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Model validation, control, and computation

Citation

Newlin, Matthew Philip (1996) Model validation, control, and computation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-01032008-090000

Abstract

Engineering in general is concerned with controlling and predicting future behavior with some certainty despite having only imperfect information. Although feedback can be an exceptionally effective engineering tool and is often easy to apply, the behavior of a system under feedback can be extremely sensitive to model mismatch, which is always present. The potential for unpredictable behavior is a major drawback to the engineering application of feedback. Robust control theory addresses this difficulty by parametrizing a family of feedback controllers that are less sensitive to model mismatch.

Despite encouraging early applications, robust control theory has so far been deficient in analysis of systems, synthesis of controllers, connection to real problems, and applicability to nonlinear problems. Further, results on the computational complexity of robust control problems that necessitate either bounds computation or a restricted class of problems have cast doubts about the potential utility of the area.

Initial work in robust control focused on complex uncertainty in the frequency domain. A perceived deficiency is that such model sets are unrealistic: uncertainty in mass, stiffness, aero-coefficients, and the like are naturally modeled as real variations. This thesis includes initial work on practical upper bound computation and substantially improved lower bound computation for moderately large robust control analysis problems that include such real parametric uncertainty, despite the computational complexity of the problems. Although better upper bound computation than that described here is now available for small problems, such is not the case for large problems. The improved lower bound computation chronicled here is desirable because the initial lower bound computation for problems with real parametric uncertainty is not as reliable as in the complex case. Additionally, this thesis shows that branch and bound is a limited but critical tool for better computation, a fact that previously has gone unrecognized.

Together, these contributions allow for the practical computation of robust control problems of engineering interest and provide the basis not only for applications that may ultimately determine the utility of the robust control paradigm but also for the computation of various outgrowths of the [mu] framework, which is the basis for computational robust control.

One such outgrowth is the model validation problem. Model validation tests whether a robust control model in the [mu] framework is consistent with experimentally determined time histories quite a different problem than standard system identification. This thesis shows that the model validation problem is indeed closely related to the standard [mu] problem and its computation.

The practical computation of the model validation problem, which should follow naturally from the work presented here, provides the basis for the connection between robust control theory and practical applications. Future work along these lines should elevate the application of robust control theory from chance and intuition to a standard engineering tool.

Further, the techniques that render the model validation problem similar to the standard [mu] problem are applicable to a great variety of systems analysis and design problems. This newly perceived generality of the [mu] paradigm may ultimately provide a unifying framework for the many seemingly disparate aspects of systems and control design.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Doyle, John Comstock
Thesis Committee:
  • Doyle, John Comstock (chair)
  • Burdick, Joel Wakeman
  • Murray, Richard M.
  • Smith, Roy
Defense Date:22 September 1995
Record Number:CaltechETD:etd-01032008-090000
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-01032008-090000
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:24 Jan 2008
Last Modified:26 Dec 2012 02:26

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