Dynamic response of an inverted pendulum system in water under parametric excitations for energy harvesting: a conceptual approach

Saqib Hasnain, Karam Dad Kallu, Muhammad Haq Nawaz, Naseem Abbas, Catalin Iulin Pruncu

Research output: Contribution to journalArticle

Abstract

In this paper, we have investigated the dynamic response, vibration control technique, and upright stability of an inverted pendulum system in an underwater environment in view point of a conceptual future wave energy harvesting system. The pendulum system is subjected to a parametrically excited input (used as a water wave) at its pivot point in the vertical direction for stabilization purposes. For the first time, a mathematical model for investigating the underwater dynamic response of an inverted pendulum system has been developed, considering the effect of hydrodynamic forces (like the drag force and the buoyancy force) acting on the system. The mathematical model of the system has been derived by applying the standard Lagrange equation. To obtain the approximate solution of the system, the averaging technique has been utilized. An open loop parametric excitation technique has been applied to stabilize the pendulum system at its upright unstable equilibrium position. Both (like the lower and the upper) stability borders have been shown for the responses of both pendulum systems in vacuum and water (viscously damped). Furthermore, stability regions for both cases are clearly drawn and analyzed. The results are illustrated through numerical simulations. Numerical simulation results concluded that: (i) The application of the parametric excitation control method in this article successfully stabilizes the newly developed system model in an underwater environment, (ii) there is a significant increase in the excitation amplitude in the stability region for the system in water versus in vacuum, and (iii) the stability region for the system in vacuum is wider than that in water.

Original languageEnglish
Article number5215
Number of pages15
JournalEnergies
Volume13
Issue number19
DOIs
Publication statusPublished - 7 Oct 2020

Keywords

  • energy harvesting
  • hydrodynamics forces
  • parametric excitations
  • stability border
  • underwater inverted pendulum

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