Control of In-Room Temperature Field via Damping Assignment to Nonlinear Koopman Mode

This article addresses a control problem on air-conditioning systems in a room that is regarded as a control practice of nonlinear distributed parameter systems. Specifically, we consider designing a controller to suppress an oscillatory response of the in-room temperature field. The main idea of this article is to apply the emergent theory of the Koopman operator and Koopman mode decomposition (KMD) for nonlinear dynamical systems and to formulate a technique of damping assignment to a nonlinear Koopman mode in a fully data-driven manner. Its effectiveness is examined by numerical simulations of a simple 2-D problem guided by the measurement of practical room space. A finite-element commercial package is also used for validating the technique in a practical 3-D problem.