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.

Pole placement tuning of proportional integral derivative feedback controller for knee extension model

“…The effectiveness of the feedback controllers declines when the knee and muscles experience fatigue and spasticity [2]- [5]. The feedback controllers were only tuned during the simulation design stage, where muscle non-linearity effects and other non-linear disturbances were either ignored or represented by a single predicted value to characterise the non-linear response of the muscle model [3]. However, the non-linear effects of genuine human muscles change with time, and different people exhibit various non-linear muscle responses.…”

“…An accurate simulation model incorporating the non-linear effects of muscles is also necessary to guarantee the performance of the controller [8]. Several feedback controllers, such as proportional-integral-derivative (PID) [9], fuzzy logic [10], neural network [11] and adaptive controllers [3], have been proposed. However, the proposed feedback control system demonstrates a decline in control performance in the presence of non-linearities.…”

“…Notably, the PID feedback controller will perform poorly and fail if the gain parameters are incorrectly tuned. Several methods, including manual tuning, the Ziegler-Nichols (ZN) tuning method [14], [15], pole placement [16], genetic algorithm (GA) [9], gradient descent (GD) [17] and particle swarm optimisation (PSO), are available for the tuning of the PID feedback controller [3]. The open-loop ZN tuning method only applies to the first-order system, whilst the closed-loop ZN tuning method applies to the linear system [18], [19].…”

“…However, tuning a system that requires a transient response involving rise time, time delay, overshoot, steady state error and oscillation is difficult. These parameters must be extracted using digital signal processing, such as a system identification controller, for performance evaluation [3]. Overall, the GD, GA and PSO optimisation methods are complex and time consuming to prepare for the optimised gain settings.…”