Comparison of Controller's Performance for a Knee Joint model based on Functional Electrical Stimulation Input

Abstract

This paper aims to design three linear controllers PID (Proportional Integral Derivative), Piecewise-Affine Proportional Integral Derivative(PWA-PID), and Generalized Predictive Control(GPC)) for knee joint positioning based on functional electrical muscle stimulation and evaluate their performance. The model is approximated to a Hammerstein that separate static non-linearities from linear dynamics. The controllers are designed, and applied to the function that cancels static non-linearity. Additionally, the controllers' performance is evaluated based on the error indexes: Mean Squared Error (MSE), Integral of the Error (IE), Integral Absolute Error (IAE), Integral Squared Error (ISE), Integral Time Absolute Error (ITAE), Integral Time Squared Error (ITSE), and Good-hart, overshoot, settling time, and input signal variance. The results shown GPC having lower overshoot, settling time, and input variance, with overshoot five times lower than PWA-PID and eighteen times lower than PID. Also, GPC and PWA-PID controllers performed better than the PID, since they consider the physical system constraints, with the GPC being the most appropriate to knee joint positioning, due to robust control signal increment constraints.