论文标题
关于嵌入内部模型的控制系统的鲁棒性
About Robustness of Control Systems Embedding an Internal Model
论文作者
论文摘要
鲁棒性是任何控制系统的基本属性。在线性输出调节的背景下，证明，嵌入外源信号的内部模型是必要的，足以实现对所需的参考信号的跟踪，尽管外部干扰和参数不确定性。该结果通常称为“内部模型原理”。将这种线性结果的完整扩展到一般的非线性系统仍然是一个开放的问题，这对在非线性设置中可能实现的不确定性和所需控制目标的大量替代定义加剧了。在本文中，我们开发了一个一般框架，其中所有这些不同的概念都可以以统一的方式正式表征。经典的结果在提议的设置中重新解释，并提出了新的结果和见解，重点是对任意谐波内容的强大拒绝/跟踪。此外，我们通过反示例表明，在连续的非结构化不确定性的相关情况下，存在一些问题，而没有平滑的有限维鲁棒调节剂可以确保确切的调节。
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired reference signals in spite of external disturbances and parametric uncertainties. This result is commonly known as "internal model principle". A complete extension of such linear result to general nonlinear systems is still an open problem, which is exacerbated by the large number of alternative definitions of uncertainty and desired control goals that are possible in a nonlinear setting. In this paper, we develop a general framework in which all these different notions can be formally characterized in a unifying way. Classical results are reinterpreted in the proposed setting, and new results and insights are presented with a focus on robust rejection/tracking of arbitrary harmonic content. Moreover, we show by counter-example that, in the relevant case of continuous unstructured uncertainties, there are problems for which no smooth finite-dimensional robust regulator exists ensuring exact regulation.
