Studies on Stable Stabilizing Controllers for a Rotational Pendulum

Seiji Tanaka, Xin Xin, and Taiga Yamasaki


Strong stabilization, stable controller, pole zero, rotational pendulum


This paper investigates an unsolved problem of the strong stabilization (the stabilization by using a stable controller) for the rotational pendulum, which consists of a driven arm rotating in the horizontal plane and a pendulum attached to that arm free to rotate in the vertical plane. This paper shows the existence and a design method of stable stabilizing controllers for the UEP (upright equilibrium point) of the rotational pendulum where the pendulum is at the upright position and the arm is at a desired position. To this end, this paper designs a specific output using the angles of arm and pendulum with an adjustable parameter and employs the pole--zero relation of the linearized model of the rotational pendulum at the UEP. This paper presents the range of the adjustable parameter such that the linearized model is strongly stabilizable. The simulation results were presented to validate the obtained theoretical results. This paper provides numerical simulation results to validate the theoretical results and show the robustness of the presented controller against certain parametric uncertainties of the system.

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