| This dissertation will present two complete design methodologies for controlling stable, distributed parameter systems. Both methodologies do not require the usual truncation of the infinite-dimensional plant at the onset of the design process. The first, is applicable to minimum phase plants, and the other is for nonminimum phase systems. These methodologies have been used for the mixed-sensitivity design of a cantilever beam subject to low-requency, distributed disturbances. The Euler-Bernoulli model containing both viscous and structural damping was used to represent the plant in this research.; By comparing the closed-loop performance of the beam with the sensor and actuator nearly collocated with that of the collocated system, a comparison of the two methodologies was made. In addition, this thesis explores the differences between these two types of plants and the issues that must be considered when controlling these systems.; Despite the fact that the methodologies presented herein are based on frequency-domain H∞ theory, they are relatively simple to use. One methodology is so simple that the optimal controller is found by substituting the design requirements into a single equation. The optimum controller, sensitivity, and complimentary-sensitivity functions for the closed-loop system are derived analytically as a function of the design requirements and system parameters.; Much of the work in this thesis is a synthesis of and expansions to many different areas of research including skew Toeplitz theory, generalized PDE solution techniques, Mittag-Leffler product expansions, and classical H ∞ mixed-sensitivity design. Significant contributions include the most pragmatic demonstration of skew Toeplitz theory to date, the introduction of relaxed skew Toeplitz (RST) controllers, and innovative simulation techniques used to verify the control designs. Furthermore, a novel set of weighting functions were presented that not only reduce the mixed-sensitivity H ∞ optimization down to a 1-block problem, but are also far superior to weights used in other sources. They provide an elegant mechanism for shaping the sensitivity and complimentary-sensitivity responses of the closed-loop system. |
