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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:55:26 +0000Robust Analysis of Feedback Systems with Parametric and Dynamic Structured Uncertainty
https://resolver.caltech.edu/CaltechETD:etd-02012005-084251
Authors: {'items': [{'email': 'ricardo@conae.gov.ar', 'id': 'Sánchez-Peña-Ricardo-Salvador', 'name': {'family': 'Sánchez Peña', 'given': 'Ricardo Salvador'}, 'show_email': 'NO'}]}
Year: 1989
DOI: 10.7907/MM2J-E556
<p>This thesis presents the first general program implementation of the algorithm by deGaston and its generalization by Sideris and deGaston to compute the Multivariable stability margin or Structured singular value of a feedback system under real (independent or related) parametric uncertainty. An improved implementation of the algorithm mentioned above is also considered, which simplifies significantly the code and increases the computational speed. The latter also allows a simple and fast analysis by just checking the extreme values of the set of parameters, with a high probability of achieving the actual stability margin; this being supported by an intense statistical analysis performed at the end of this thesis.</p>
<p>A great deal of work has recently been done related to this class of uncertain systems initiated by the well known theorem of Kharitonov. A connection is made in Chapter 4 between these procedures and the above ones in terms of generality of the class of uncertain polynomials considered. A theorem characterizing the set of polynomials whose robust stability can be determined by a finite number of tests is addressed. Sufficient conditions to determine when the latter conditions apply are also given, which in some cases can considerably simplify the analysis. In particular cases, polynomials with related uncertain parameters can be treated in the same way as independent parameters as shown in two examples.</p>
<p>The main part of this thesis is concerned with the analysis of more general type of uncertainties. In particular, the analysis of robust stability for the case when unstructured dynamic uncertainty is combined with real parametric uncertainty is treated in Chapter 5. This can also be applied in the analysis of robust performance for plants with parametric uncertainty. Chapter 6 generalizes the latter to the most general case in which structured dynamic and real parametric uncertainty appear simultaneously in the plant. A computational scheme is given in both cases which uses the algorithm mentioned in the first part and is applied to several examples.</p>
<p>At the end, an example of the robust analysis of an experimental aircraft demonstrates how a practical situation can be handled by this procedure.</p>https://thesis.library.caltech.edu/id/eprint/425Elementary solutions for the H infinity- general distance problem- equivalence of H2 and H infinity optimization problems
https://resolver.caltech.edu/CaltechETD:etd-05152007-142515
Authors: {'items': [{'id': 'Kavranoglu-D', 'name': {'family': 'Kavranoglu', 'given': 'Davut'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/y2q9-nq75
This thesis addresses the H[infinity] optimal control theory. It is shown that SISO H[infinity] optimal control problems are equivalent to weighted Wiener-Hopf optimization in the sense that there exists a weighting function such that the solution of the weighted H2 optimization problem also solves the given H[infinity] problem. The weight is identified as the maximum magnitude Hankel singular vector of a particular function in H[infinity] constructed from the data of the problem at hand, and thus a state-space expression for it is obtained. An interpretation of the weight as the worst-case disturbance in an optimal disturbance rejection problem is discussed.
A simple approach to obtain all solutions for the Nehari extension problem for a given performance level [gamma] is introduced. By a limit taking procedure we give a parameterization of all optimal solutions for the Nehari's problem.
Using an imbedding idea [12], it is proven that four-block general distance problem can be treated as a one-block problem. Using this result an elementary method is introduced to find a parameterization for all solutions to the four-block problem for a performance level [gamma].
The set of optimal solutions for the four-block GDP is obtained by treating the problem as a one-block problem. Several possible kinds of optimality are identified and their solutions are obtained.https://thesis.library.caltech.edu/id/eprint/1824Constrained H[infinity]-optimization for discrete-time control systems
https://resolver.caltech.edu/CaltechETD:etd-11282007-130457
Authors: {'items': [{'id': 'Rotstein-H-P', 'name': {'family': 'Rotstein', 'given': 'Hector P.'}, 'show_email': 'NO'}]}
Year: 1993
DOI: 10.7907/51VE-9H34
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In order to formulate a problem in the [...]-optimal control framework, all specifications have to be combined in a single [...]-norm objective, by an appropriate selection of weighting functions. If some of the specifications have the form of hard time domain constraints, the task of finding weighting functions that achieve a satisfactory design can become arduous. In this thesis, a theory for constrained [...]-control is presented, that can deal with the standard [...] objective and time domain constraints. Specifically, the following time domain constrained problem is solved: given a number [...], and a set of fixed inputs [...], find a controller such that the closed loop transfer matrix has an [...]-norm less than [...], and the time response [...] to the signal [...] belongs to some pre-specified set [...] for each [...]. Constraints are only imposed over a finite horizon, and this allows the formulation of a two step procedure. In the first step, the optimal way of clearing the constraints is found by computing a solution to a convex non differentiable problem. In the second, a standard unconstrained [...]-problem is solved. The final controller results from putting together the solution to both subproblems.
The objective function for the minimization, and the solution to the whole problem are constructed using state-space formulas. The ellipsoid algorithm is argued to be a convenient procedure for performing the optimization since, if carefully implemented, it can deal with the two main characteristics of the problem, i.e., nondifferentiability and large-scale. The validity of assuming constraints over a finite horizon is justified by presenting a procedure for computing a solution that gives an overall satisfactory behavior. For clarity of exposition, this thesis starts by discussing a very special instance of the problem, and then proceeds to give the solution to the general case. Also, a benchmark problem for robust control is solved to illustrate the applicability of the theory.
https://thesis.library.caltech.edu/id/eprint/4676