Linear-Form Discretization and its Application to Lewis Oscillators

Triet Nguyen Van and Noriyuki Hori

Keywords

Lewis Oscillator, linearlike expression, exact discretization, limit cycle, discretetime integrator gains

Abstract

This is a compulsory section. A discretization method proposed for 2nd-order nonlinear system in our previous study is modified to accommodate two design parameters in the resulting model. The nonlinear system is expressed in a linear-like form with state-dependent system matrix and includes the two design parameters, which decide how nonlinear terms are distributed among the linear terms. The resulting linear-form system is then discretized in a way that would be exact if the system were indeed linear. Lewis oscillator is used as an example and discretized to show by simulations that the two design parameters affect the shape of the limit cycles and have potential for improving the accuracy of the model with improved ease than the previous method. As in the previous method, the proposed model gives better results than the forward-difference model and the non-standard model, with which limit cycles and numerical stability were found to disappear for Lewis oscillators.

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