Multiperiodic Repetitive Control for Functional Electrical Stimulation-Based Wrist Tremor Suppression

Intention tremor refers to the rhythmic and involuntary contraction and relaxation of muscles with movement toward a target, which is a common sequela of multiple sclerosis and usually occurs in the distal joints of the upper limb. Functional electrical stimulation (FES) is feasible for tremor suppression because of its fewer side effects, low cost, and portability. Most existing FES-based design methods assume that tremor is a single-frequency signal, though it is multifrequency in reality. The idealized simplification will limit the performance of tremor suppression. To address the problem, this article proposes an FES-based multiperiodic repetitive control (MP-RC) scheme to suppress multiple frequency wrist tremors. First, a nonlinear wrist musculoskeletal model with a Hammerstein structure is established. Then, a control strategy combining the model inverse linearization control and MP-RC is proposed for tremor suppression. A frequency-modified inverse RC algorithm and a gradient-based RC algorithm are developed to regulate the FES level. Finally, comparative experiments on four unimpaired participants and an intention tremor patient are conducted to validate the effectiveness of the proposed control schemes. Experimental results show that the MP-RC scheme can suppress tremors by up to 90.52%. Compared with the traditional filter-based feedback controller and the single-periodic repetitive controller, the proposed multiperiodic repetitive controller can achieve an average of 26% and 16% improvement, respectively, in tremor suppression, demonstrating the advantages of the proposed design.