This paper discusses the stability of systems controlling patient body weight support systems which are used in gait re-education. These devices belong to the class of underactuated mechanical systems. This is due to the application of elastic shock-absorbing connections between the active part of the system and the passive part which impacts the patient. The model takes into account properties of the system, such as inertia, attenuation and susceptibility to the elements. Stability is an essential property of the system due to human-device interaction. In order to demonstrate stability, Lyapunov's theory of stability, which is based on the model of system dynamics, was applied. The stability of the control system based on a model that requires knowledge of the structure and parameters of the equations of motion was demonstrated. Due to inaccuracies in the modeling of the rope (one of the basic elements of the device), an adaptive control system was introduced and its stability was also proved. The authors conducted simulation and experimental tests that illustrate the functionality of the analyzed control systems.
Keywords: adaptive control; control theory; gait rehabilitation system; model-based control; stability; underactuated mechanical system.