Transactions of the JSME (in Japanese)
Online ISSN : 2187-9761
ISSN-L : 2187-9761
Dynamics & Control, Robotics & Mechatronics
State estimation based on nonlinear Kalman filter for fluid systems described by Burgers’ equation
Takashi SHIMIZUTomoaki HASHIMOTO
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2021 Volume 87 Issue 901 Pages 21-00061

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Abstract

Burgers’ equation is a fundamental equation for describing several flow phenomena such as traffic, shock waves, turbulence. Burgers’ equation consists of the advective and diffusive terms, which can be used to represent fundamental properties of flow phenomena. Hence, using Burgers’ equation can be regarded as a natural first step towards developing a method for controlling flows. In the previous study, an optimal control method has been proposed for Burgers’ equation. However, the optimal feedback control method is inapplicable to systems whose all state variables are not exactly known. In general, it is usual that the state variables of systems are measured through output sensors, hence, only limited parts of them can be used for designing control inputs. In fact, it is unrealistic that the flow velocities of fluid systems are exactly known for all spatial domains. Hence, it should be supposed that the flow velocities of limited parts of spatial domain can be only used for designing control inputs. In order to apply the optimal feedback control method to the fluid systems described by Burgers’ equation, we need to establish a state estimation method for Burgers’ equation with limited measurable state variables. The objective of this study is to establish a state estimation method for Burgers’ equation. In this study, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation under the assumption of limited measurable flow velocities. The effectiveness of the proposed method is verified by numerical simulations.

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© 2021 The Japan Society of Mechanical Engineers
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