| The first part of this work extends principal component analysis (PCA) to random elements of abstract Hilbert spaces. Using only standard functional analysis, it is shown that the optimal PCA subspace is spanned by the eigenvectors of the covariance operator and the linear variety that minimizes average squared error contains the mean of the distribution. An immediate application is converting a nonlinear parametrization of a dynamical system model to an optimal linear one. This makes possible adaptive control of such systems by using established linear estimation techniques.; The second part describes the modeling of an electrohydraulic pressure servo valve and brake hydraulic system, and the design of an inner-loop controller which can be used with independent antiskid or auto-brake controllers. The effects of connecting lines on stability and performance are explicitly taken into account in control design by using analytical solutions to two-dimensional viscous compressible model of fluid motion in the pipes. The modal approximation technique is used in the simulations. In order to facilitate control design, singular perturbation analysis is employed to reduce the order of the model in a systematic fashion. Combining partial feedback linearization and linear H-infinity control, stability robustness against oil parameter variations and component wear is guaranteed. The closed-loop response is almost linear, fast, sufficiently damped, consistent over the whole operating range and the asymmetry between filling and dumping is significantly reduced.; The third part gives an overview of extremum-seeking control and presents an antiskid controller for transport aircraft. The controller does not assume knowledge of tire-runway friction characteristics. Information about the local slope of the friction coefficient function is obtained from phase difference measurements of an injected sine wave. The Popov criterion is used to show robust stability. A realistic model of the MD-90 aircraft and brake system is described. The proposed controller is compared via simulations with the controller currently installed in aircraft. The results indicate that the proposed controller has similar or better stopping performance, and operates much smoother without introducing strut vibrations. |
