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

这个建议涉及一个新的小波包为基础的设计方法，有效地实现数字控制器的工作在非常高的采样率，但由于紧凑的原因，制作在超大规模集成电路芯片的表面积有限。在超大规模集成电路技术中，在芯片表面积A、该芯片可以执行的计算数量N和实现这些计算所花费的时间T之间存在折衷。 一般来说，在适当的归一化下，Δ T2 = N。 在控制设置中，在固定采样率和给定控制器下，这种折衷限制了在每个采样间隔上可以处理的比特数。 因此，有限字长（FWL）效应开始起作用，并且快速采样限制了整体实现精度。 发生这种情况的一个激励性例子是半导体激光器阵列的稳定和控制，其相干锁相动力学是开环不稳定的。 稳定的锁定将允许在许多重要应用中使用这种阵列。 潜在的动力学是在数百兆赫。 然而，物理的鲁棒性需要一个控制器芯片的表面积相比，这些阵列上的小表面fabricatedThe方法，我们建议涉及基于小波包的技术，利用频谱差异在不同的子带的输入到一个所需的控制器，以尽量减少FWL的影响所造成的信号，而不是系数量化，同时保持所需的芯片表面积。 这将通过明智地使用多速率技术，在浮点计算的假设。 基本思想是认识到，为了实现所述量化精度水平，较高能量的信号必须被分配较高数量的比特。 我们的方法要求控制器的输入，被分成几个子带。 由于子带信号具有比原始控制器输入更小的频谱支持，因此可以以更小的采样率来处理每个子带信号。 然后，根据子带包含的能量水平，由不同的控制器部分以不同的比特分辨率处理每个这样的信号。 然后，控制器部分以原始采样率重新组合。 净效果是在不增加芯片面积的情况下提高了控制输入的分辨率。目标是通过选择分配给每个子带信号的分辨率以及执行频带分割的方式来最小化总体量化器引起的失真。 该思想基本上类似于子带编码，其已经导致信号处理中的数据压缩的显著改进。 我们认为，改进应该是更实质性的控制设置，显示在控制器设计方面的技术问题是非常不同的子带编码文献，并制定一些精确的技术问题，建议的研究是针对。 最后，作为本理论研究的一部分而开发的一些技术将在该大学的实验性激光阵列控制试验台上得到验证

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