Series expression of the system for linear approximation based on relative degree structure stabilization of the cart pendulum system

In this paper, the problem of the stabilization of an inverted pendulum on a cart is discussed by using modified approximate linearizing method. The main result is to propose the modification of the linear approximation using a new expression of the system. This modification has two steps. The first step involves defining the series expression of the system via the relative degree structure of the system. The series expression is one of the system expressions which makes the inherent linearity of the system explicit. In the second step, the series expression is modified to reduce the affection of nonlinear part ignored in linear approximation. The procedures of the modification are demonstrated via the problem of stabilization of an inverted pendulum on a cart.