Linear approximation is the first term of Taylor expansion in the neighbor of the considered equilibrium, and this method does not mention the higher order term. Applying the nonlinear transformations of input and coordinate, the accuracy of the approximation increases or decreases.
In this paper, the nonlinear transformations are designed in order to increase accuracy of the approximation. The first step involves defining the series of expression of the system via the relative degree structure of the system. The series expression 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 the linear approximation. The procedure is demonstrated for the problem of stabilization of an inverted pendulum on a cart.
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