Nonlinear stabilizing control of underactuated inertia wheel pendulum based on coordinate transformation and time-reverse strategy

Inertia wheel pendulum (IWP) is a typical underactuated nonlinear mechanical system. This paper concerns the stabilizing control problem for this nonlinear system. A control strategy based on coordinate transformation and time reverse is presented. The proposed strategy consists of three steps. First, a coordinate transformation is constructed for the IWP. It changes the IWP into a cascade nonlinear system and transforms the stabilization of the IWP into that of the cascade system. Second, the dynamics of the cascade system is analyzed and a time-reverse strategy is used to construct a trajectory for the cascade system. After that, two methods of designing controller for the cascade system are developed to track the constructed trajectory. It ensures the stabilizing control of the cascade system to be achieved. And thus, the stabilization control objective of IWP is realized. In order to test the validity of our proposed theoretical results, a numerical example is given finally. The simulation results demonstrate its effectiveness and its superiority over others.

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