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 and Catalin Iulin Pruncu
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Saqib Hasnain: School of Mechanical Engineering, Pusan National University, 30 Jangjeon-dong, Guemjeong-gu, Busan 46241, Korea
Karam Dad Kallu: Robotics and Intelligent Machine Engineering (RIME), School of Mechanical and Manufacturing Engineering (SMME), National University of Science and Technology (NUST), H-12, Islamabad 44000, Pakistan
Muhammad Haq Nawaz: School of Engineering and Information Technology (SEIT), University of New South Wales at Australian Defense Force Academy, Canberra 7916, Australia
Naseem Abbas: Department of Mechanical Engineering, University of Central Punjab, Lahore 54000, Pakistan
Catalin Iulin Pruncu: Mechanical Engineering, Imperial College London, London SW7 2AZ, UK

Energies, 2020, vol. 13, issue 19, 1-15

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.

Keywords: underwater inverted pendulum; parametric excitations; stability border; hydrodynamics forces; energy harvesting (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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