A predictor-based compensation for electromechanical delay during neuromuscular electrical stimulation-II

Abstract

Neuromuscular electrical stimulation (NMES) is a promising technique to restore functional mobility in persons with paraplegia. Closed-loop control of NMES allows precise and accurate limb control in critical tasks such as gait restoration or gait retraining. However, a major cause of degraded performance and instability during NMES control is electromechanical delay (EMD). Uncertainty, exogenous disturbances (e.g., spasticity), and particularly, unknown nonlinear muscle force-length and muscle force-velocity relationships in the musculoskeletal system complicate control design to compensate for EMD. Despite these difficulties, a predictorbased control method that compensates for EMD in the uncertain musculoskeletal system is developed in this paper. The developed control method is an improvement over our previous work in which only proportional-derivative (PD)-type delay compensating controller was developed for a completely unknown nonlinear musculoskeletal system. The result incorporates integral control in the previous PD-based control design (i.e., a PID-type delay compensating controller is developed) and is shown to achieve uniformly ultimately bounded tracking.

Control of functional electrical stimulation in the presence of electromechanical and communication delays

“…To achieve our control objective, we utilized the controller developed in [20]. We will refer to this controller as PID with Delay Compensation (PID-DC) controller.…”

“…This controller was proven to achieve semi-global uniformly ultimately bounded tracking for a nonlinear and unknown musculoskeletal dynamics system with bounded disturbances. Further details about the stability analysis can be found in [20]. The input to the system from the PID-DC controller is defined as…”

“…978-1-4673-1969-0/13/$31.00 ©2013 IEEE [20]. In this paper we evaluate its control performance on an FES based teleoperation system.…”

“…However, the delay compensating controller in [19] is based on proportional and derivative control and lacks integral control actuation. Motivated by this limitation, the controller in [20] was developed to incorporate the integral control action along with the PD control and delay compensation. The control development, and its Lyapunov-based stability analysis, were presented in 6th Annual International IEEE EMBS Conference on Neural Engineering San Diego, California, 6 -8 November, 2013…”

A Modified Dynamic Surface Controller for Delayed Neuromuscular Electrical Stimulation

“…In (1), J ∈ ℝ is the unknown inertia of the combined knee and leg extension machine swing arm, M e ( q ) ∈ ℝ is the moment generated by the passive elastic properties of the muscles, $M_{v}false(\dot{q}false)\in ℝ$ is the moment generated by the passive viscous properties of the muscles, and M g ( q ) ∈ ℝ is the gravitational torque acting on the shank. The definitions of the functions M g ( q ), $M_v\left(\dot{q}\right)$ M e ( q ) can be found in [20], [37], [38]. Any disturbances or unmodeled effects in the system are lumped into the unknown function d(t) ∈ ℝ and τ ∈ ℝ is the EMD associated with NMES and is assumed to be known.…”