Experimental study of stabilization of the inverted pendulum with horizontal and vertical movement via exact linearization based on the dynamic extension

This paper discuss about the problem of the stabilization of the inverted pendulum on the cart which moves not only in the horizontal direction but also in the vertical direction. This stabilizing problem is addressed by the exact linearization via dynamic extension. The conditions for the system to be the exact linearizable via dynamic extension is derived by restricting the form of the extension and the input transformation which converts the system to satisfy the conditions is derived. After applying the input transformation, the system is extended and applied a feedback transformation. Then the linear controllable system associated with the inverted pendulum system is derived. The validity of this linearization is shown by the several numerical simulations and experiments. In the experiments, the inverted pendulum system is realized by means of the 3-link manipulator.