Adaptive Sliding Mode Feedback Control Algorithm for a Nonlinear Knee Extension Model

Abstract

Functional electrical stimulation (FES) has been widely used to treat spinal cord injury (SCI) patients. Many research studies employ a closed-loop FES system to monitor the stimulated muscle response and provide a precise amount of charge to the muscle. However, most closed-loop FES devices perform poorly and sometimes fail when muscle nonlinearity effects such as fatigue, time delay response, stiffness, spasticity, and subject change happen. The poor performance of the closed-loop FES device is mainly due to discrepancies in the feedback control algorithms. Most of the existing feedback control algorithms were not designed to adapt to new changes in patients with different nonlinearity effects, resulting in early muscle fatigue. Therefore, this research proposes an adaptive sliding mode (SM) feedback control algorithm that could adapt and fine-tune internal control settings in real-time according to the current subject’s nonlinear and time-varying muscle response during the rehabilitation (knee extension) exercise. The adaptive SM feedback controller consists mainly of system identification, direct torque control, and tunable feedback control settings. Employing the system identification unit in the feedback control algorithm enables real-time self-tuning and adjusting of the SM internal control settings according to the current patient’s condition. Initially, the patient’s knee trajectory response was identified by extracting meaningful information, which included time delay, rise time, overshoot, and steady-state error. The extracted information was used to fine-tune and update the internal SM control settings. Finally, the performance of the proposed adaptive SM feedback control algorithm in terms of system response time, stability, and rehabilitation time was analysed using a nonlinear knee model. The findings from the simulation results indicate that the adaptive SM feedback controller demonstrated the best control performance in accurately tracking the desired knee angle movement by having faster response times, smaller overshoots, and lower steady-state errors when compared with the conventional SM across four reference angle settings (20°, 30°, 40°, and 76°). The adaptive feedback SM controller was also observed to compensate for muscle nonlinearities, including fatigue, stiffness, spasticity, time delay, and other disturbances.