## 4 Discussion  
As shown in Figure 4, the results of the simulations highlighted that the proposed architecture is able to provide sufficiently accurate impulse (FI) values for different selections of the control parameters. In particular, the model showed low deviation values of force impulse and duration in two of the configurations studied, i.e., the ones corresponding to P1 and P2 profiles. For these profiles, the larger error observed was related to the duration of the force profiles in the R2 condition, when an impulsive force lasting only 75 ms had to be tracked by the control system. As expected, this condition is particularly demanding since it requires high dynamics and accuracy. However, the TI observed (about 89 ms) is still appropriate for the application. On the other hand, the R1 reference profile, lasting 250 ms, was more efficiently tracked. Similar behavior was observed in HIL testing, although the tracking accuracy, especially for the R2 profile, was definitely lower than the one observed in MIL simulations. The TI accuracy observed was particularly high, with low deviations for all the selections of control parameters (see Table 5). This result confirms that the electric actuated solution presented in this work can achieve particularly fast responses, which are fundamental to reduce the overlap between the perturbation and the active neuromuscular response of the subject. This condition is necessary to avoid biased analyses of postural control, and it could not be achieved by a former, pneumatic actuated solution presented in previous research [30]. Furthermore, as presented in Figure 6, the HIL testing showed high repeatability of the stimuli, which was confirmed for most of the configurations considered as highlighted by the low FI CV values reported in Table 5. This result is relevant to ease the definition of clinical protocols that, in addition, must guarantee the safety of the experimentation thus ensuring to obtain a measure of the subject's postural performance comparable over time. As shown in Table 5, better performances were achieved by shortening Hp, i.e., the prediction power of the controller. This is likely because the controller bases its computation on a highly simplified model, whose linearity could serve as a sufficient approximation of the reality only for limited future time intervals. The mismatch observed between MIL and HIL results, especially for the R2 force profile, can be also motivated by the approximations considered for the modeling of the plant. In particular, as discussed in Section 2.2, the nonlinearities involved in the impact phase were generally left out from the definition of the model for the sake of simplicity. This strong approximation was necessary to evaluate the feasibility of the study, and to test the efficacy of the MPC algorithm, in such a complex scenario where several parameters are unknown and cannot be easily measured. A more accurate model representation of the actuation system, including, for example, the inertia of the piston and the driver response and update times, could also improve the efficiency of the control system as it takes into account the latency between the start of the reference signal and the start of the perturbation. Among the several aspects to be considered, the finite response time of the actuation system has likely the most significant impact on the MPC strategy, since the controller assumes