Performance limitations of observer-based feedback for transient energy growth suppression

TL;DR

This paper reveals a fundamental limitation of observer-based feedback control in suppressing transient energy growth, showing it cannot prevent energy growth in systems with initial disturbances, unlike alternative output feedback methods.

Contribution

It establishes a theoretical performance limitation of observer-based feedback for transient energy growth suppression and suggests alternative output feedback approaches may overcome this issue.

Findings

Observer-based feedback cannot prevent transient energy growth in systems with initial disturbances.

Performance limitation applies when the uncontrolled system exhibits transient energy growth.

Alternative output feedback methods may avoid these limitations.

Abstract

Transient energy growth suppression is a common control objective for feedback flow control aimed at delaying transition to turbulence. A prevailing control approach in this context is observer-based feedback, in which a full-state feedback controller is applied to state estimates from an observer. The present study identifies a fundamental performance limitation of observer-based feedback control: whenever the uncontrolled system exhibits transient energy growth in response to optimal disturbances, control by observer-based feedback will necessarily lead to transient energy growth in response to optimal disturbances for the closed-loop system as well. Indeed, this result establishes that observer-based feedback can be a poor candidate for controller synthesis in the context of transient energy growth suppression and transition delay: the performance objective of transient energy growth suppression can never be achieved by means of observer-based feedback. Further, an illustrative example is used to show that alternative forms of output feedback are not necessarily subject to these same performance limitations, and should also be considered in the context of transient energy growth suppression and transition control.