Shape Control of Distributed Parameter Systems: Modeling and Performance Analysis

A new method of analyzing self-adjoint linear distributed parameter shape control systems is presented, based upon 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 extant control analysis and design techniques and software. Design measures are presented over both temporal and spatial bandwidths. A modelling correction is introduced to accomodate modal truncation, while maintaining static and band-limited dynamic shape fidelity.