Comparison of two Models Used to Describe the Ankle Torque in Response to Functional Electrical Stimulation

Abstract

Modeling the response of the electrically stimulated muscle is an essential step during control system design with a functional electrical stimulator. A Hammerstein model, which consists of a static nonlinear block and a linear dynamic block, is widely used in related works. In this paper, the static nonlinear block represented by a polynomial expansion or a sigmoid function of the Hammerstein model structure was applied. Therefore, our study aimed at comparing the prediction accuracy of the two models under muscle isometric contraction condition. The right ankle joint of a healthy subject was fixed at 90° and surface electrical stimulation electrodes were placed at the right tibialis anterior muscle. The stimulation amplitude was modulated with two candidate test signals, i.e., the triangular signal and the staircase signal. Then, the stimulation amplitude was the model input and the measured ankle torque was the model output. An index, namely the best fit rate, was used to assess the performance of the two models. The validation results of the polynomial Hammerstein model (PHM) and the sigmoid Hammerstein model (SHM) were 76.84% and 77.53%, respectively. Besides, the cross-validation results of the PHM and the SHM were 73.36% and 75.9%, respectively. Above all, the results showed that the model with the sigmoid function performs slightly better in the model simulation and prediction.