Discrete-time model-based output regulation of fluid flow systems

Abstract

Model-based discrete-time output regulator design is proposed for fluid flow systems using a geometric approach. More specifically, a class of vortex shedding and falling thin film phenomena modelled by complex Ginzburg–Landau equation (CGLE) and Kuramoto–Sivashinsky equation (KSE) are considered. Differently from a traditional continuous-time controller design, a novel discrete-time modelling technique is proposed in a general infinite-dimensional state-space setting, which does not pertain any spatial approximation or model reduction, and preserves model intrinsic properties (such as stability, controllability and observability). Based on the time discretized plant model (CGLE and KSE systems) by the Cayley–Tustin method, discrete regulator regulation equations are established and facilitated for an output regulator design to achieve fluid flow control and manipulation. To address model instability, a spectrum analysis is utilized in stabilizing continuous-time CGLE and KSE systems, and a link between discrete- and continuous-time closed-loop system stabilizing gains is established. Finally, the proposed methodology is demonstrated through a set of simulation cases, by which the output tracking, disturbance rejection, and model stabilization are achieved for the considered CGLE and KSE systems.