Reduced Ordered Modelling of Time Delay Systems Using Galerkin Approximations and Eigenvalue Decomposition

Chakraborty, Sayan and Kandala, Shanti Swaroop and Vyasarayani, C P (2018) Reduced Ordered Modelling of Time Delay Systems Using Galerkin Approximations and Eigenvalue Decomposition. IFAC-PapersOnLine, 51 (1). pp. 566-571. ISSN 2405-8963

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Abstract

In this paper, we develop ordinary differential equations (ODEs) based approximations for linear delay differential equations (DDEs). Using the shift of time transformation, the DDE is converted into an equivalent partial differential equation (PDE) with boundary conditions (BCs). The obtained PDE along with BCs is then approximated into a system of linear ODEs using Galerkin approximations. The eigenvalues of these ODEs approximate the characteristic roots of the original DDE. By only retaining the dynamics of these ODEs corresponding to converged eigenvalues of the original DDE, these ODEs are further reduced using eigenvalue decomposition method. The time responses obtained for the Galerkin approximated system models are compared with the same obtained using the direct numerical simulation and the results are found to be satisfactory.

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