## 6 Experimental Trials  
In the model simulations, real-time control of the piston velocity allowed accurate and reliable force tracking. In our previous works [42; 43], the AP was driven during phase II in open loop, hence valves' command signals had to be finely tuned to achieve the desired velocity at impact. However, this control strategy did not provide a reliable behavior, especially when the initial distance between striker and stricken body changed significantly. Therefore, experimental trials carried out with the test-bench were primarily aimed at verifying the effectiveness of motion closed-loop control and eventually the confirmation of the results outlined in Figure 12b. Moreover, it was crucial to test the force tracking performance under different selected components (valves and cylinders). A comparison between the performance of cylinders \(\mathrm{C_{a}}\) and \(\mathrm{C_{b}}\) is presented in Figure 13a-b when \(\mathrm{V_{b}}\) valves were selected. Each plot shows five consecutive perturbations in fixed constraints configuration (i.e., both AP and stricken body carts locked). Consistently with simulations of Figure 12a, the two cylinders behaved similarly, with comparable performance in magnitude and impulse accuracy, as well as in rise and fall time. Oscillations in the force signal were observed during phase II just before impact (t = 0, Figure 13), likely related to inertial effects on load cell and connected masses. Those oscillations were smoothed out in the following trials, when the piston motion was closed loop controlled during phase II (Figures 14 and 15, at the bottom). As shown in Figure 13c, valves \(\mathrm{V_{a}}\) behaved significantly worse than \(\mathrm{V_{b}}\), with the latter demonstrating better dynamics while allowing a more accurate behavior of the contact force profile for lower duration of the impulse. Some differences were highlighted also in the switching phase from phase II to III, where the \(\mathrm{V_{a}}\) valves seemed to be more sensitive to sudden variations in the command signal. However, this result confirms the need for high flow rate and short response time in order to meet the performance requirements of the application. Figure 12: Evaluation of force tracking accuracy (fixed constraints, desired impulse duration = 250 ms, \(\mathrm{k_{p}}\) = 3.1, \(\mathrm{k_{i}}\) = 23.9, valve \(\mathrm{V_{b}}\)): _Ref_ refers to the reference force profile. (**a**) Comparison of performance provided by cylinders \(\mathrm{C_{a}}\) and \(\mathrm{C_{b}}\); (**b**) influence of initial distance \(dx\) between perturbator tip and stricken mass, using cylinder \(\mathrm{C_{a}}\). As shown in Figure 13, the system demonstrated a good tracking accuracy in fixed constraints configuration. Figure 14 shows the force tracking results when \(\rm C_{b}\) and \(\rm V_{b}\) were selected in a more realistic scenario, i.e., when both carts were free to move under viscoelastic constraints. Although force profile tracking was less accurate, the perturbations were still repeatable and capable of providing quite accurate values of the force impulse. Figure 14: Experimental force tracking, with viscoelastic constraints and closed loop control during phase II. Cylinder \(\rm C_{b}\) and valve \(\rm V_{b}\). The square waveform is the reference force profile. Six consecutive perturbations are shown. Figure 13: Experimental force tracking, with fixed constraints and open loop control during phase II. (**a**) Cylinder \(\rm C_{a}\) and valve \(\rm V_{b}\); (**b**) cylinder \(\rm C_{b}\) and valve \(\rm V_{b}\); (**c**) cylinder \(\rm C_{b}\) and valve \(\rm V_{a}\). The square waveform in each plot is the reference force profile _Ref._ Each plot shows five consecutive perturbations.