Cheap control tracking performance for non‐right‐invertible systems

Abstract

A fundamental limitation exists in the achievable tracking performance of non-right-invertible systems. This limitation manifests itself in the cheap control tracking cost, which we show to be a function of the plant non-minimum phase zeros and of the variation with frequency of the plant direction. The cheap control tracking cost is further connected with an integral relation that constrains the performance of any stable closedloop system where the plant has a single input and two outputs.

Fundamental performance limitations in tracking sinusoidal signals

“…3. Here, is a matrix Blaschke factor of the form (20) The input and output of the system are and respectively. Let us first consider the following problem.…”

“…The study in [5] has since been extended to more general references [6], [7], and discrete-time systems [18]. There have also been generalizations to nonright-invertible plant [20], [3], to the cases where the controller has previewed information of [7], where the plant input is subject to saturation [12], and where the tracking performance measure includes the input energy [4], respectively. It has been shown that, consistent with common intuitions, the preview of the reference can reduce the best achievable tracking error and on the other hand any input saturation or any input energy constraint would likely increase the best achievable tracking error.…”