Abstract
A multiresolutional signal decomposition allows a signal to have equivalent representations at different scales or levels of detail. This idea can be extended to a control system by having a multiresolutional representation of the plant and of the controller. One important purpose for developing a multiresolutional control system is to have the capability of controlling a plant with a high resolution representation using a low resolution controller. A multiresolutional controller could also be used to control only a particular aspect of a plant. We take a first step towards achieving a multiresolutional control system in this paper. We model the plant using a best, orthonormal wavelet packet basis and then determining the optimal controller using the same wavelet packet basis or another related wavelet packet basis. This paper presents a theorem for designing a wavelet packet controller which minimizes the sensitivity function for a SISO system. We also present new theoretical results on wavelet packets required for making the implementation of this multiresolutional controller very practical.
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