Mathematical Sciences: Minimal Order Dynamic Pole Assignment Problems

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9224541 Wang This project addresses the problem of pole assignment by output feedback with dynamic compensation. Its goals are to find the minimal order among real dynamic compensators needed for arbitrary pole assignability and to derive a formula for the degree of the Rosenthal compactification of dynamic compensator space. Techniques involving the Schubert calculus developed by the principal investigator in solving the static output feedback pole assignment problem are expected to be important in the study of the minimal order dynamic compensator problem. The poles of a linear system determine its frequencies and amplitudes of vibration, and their locations determine whether or not the system is stable. Therefore, in control design for a physical system such as an airplane or robot arm, a major objective is to move the poles of the plant into its stability region, i.e., a region where the principle modes of vibration die out at a prescribed rate, using output feedback. Output feedback usually involves a dynamic compensator and the higher the order of that compensator, the more complicated the controller needed to shift the poles becomes.Therefore, it is important to be able to design minimal order dynamic compensators. This project will brings the method of algebraic geometry to bear on this problem. ***