A new discrete-time model for a van del Pol Oscillator

This paper proposes a new discretization model for a second-order nonlinear system whose dynamics are governed by an ordinary differential equation of a van der Pol type, for which an analytical solution is not known. The method is based on a linear-like expression of the nonlinear system and its discrete-time system expression in delta form, where continuous-time system parameters appear directly and discrete-time parameters are contained in the integrator gains. These gains are, in general, functions of continuous-time parameters and the sampling interval for linear systems, but also of system states and inputs for nonlinear systems. The developed model becomes an exact discrete-time model as the van der Pol equation approaches a linear equation. Simulations show that the proposed model gives limit cycles that are more accurate than those of the Mickens and forward-difference models, which can loose limit cycles and numerical stability.