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

这项建议涉及一种新的基于小波包的设计方法，以有效地实现在非常高的采样率下工作的数字控制器，但原因是在有限表面积的VLSI芯片上制造的紧凑。在VLSI技术中，在芯片表面积A和实现这些计算所需的时间T之间存在权衡。通常，在适当的归一化AT2=N下，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)效应开始发挥作用，而快速采样限制了整体实现的精度。发生这种情况的一个激励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的应用中使用这种阵列。潜在的动态以数百兆赫为单位。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，该技术利用所需控制器输入的不同子带中的频谱差异，在保持所需芯片表面积的同时，最大限度地减少由信号而不是系数量化引起的FWL影响。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。基本思想是认识到，为了实现所述级别的量化精度，必须为较高能量的信号分配较高的比特数。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级别，由不同的控制器部分以不同的位分辨率处理每个这样的信号。然后，以原始采样率重组控制器部分。其最终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和执行频带分割的方式来最小化量化器引起的总体失真。这个想法基本上类似于子带编码，这导致了信号处理中数据压缩的显著改善。我们认为在控制设置方面应该有更大的改进，表明控制器设计环境中的技术问题与子带编码文献中的技术问题有很大的不同，并阐述了建议研究所针对的一些精确的技术问题。最后，作为这项理论研究的一部分而开发的一些技术将在该大学提供的实验激光阵列控制试验台上进行验证

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