Abstract

Walking is a fundamental aspect of human life. However, for individuals who have lost one or
both legs, walking unaided is unfeasible. As a result, extensive research has been conducted on
various types of prosthetic devices. Most of traditional prostheses for above-knee (AK) amputees
rely on passive mechanisms which often cause to an awkward gait due to the lack of actuators and
external controllers. Conversely, active-mode prostheses can adjust the knee joint angle to mimic
a natural leg. However, these devices are costly, heavy, and require a substantial amount of energy
to function. Alternatively, semi-active prostheses with smart materials have demonstrated potential
to achieve stable motion without the need for expensive sensors and actuators.
The present research investigates the modeling and control of a double-ended single coil
magneto-rheological (MR) fluid damper with annular gap for a prosthetic leg application. Based
on Bingham plastic characteristics for MR fluids a quasi-static modeling of MR damper is
developed to estimate the generated damping force of the damper. Analytical magnetic circuit
analysis based on Ampere’s law is conducted to predict the magnetic flux density in the annular
gap of the MR damper. A design optimization problem is formulated to identify the optimal
geometrical design variables of the MR damper to maximize the dynamic range (ratio of the
maximum to minimum damping force of the MR damper) subject to geometrical constraints. The
optimization problem is solved using combined Genetic Algorithm (GA) and Sequential Quadratic
Programming (SQP) methods. Using the optimal parameters, a magneto-static finite element (FE)
model of the magnetic circuit is developed in open-source Finite Element Method Magnetics
(FEMM) software. Results from FE model for the magnetic flux density in the MR damper gap is
compared to those obtained from the analytical approach.
Dynamic modeling of the MR damper based on Bouc-Wen model is also investigated to
simulate the inherent hysteresis phenomenon in MR dampers. The characteristic parameters of
Bouc-Wen model are calculated using simple close-form mathematical expressions. A new
algorithm is developed to automatically extract model parameters from the experimental dataset
allowing faster parameter estimation than conventional optimization approaches.
A dynamic model of the prosthetic leg integrated with MR damper is developed using the
Lagrange method, followed by an analysis of the desired hip and knee angles throughout the gait
cycle. A polynomial approximation is then formulated to estimate the knee angle based on the hip
joint angle. Finally, simulation experiments are conducted to evaluate the performance of three
control methods (feed-forward control, robust inverse dynamic control, and adaptive inverse
dynamic control) in supporting the amputee to achieve a natural gait.