Dynamic stabilization and feedback control of the pendulum in any desired position

One example of stabilizing a statically unstable system is the dynamic stabilization of the pendulum by means of oscillations of its suspension point. The pendulum whose suspension point oscillates in the vertical direction which stabilizes it in the inverted position is the so-called Kapitza pendulum. It turns out that it is possible to stabilize the pendulum in other positions by choosing the right direction of oscillations of the pendulum's suspension point. In addition, if the direction of oscillations of the pendulum suspension point can change over time, some interesting control problems may arise, such as transition of the pendulum from point to point or active damping control. This paper presents the experimental results that confirm the occurrence of the above-mentioned processes in practice. The work also describes the analytical approximation of the pendulum motion. Moreover, it turns out that the results obtained with this approximation largely agree in the experiment, which was also presented in this work. (C) 2020 Elsevier Ltd. All rights reserved.