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The Influence on Stability Robustness of Compromising on the Zero Tracking Error Requirement in Repetitive Control

机译:重复控制对妥协稳定性的影响对零跟踪误差的要求

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Repetitive control (RC) can be used to design active vibration isolation mounts that aim to cancel the influence of spacecraft vibrations on fine pointing equipment. It can cancel the influence of slight imbalance in momentum wheels, reaction wheels, and CMGs. Because RC aims for zero error, it requires reasonably accurate knowledge of the system dynamics all the way to Nyquist frequency. As a result, special methods are needed to establish robustness to model error. A series of publications have demonstrated a method of averaging a cost function over models to increase the robustness. A previous paper improves on this by adjusting the learning rate as a function of frequency to further improve robustness, but there is still a hard limit on phase error. This paper considers yet one more approach, and all three can be used simultaneously. Here we compromise on the zero tracking error requirement for frequencies that require extra robustness. This allows one to extend this hard limit making RC tolerate larger model errors. A quadratic cost is used that penalizes not just the rate of change of the input function, but also the size of the input function. We first establish how to do this for the sister field of iterative learning control, and then the frequency response characteristics are produced for design of repetitive control. The method can improve tracking error for a frequency interval above the frequency at which one would otherwise have to cut off the learning because of model error. Model uncertainty can be used directly in the design process to produce stable RC laws for any level of uncertainty. The design approach differs from typical earlier work that used a sharp frequency cutoff, and instead uses a minimal amount of attenuation needed to produce stability
机译:重复控制(RC)可用于设计主动隔振安装架,其目的是消除航天器振动对精确指向设备的影响。它可以消除动量轮,反作用轮和CMG轻微失衡的影响。由于RC的目标是零误差,因此它需要对系统动力学直至Nyquist频率的合理准确的了解。结果,需要特殊的方法来建立建模误差的鲁棒性。一系列出版物展示了一种对模型的成本函数求平均值以提高鲁棒性的方法。先前的论文通过将学习率作为频率的函数进行调整来进一步改善鲁棒性,从而对此进行了改进,但是相位误差仍然存在严格的限制。本文考虑了另一种方法,并且可以同时使用所有这三种方法。在这里,对于需要额外鲁棒性的频率,我们折衷了零跟踪误差的要求。这使得人们可以扩展这一硬性限制,从而使RC能够容忍更大的模型误差。使用二次成本不仅惩罚输入函数的变化率,而且惩罚输入函数的大小。我们首先确定如何在迭代学习控制的姊妹领域做到这一点,然后为重复控制设计产生频率响应特性。该方法可以在频率间隔以上的频率间隔内改善跟踪误差,否则该频率间隔会由于模型误差而不得不终止学习。模型不确定性可直接用于设计过程中,以针对任何级别的不确定性产生稳定的RC律。该设计方法不同于典型的早期工作,该工作使用了急剧的频率截止,而是使用了产生稳定所需的最小衰减量。

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