This paper describes a novel, energy space based approach to the swing-up of an inverted pendulum. The details of the swing-up problem have been described. Equations of the velocity-controlled have been presented. Design of the controller based on energy space notion has been elaborated. The control algorithm takes into account state constraints and control signal constraints. Parameters of the controller have been optimized by means of the Differential Evolution method. A numerical simulation of the inverted pendulum driven by the proposed controller has been conducted, its results have been presented and elaborated. The paper confirms that the proposed method results in a simple and effective swing-up algorithm for a velocity-controlled inverted pendulum with state constraints and control signal constraints.
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In the article construction and application of the EDP is introduced. This construction is based on the transformation of the traditional phase space into the energy space. After this transformation the state vector and its derivative determine the energy flow plane. The angle between these vectors shows energy flow direction. Application of such a construction in recognizing the energy flow synchronization is shown.
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