Shape Control of Distributed Parameter Systems: Modeling and Performance Analysis
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abstract
A method of analyzing self-adjoint linear distributed parameter shape control systems is presented. It is based on their input-output representation in a spatially and temporally transformed frequency space. The analysis is specialized to the shape control problem by expanding the plant spatial response in orthogonal functions, e.g., a generalized Fourier spatial transform; for example, a Zernike polynomial basis can be introduced for deformable mirror optical wavefront correction tasks. The spatially transformed plant models are amenable to control analysis and design techniques and software. Design measures are presented over both temporal and spatial bandwidths. A modeling correction is introduced to accommodate modal truncation while maintaining static and bandlimited dynamic shape fidelity.
