A Modified Dynamic Surface Controller for Delayed Neuromuscular Electrical Stimulation

A widely accepted model of muscle force generation during neuromuscular electrical stimulation (NMES) is a second-order nonlinear musculoskeletal dynamics cascaded to a delayed first-order muscle activation dynamics. However, most nonlinear NMES control methods have either neglected the muscle activation dynamics or used ad hoc strategies to tackle the muscle activation dynamics, which may not guarantee control stability. We hypothesized that a nonlinear control design that includes muscle activation dynamics can improve the control performance. In this paper, a dynamic surface control approach was used to design a proportional-integral-derivative (PID)-based NMES controller that compensates for electromechanical delays in the activation dynamics. Because the muscle activation is unmeasurable, amodel-based estimator was used to estimate the muscle activation in real time. The Lyapunov stability analysis confirmed that the newly developed controller achieves uniformly ultimately bounded tracking for the musculoskeletal system. Experiments were performed on two able-bodied subjects and one spinal cord injury subject using a modified leg extension machine. These experiments illustrate the performance of the new controller and compare it with a previous PID-based controller with delay compensation controller that did not consider muscle activation dynamics in the control design. These experiments support our hypothesis that a control design that includes muscle activation improves the NMES control performance.