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 (PDE) constrained by a boundary condition and 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. We validate our formulation by deriving analytical expressions for the stability margins of the double-pendulum human stance model. Numerical examples demonstrate that proportional–derivative–acceleration (PDA) feedback generally, but not always, results in larger stability margins than proportional–derivative (PD) feedback in the presence of reflex delays.
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July 2016
Research-Article
Stability of Human Balance With Reflex Delays Using Galerkin Approximations
Zaid Ahsan,
Zaid Ahsan
Department of Mechanical
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
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Thomas K. Uchida,
Thomas K. Uchida
Department of Bioengineering,
James H. Clark Center,
Stanford University,
318 Campus Drive,
Stanford, CA 94305
James H. Clark Center,
Stanford University,
318 Campus Drive,
Stanford, CA 94305
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Akash Subudhi,
Akash Subudhi
Department of Mechanical
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
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C. P. Vyasarayani
C. P. Vyasarayani
Department of Mechanical
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
e-mail: vcprakash@iith.ac.in
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
e-mail: vcprakash@iith.ac.in
Search for other works by this author on:
Zaid Ahsan
Department of Mechanical
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
Thomas K. Uchida
Department of Bioengineering,
James H. Clark Center,
Stanford University,
318 Campus Drive,
Stanford, CA 94305
James H. Clark Center,
Stanford University,
318 Campus Drive,
Stanford, CA 94305
Akash Subudhi
Department of Mechanical
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
C. P. Vyasarayani
Department of Mechanical
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
e-mail: vcprakash@iith.ac.in
and Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi, Sangareddy 502285,
Telangana, India
e-mail: vcprakash@iith.ac.in
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 28, 2015; final manuscript received October 27, 2015; published online December 10, 2015. Assoc. Editor: Hiroshi Yabuno.
J. Comput. Nonlinear Dynam. Jul 2016, 11(4): 041009 (9 pages)
Published Online: December 10, 2015
Article history
Received:
March 28, 2015
Revised:
October 27, 2015
Citation
Ahsan, Z., Uchida, T. K., Subudhi, A., and Vyasarayani, C. P. (December 10, 2015). "Stability of Human Balance With Reflex Delays Using Galerkin Approximations." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041009. https://doi.org/10.1115/1.4031979
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