Stability of human balance with reflex delays using Galerkin approximations

Zaid, A and Uchida, T K and Subudhi, A and Vyasarayani, C P (2015) Stability of human balance with reflex delays using Galerkin approximations. Journal of Computational and Nonlinear Dynamics, 11 (4). 041009-1. ISSN 1555-1415

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Abstract

Falling is the leading cause of both fatal and nonfatal injury in the elderly, often requiring expensive hospitalization and rehabilitation. We study the stability of human balance during stance using inverted single- and double-pendulum models, accounting for physiological reflex delays in the controller. The governing second-order neutral delay differential equation (NDDE) is transformed into an equivalent partial differential equation constrained by a boundary condition, then into a system of ordinary differential equations (ODEs) using the Galerkin method. The stability of the ODE system approximates that of the original NDDE system; convergence is achieved by increasing the number of terms used in the Galerkin approximation. Numerical examples demonstrate that proportional-derivative-acceleration feedback results in larger stability margins than proportional-derivative feedback in the presence of reflex delays. The study of balance is critical for guiding development of diagnostic criteria, assistive devices, and rehabilitation strategies for the growing elderly population.

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IITH Creators:
IITH CreatorsORCiD
Vyasarayani, C Phttp://orcid.org/0000-0002-3396-0484
Item Type: Article
Uncontrolled Keywords: Stability , Galerkin method , Delays , Feedback , Partial differential equations , Pendulums , Wounds , Physiology , Delay differential equations , Control equipment
Subjects: Physics > Mechanical and aerospace
Divisions: Department of Mechanical & Aerospace Engineering
Depositing User: Team Library
Date Deposited: 16 Nov 2015 06:22
Last Modified: 11 Aug 2017 06:56
URI: http://raiith.iith.ac.in/id/eprint/2029
Publisher URL: https://doi.org/10.1115/1.4031979
OA policy: http://www.sherpa.ac.uk/romeo/issn/1555-1415/
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