Identification of nonlinear systems using hybrid functions
Dosthosseini, R., Sheikholeslam, F. and Kouzani, A. Z. 2010, Identification of nonlinear systems using hybrid functions, in ICCA 2010 : Proceedings of the 8th IEEE International Conference on Control and Automation, IEEE, [Piscataway, N.J.], pp. 1994-1998, doi: 10.1109/ICCA.2010.5524064.
Most real systems have nonlinear behavior and thus model linearization may not produce an accurate representation of them. This paper presents a method based on hybrid functions to identify the parameters of nonlinear real systems. A hybrid function is a combination of two groups of orthogonal functions: piecewise orthogonal functions (e.g. Block-Pulse) and continuous orthogonal functions (e.g. Legendre polynomials). These functions are completed with an operational matrix of integration and a product matrix. Therefore, it is possible to convert nonlinear differential and integration equations into algebraic equations. After mathematical manipulation, the unknown linear and nonlinear parameters are identified. As an example, a mechanical system with single degree of freedom is simulated using the proposed method and the results are compared against those of an existing approach.
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