Dynamics and vibrational control of an underwater inverted pendulum

This paper discusses the dynamics and vibrational control problem of an underwater inverted pendulum system. The system's equations of motion are obtained by using the Lagrange equation. The vibrational control technique is applied to stabilize the inverted pendulum in water. Furthermore, stability analyses in terms of stable-unstable region for the underwater inverted pendulum system is presented. While a number of control techniques for the stabilization problem of an inverted pendulum in air by oscillating the support point have been developed, but a similar technique for the system in water has not yet been investigated. The dynamics of any system in liquid is strongly influenced by the density of the liquid and the relative velocity of the surrounding liquid. Also, it becomes a challenging task to stabilize the system in the presence of the hydrodynamic forces acting on it. Simulation results reveal that the application of the vibrational control technique newly developed in this paper can successfully stabilize the system in water under the influence of hydrodynamic forces.