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

This is the first part of a two-part paper on the design of intelligent controllers for a class of exercise machines. The control objective is to cause the user to exercise in a manner which optimizes a criterion related to the user’s mechanical power. The optimal exercise strategy is determined by a biomechanical behavior of the individual user, which is assumed to satisfy an affine force–velocity relationship dependent on the body geometric configuration. Consequently, the control scheme must simultaneously: 1) identify the user’s biomechanical behavior; 2) optimize the controller; and 3) stabilize the system to the estimated optimal states. Moreover, to ensure that the exercise machine is safe to operate, the control system guarantees that the interaction between the exercise machine and the user is passive. In this first part of the paper, we formulate the control problem and propose a controller structure which satisfies the safety requirement and is capable of causing the user to execute an arbitrary exercise strategy if the user’s biomechanical behavior is known. The controller is of the form of a dynamic damper and can be implemented using only passive mechanical components. Part II of this paper is concerned with the self-optimization problem, in which both the determination of the optimal exercise strategy and the execution of that strategy, when the user’s biomechanical behavior is unknown, must be considered.