Approximate discrete-time nonlinear output regulation of linear motor inverted pendulum and experimental study

In the past two decades, nonlinear output regulation problem has attracted extensive attentions in control society, which is mainly focused on theoretical developments on simulation level. This paper presents experimental results on the approximate discrete-time nonlinear output regulation problem for a linear motor inverted pendulum system. The key for solving the discrete-time nonlinear output regulation problem lies in how to solve a set of algebraic functional equations known as discrete regulator equations. Since the equations are very complicated, the exact solution of the discrete regulator equations can not be obtained. In this paper, we establish the discrete-time mathematical model of the linear motor inverted pendulum system and then solve the discrete-time nonlinear output regulation problem by neural network approximation method. Finally, we verify the control algorithm by experiment and compare our method with polynomial approximation method.