Naoto Hiramatsu | Searcharxiv

arXiv2022

Control of Oscillatory Temperature Field in a Building via Damping Assignment to Nonlinear Koopman Mode

This paper addresses a control problem on air-conditioning systems in buildings that is regarded as a control practice of nonlinear distributed-parameter systems. Specifically, we consider the design of a controller for suppressing an oscillatory response of in-room temperature field. The main idea in this paper is to apply the emergent theory of Koopman operator and Koopman mode decomposition for nonlinear 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 guided by measurement of a practical room space.

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arXiv2020

Koopman Mode Decomposition of Oscillatory Temperature Field inside a Room

Koopman mode decomposition (KMD) is a technique of nonlinear time-series analysis capable of decomposing data on complex spatio temporal dynamics into multiple modes oscillating with single frequencies, called the Koopman modes (KMs). We apply KMD to measurement data on oscillatory dynamics of a temperature field inside a room that is a complex phenomenon ubiquitous in our daily lives and has a clear technological motivation in energy-efficient air conditioning. To characterize not only the oscillatory field (scalar field) but also associated heat flux (vector field), we introduce the notion of a temperature gradient using the spatial gradient of a KM. By estimating the temperature gradient directly from data, we show that KMD is capable of extracting a distinct structure of the heat flux embedded in the oscillatory temperature field, relevant in terms of air conditioning.

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