A Discrete-time Linearization Feedback Control for the Van der Pol Oscillator

This paper proposes a discrete-time feedback linearization for the Van der Pol oscillator, a well-known example for nonlinear systems. An approximate discrete-time model of the Van der Pol oscillator is derived by using a method called continualized discretization method. The discrete-time control input is a least-squares solution of an equation, which is derived by equating the discrete-time model of the Van der Pol oscillator and an exact discrete-time model of the desired linear system. The proposed method enables us to stabilize and suppress the self-oscillation of the Van der Pol system by the discrete-time controller. Simulation results show that the proposed controller has better performances than the conventional one derived by the forward-difference method in all the tested cases for system parameters and sampling period.