Control system design for dynamical systems with statistical model uncertainty.

摘要

This dissertation is devoted to the study of control systems for which the plant models are uncertain. The plant model uncertainty considered is of statistical nature. The model uncertainty is assumed to be given in terms of first- and second-order statistics of random model parameters, or alternatively, by a joint probability distribution.; The first problem is the characterization of the eigenvalue variance of an uncertain matrix. The variance of an uncertain eigenvalue is expressed approximately in terms of the statistics of the matrix uncertain parameters. The variance expression is then used to construct uncertainty cost functions used to optimize the robustness of a control system design in a state-space framework. An example from the aerospace industry is presented to illustrate the methodology. The second problem is analogous to the first one. The root variance of an uncertain polynomial is calculated approximately as a function of uncertain polynomial parameters. It is then used to construct design cost functions used to optimize the robustness of a control system design in a transfer function framework. A DC servomotor control system design is presented. In order to illustrate the methodology. The third part of this work describes the application of the root variance formula to the construction of the stochastic root locus (SRL). The SRL is here defined in such a way that it reduces to the root locus if the model uncertainty is reduced to zero. A seismic structural control application is employed for illustration purposes. Finally, the problem of model uncertainty characterization is addressed within a statistical framework. Both coprime factor and additive uncertainty structures are studied. A gaussian structure of the joint probability distribution for the uncertain plant parameters is assumed, and elliptical contours of uncertainty are then plotted in the complex plane. The idea in mind is to translate statistical model uncertainty into weighting factors instrumental in an H∞ control system design.; The last part of the document includes the conclusions and suggestions for further study of the problem.