Robust control of the Kuramoto-Sivashinsky equation

Abstract

Dissimilarities between an active flow control model and the physical system can be accounted for by use of a robust controller. Modeling errors and uncertainty in the parameters cause controller performance to decrease, and, in some cases, can even destabilize the closed-loop system. This paper shows that, whilst H2 optimal control provides excellent nominal performance, perturbations in the plant cause significant degradation of robust performance. In an effort to increase the robustness, structured parametric uncertainty is accounted for in the model and used to design a μ-controller for the Kuramoto-Sivashinsky equation. To this end, the structure in which the uncertainty presents itself is derived from the partial differential equation and its discretization. This proves that μ-synthesis is feasible for active flow control applications, showing that robust performance can be maintained in the presence of perturbations in the plant and guaranteeing robust stability for an acceptable range of uncertainty. Future research should include mixed feedback-feedforward or aggregated actuator/sensor configurations, which could further increase robust performance and stability characteristics.