Dynamic surface control of neuromuscular electrical stimulation of a musculoskeletal system with activation dynamics and an input delay

Neuromuscular electrical stimulation (NMES) is the application of an external electrical potential across a neuromuscular effector to generate desired limb movements. Some of the challenges faced during closed-loop control of NMES include: an electromechanical delay (EMD) in the neuromuscular activation dynamics and uncertain nonlinear musculoskeletal dynamics. In this paper, a dynamic surface control (DSC) approach was used to design an NMES controller that compensates for EMD in the activation dynamics. EMD was modeled as a known constant delay embedded in the control input to the first-order muscle activation dynamics that is cascaded to the second-order uncertain musculoskeletal system. The DSC approach was employed to avoid the “explosion of terms” associated with an integrator backstepping approach. The Lyapunov stability analysis confirmed that the DSC approach achieves semi-global uniformly ultimately bounded (SGUUB) tracking for the delayed musculoskeletal system. Simulations were performed on a 1-degree of freedom knee extension dynamics to illustrate the performance of the developed controller during a trajectory tracking task.