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

本提案涉及一种新的基于小波包的设计方法，用于有效地实现以非常高的采样率运行的数字控制器，但由于在具有有限表面积的VLSI芯片上制造的紧凑性的原因。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次数N）和执行这些计算所需的时间T之间存在权衡。一般来说，在合适的归一化下，AT2 = n。在控制设置中，在固定的采样率和给定的控制器下，这种权衡限制了在每个采样间隔内可以处理的比特数。因此，有限字长（FWL）效应开始发挥作用，快速采样限制了总体实现精度。一个激励的例子是半导体激光阵列的稳定和控制，其相干锁相动力学是开环不稳定的。稳定锁定将允许在许多重要的应用程序中使用这种数组。潜在的动力以几百兆赫为单位。然而，物理稳健性要求控制器芯片表面积与制造这些阵列的小表面相比。我们提出的方法涉及基于小波包的技术，该技术利用输入到所需控制器的不同子带中的频谱差异，以最大限度地减少信号引起的FWL影响，而不是系数量化，同时保持所需的芯片表面积。这将通过在浮点计算的假设下明智地使用多速率技术来实现。基本思想是要认识到，为了达到上述量化精度水平，必须为更高能量的信号分配更高的比特数。我们的方法要求控制器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，因此每个子带信号都可以以更小的采样率进行处理。然后，根据子带包含的能量水平，不同的控制器部件以不同的位分辨率处理每个这样的信号。然后以原始采样率重新组合控制器部分。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带分裂的方式，最大限度地减少总体量化器引起的失真。这个想法本质上类似于子带编码，这大大提高了信号处理中的数据压缩。我们认为，在控制设置方面的改进应该更加实质性，表明控制器设计上下文中的技术问题与子带编码文献中的技术问题非常不同，并制定了一些精确的技术问题，这些技术问题是所提议的研究所针对的。最后，作为理论研究的一部分所开发的一些技术将在该大学可用的实验性激光阵列控制测试台上进行验证

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