Study of the interaction between a one degree of freedom force augmenting device and a human operator

In this paper a one degree of freedom (DOF) force augmenting device (FAD) is presented. A laboratory set-up has been built and some tests of the interaction between the FAD and a user were performed. The stability of the closed loop system is essential for the performance of the FAD. The FAD by itself is a stable device, but what is important is to assure the stability of the interaction between the FAD and a human being. To deal with this matter, two situations were analyzed. The case of no delays in the model is first considered. This situation might appear unrealistic, for this reason, a second analysis is performed considering a human model with delays. In order to deal with delays a Rekasius substitution is used. To perform the stability analysis, it is sufficient to apply the Routh-Hurtwitz criteria. Attempts with other techniques have given more conservative stability results. The stability has been proven for delays smaller than upper-bounds which have been computed. None of these upper-bounds are reached by any healthy human being. Therefore, we can assure that the whole system is stable for most of the practical situations. This proves the robustness of the closed loop system with respect to delays. In real time experiments, measurement from the sensors are normally noisy. In order to reduce the effect of the noise, a low pass filter was included. The introduction of this filter alters the order of the system, changing the stability conditions of the whole set up. So the stability analysis is performed again with the inclusion of the filter.