Stability Analysis and Design of a Nonlinear Neuromuscular Control System of a Myoelectric Prosthetic Hand

A neuromuscular control system of a myoelectric prosthetic hand (PH) constitutes a nonlinear system with a dead zone whose magnitude is equal to its joint angle when the PH just grasps an object. This is because the neuromuscular control system remains an open-loop system until the PH grasps the object but it constitutes a feedback control system after the PH griped the object in which a torque induced in the fingers of the PH is fed back. To improve the transient performance of the control system, it is desirable to make the feed-forward gain as large as possible, so long as the stability of the system is not impaired. It is also desired that the control system remains stable even when the PH lifts a heavy or rigid object, because this makes the closed loop gain large and leads to the closed system unstable. According to the theory of stability analysis of nonlinear systems, we can only know the sufficient conditions that the system should be stable. Thus the nonlinear theory on stability is insufficient to be used to design the neuromuscular control system for improving its transient responses. This paper shows that the nonlinear system with a dead zone can be approximated to a linear feedback system and that well-known methods of analysis and design on linear control systems can be applicable. It is also shown through various simulation results that errors induced by approximation are practically negligible and thus the design methods are quite accurate.