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A Simple Robust Controller for the Approximate Regulation of Almost Periodic Signals for Linear Systems

机译：一个简单的鲁棒控制器，用于线性系统几乎周期信号的近似调节

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摘要

By using a delay line as a signal generator, we design a simple robust controller for the approximate regulation (i.e., approximate asymptotic tracking and rejection) of almost periodic signals for linear systems. As opposed to the related existing results, our controller design does not require online parameter tuning. Besides the usual assumptions about stabilizability, detectability, and nonexistence of transmission zeros for the plant, the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy . Based on this information alone, we can only design a robust controller achieving, in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller, . Here, is the output of the plant and is an arbitrary almost periodic reference signal taken from an infinite-dimensional generalized Sobolev space of almost periodic functions. In this paper, we also study robust output regulation in the limiting case where . It turns out that, due to the general loss of exponential closed loop stability, asymptotic tracking/rejection can also be lost as , unless the exogenous signals are smooth enough. This last result extends some recent theorems on (nonrobust) open loop output regulation for infinite-dimensional exosystems. The results of this paper are new and potentially useful for finite-dimensional plants, but the main results are also true for infinite-dimensional systems with bounded control and observation operators.
机译：通过使用延迟线作为信号发生器，我们设计了一个简单的鲁棒控制器，用于线性系统的几乎周期性信号的近似调节（即近似渐近跟踪和抑制）。与现有的相关结果相反，我们的控制器设计不需要在线参数调整。除了通常的关于工厂的稳定性，可检测性和不存在变速器零点的假设外，本文的控制器设计算法仅需要了解所需的跟踪精度。仅基于这些信息，我们就只能设计一个鲁棒的控制器，在未知的三角多项式扰动以及对设备和控制器的附加扰动存在的情况下实现。在这里，是工厂的输出，是从几乎周期函数的无穷维广义Sobolev空间中获取的任意几乎周期的参考信号。在本文中，我们还研究了极限情况下的鲁棒输出调节。事实证明，由于一般失去指数闭环稳定性，除非外部信号足够平滑，否则渐进跟踪/拒绝也可能会丢失。最后的结果扩展了有关无限维系外系统（非稳健）开环输出调节的一些最新定理。本文的结果是新的，对于有限维的植物可能有用，但是对于具有有限控制和观测算子的无限维系统，主要结果也是如此。

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