Title :
A new discrete-time model for a van del Pol Oscillator
Author :
Van, Triet Nguyen ; Hori, Noriyuki
Author_Institution :
Dept. of Intell. Interaction Technol., Univ. of Tsukuba, Tsukuba, Japan
Abstract :
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.
Keywords :
continuous time systems; differential equations; discrete time systems; nonlinear control systems; numerical stability; relaxation oscillators; continuous time system; differential equation; discrete time system; discretization model; nonlinear system; numerical stability; van der Pol oscillator; Accuracy; Equations; Indexes; Limit-cycles; Linear systems; Mathematical model; Numerical models; discrete-time integrator gains; discretization; limit cycle; van der Pol Oscillator;
Conference_Titel :
SICE Annual Conference 2010, Proceedings of
Conference_Location :
Taipei
Print_ISBN :
978-1-4244-7642-8