Robust periodic reference tracking by stable uncertain infinite-dimensional linear systems

A robust control scheme for tracking of periodic signals, consisting of a finite number of sinusoids, by uncertain exponentially stable infinite dimensional linear systems is presented. The scheme consists in constructing a cascade interconnection of the stable linear system and a partitioning filter and augmenting this cascade system with a simple internal model based filter. The stable system model is presumed to be unknown, but its transfer function gain at the frequencies to be tracked is assumed to be known and non-zero. A theorem guaranteeing the robust stability and performance of this scheme while tracking a sinusoidal reference is proved. The general theorem for tracking periodic signals is stated and can be established analogously. A discussion on quantitatively estimating the robustness of this scheme is presented. The efficacy of the scheme is demonstrated via simulation of an example. The simplicity of the proposed scheme, its quantitatively ascertainable robustness and a virtual lack of modeling requirements make it well suited for industrial applications.