The robust performance is computed for a set of possible models by weighting the conditional performance probability for a particular model by the probability of that model, then integrating over the set of possible models. This integration is accomplished efficiently using an asymptotic approximation. The probable performance can be optimized numerically over the class of allowable controllers to find the optimal controller. Also, if structural response data becomes available from a controlled structure, its probable performance can easily be updated using Bayes's Theorem to update the probability distribution over the set of possible models. An updated optimal controller can then be produced, if desired, by following the original procedure. Thus, the probabilistic framework integrates system identification and robust control in a natural manner.</p> <p>The probabilistic robust control methodology is applied to two systems in this thesis. The first is a high-fidelity computer model of a benchmark structural control laboratory experiment. For this application, uncertainty in the input model only is considered. The probabilistic control design minimizes the failure probability of the benchmark system while remaining robust with respect to the input model uncertainty. The performance of an optimal low-order controller compares favorably with higher-order controllers for the same benchmark system which are based on other approaches. The second application is to the Caltech Flexible Structure, which is a light-weight aluminum truss structure actuated by three voice coil actuators. A controller is designed to minimize the failure probability for a nominal model of this system. Furthermore, the method for updating the model-based performance calculation given new response data from the system is illustrated.</p>
author May, Bennett Scott
spellingShingle May, Bennett Scott
Probabilistic Robust Control: Theory and Applications
author_facet May, Bennett Scott
author_sort May, Bennett Scott
title Probabilistic Robust Control: Theory and Applications
title_short Probabilistic Robust Control: Theory and Applications
title_full Probabilistic Robust Control: Theory and Applications
title_fullStr Probabilistic Robust Control: Theory and Applications
title_full_unstemmed Probabilistic Robust Control: Theory and Applications
title_sort probabilistic robust control: theory and applications
publishDate 1998
url https://thesis.library.caltech.edu/8102/1/may_bs_1998.pdf
May, Bennett Scott (1998) Probabilistic Robust Control: Theory and Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/19jn-c337. https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011 <https://resolver.caltech.edu/CaltechTHESIS:03042014-093439011>
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