Reduced order control in microchemical systems

In this paper we examine the problem of regulation of thermal transients in a microsystem. Using second-order statistical properties we obtain the dominant structures that characterize the dynamics of an ensemble of data. These dominant structures, otherwise called empirical eigenfunctions, are the most efficient way of capturing the dynamics of an infinite dimensional process with a finite number of modes. We propose a new receding horizon boundary control scheme using these empirical eigenfunctions in a constrained optimization procedure to track a desired spatiotemporal profile. Additionally we consider a disturbance rejection problem. Finite element method simulations of heat transfer are provided and used in order to implement and test the performance of the controller.