An innovative approach is proposed for generating discrete-time models of a class of continuous-time, nonautonomous, and nonlinear systems. By continualizing a given discrete-time system, sufficient conditions are presented for it to be an exact model of a continuous-time system for any sampling periods. This condition can be solved exactly for linear and certain nonlinear systems, in which case exact discrete-time models can be found. A new model is proposed by approximately solving this condition, which can always be found as long as a Jacobian matrix of the nonlinear system exists. As an example of the proposed method, a van der Pol oscillator driven by a forcing sinusoidal function is discretized and simulated under various conditions, which show that the proposed model tends to retain such key features as limit cycles and space-filling oscillations even for large sampling periods, and out-performs the forward difference model, which is a well-known, widely-used, and on-line computable model.
Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete-Time Model
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 9, 2013; final manuscript received October 12, 2013; published online November 20, 2013. Assoc. Editor: Hashem Ashrafiuon.
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Nguyen-Van, T., and Hori, N. (November 20, 2013). "Discretization of Nonautonomous Nonlinear Systems Based on Continualization of an Exact Discrete-Time Model." ASME. J. Dyn. Sys., Meas., Control. March 2014; 136(2): 021004. https://doi.org/10.1115/1.4025711
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