A New Wavelet Packet Based Approach to Efficient High Speed Controller Design

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This proposal concerns a new wavelet packet based design methodology for efficient implementation of digital controllers operating at very high sampling rates, but for reasons of compactness fabricated on VLSI chips with limited surface area. In VLSI technology there is a tradeoff between the chip surface area, A, the number of computations, N, that this chip can perform and the time, T, taken to effect these computations. In general under suitable normalizations AT2 = N. In a control setting, under fixed sampling rate and a given controller this tradeoff limits the number of bits that can be processed over each sampling interval. Consequently, finite word length (FWL) effects come into play, and fast sampling restricts the overall implementational accuracy. A motivating example where this happens is the stabilization and control of semiconductor laser arrays whose coherent phase locking dynamics are open loop unstable. Stable locking would permit the use of such arrays in a number of important applications. The underlying dynamics are in hundreds of MegaHertz. Yet physical robustness requires a controller chip surface area that compares with the small surfaces on which these arrays are fabricatedThe methodology we propose involves wavelet packet based techniques that exploit spectral disparities in different subbands of the input to a desired controller, to minimize FWL effects caused by signal, as opposed to coefficient quantization, while maintaining a desired chip surface area. This will be done through the judicious use of multirate techniques, under the assumption of floating point computations. The basic idea is to recognize that to achieve the said level of quantization accuracy, higher energy signals must be assigned higher number of bits. Our approach requires that the controller input, be split into several subbands. Since the subband signals have smaller spectral support than the original controller input, each can be processed at smaller sampling rates. Each such signal is then processed at different bit resolutions by different controller parts, according to the level of energy that the subband contains. The controller part is then recombined at the original sampling rate. The net effect is improved resolution in the control input, without increasing the chip area. The goal is to minimize overall quantizer induced distortions, by selecting the resolution assigned to each subband signal, and the manner in which band splitting is performed. The idea is essentially similar to subband coding, that has led to substantially improved data compression in signal processing. We argue that the improvement should be even more substantial in control setting, show that the technical issues in the controller design context are very different than in the subband coding literature, and formulate some precise technical problems that the proposed research is directed toward. Finally, some of the techniques to be developed as part of this otherwise theoretical research will be validated on an experimental laser array control test bed available at this University