Robust Model Predictive Control of An Input Delayed Functional Electrical Stimulation

Abstract

Functional electrical stimulation (FES) is an external application of low-level currents to elicit muscle contractions that can potentially restore limb function in persons with spinal cord injury. However, FES often leads to the rapid onset of muscle fatigue, which limits performance of FES-based devices due to reduction in force generation capability. Fatigue is caused by unnatural muscle recruitment and synchronous and repetitive recruitment of muscle fibers. In this situation, overstimulation of the muscle fibers further aggravates the muscle fatigue. Therefore, a motivation exists to use optimal controls that minimize muscle stimulation while providing a desired performance. Model predictive controller (MPC) is one such optimal control method. However, the traditional MPC is dependent on exact model knowledge of the musculoskeletal dynamics and cannot handle modeling uncertainties. Motivated to address modeling uncertainties, robust MPC approach is used to control FES. Moreover, two new robust MPC techniques are studied to address electromechanical delay (EMD) during FES, which often causes performance issues and stability problems. This thesis compares two types of robust MPCs: a Lyapunov-based MPC and a tube- based MPC for controlling knee extension elicited through FES. Lyapunov-based MPC incorporated a contractive constraint that bounds the Lyapunov function of the MPC with a Lyapunov function that was used to derive an EMD compensation control law. The Lyapunov-based MPC was simulated to validate its performance. In the tube-based MPC, the EMD compensation controller was chosen to be the tube that eliminated output of the nominal MPC and the output of the real system. Regulation experiments were performed for the tube-based MPC on a leg extension machine and the controller showed robust performance despite modeling uncertainties