Control of Smart Exercise Machines Part I: Problem Formulation and Non-Adaptive Control

Abstract

The control of a one degree of freedom exercise machine is considered. The control objective is to cause the human user to exercise at a rate which optimizes a prescribed weigthed power criterion. The optimality condition is determined by the muscle mechanics which is assumed to satisfy a force-velocity relationship. In general, the parameters of this relationship are unknown and vary with the configuration of the exercise machine. As a consequence, the control scheme must simultaneously i) identify the parameters, ii) optimize the controller, and iii) stabilize the system to the estimated optimal states. In this paper we derive a controller which is in the form of a nonlinear dynamic damper and makes the controlled system interact passively with the user. Assuming that the human's force-velocity muscular biomechanics relationship is known, this controller allows the user to excercise in an optimal manner.