## 4 Comparison of Control Effect between BN Control and GBN Control
### Experimental Results  
In this section, we build a prototype of semi-active drop hammer shock mitigation for rapid control to verify the soft-landing effect of the GBN control strategy. The drop hammer shock mitigation system setup is shown in Figure 12. As it can be seen from the diagram of experiment setup (Figure 12a), the experiment setup also contains two parts: the mechanical part and the semi-active control part. The mechanical part of the platform is CEAST 9350 drop tower, including an MREA. The MREA was attached firmly to the bottom of the drop tower. An aluminum honeycomb was attached on the top of the MREA piston rod to eliminate the ringing in the load cells due to metal-to-metal impact. The initial drop velocity is controlled by a drop hammer control computer. The drop height of the hammer can be set in the software and moved by air pressure servo. The semi-active control part includes sensors, control computer, Xpc real-time control system, test system, and a power amplifier, which supplies power to the MREA. The Xpc real-time control system is the core of the semi-active control system, including the A/D board, D/A board, Xpc target computer, and control computer.  
Figure 12: Cont.  
The drop velocity and damping force can be measured by force and velocity sensors, respectively, and then, it transferred to an Xpc real-time control system through the test system. Note that the signal is an analog signal now, which can be converted to be a digital signal by the A/D board. The control program, as shown in Section 3, is completed on the control computer, compiled to generate the executable control code, and downloaded to the Xpc target computer. The control current can be calculated by a control program and converted to be an analog signal by the D/A board. Finally, the signal is amplified by a power amplifier and applied to the MREA.  
In the test, the GBN or the BN1 or BN2 control algorithms are used to calculate the required yield force. The applied current is then calculated using Equation (14). Note that the friction force of the MREA is not considered in Section 3, so for practical purposes, the optimal yield force is given by  
\[F_{MR\_r}=F_{MR\_t}-F_{f} \tag{31}\]  
where \(F_{MR\_r}\) is the optimal yield force in practical control and \(F_{MR\_t}\) is the yield force calculated in Section 3. Here, \(F_{f}\) is the friction force of the MREA, and \(F_{f}\) = 0.16 kN. Table 4 shows the optimal yield force and control current for an initial one drop velocity of 4.3 m/s.  
Figure 12: Semi-active drop hammer shock mitigation for rapid control experiment setup.  
Figure 13 shows the experimental semi-active control performance of a shock mitigation system under the GBN control and BN control. For the GBN control, the hammer comes to a rest at the stroke of 10.26 cm, which is slightly over the available stroke of 10 cm, i.e., the soft landing can be achieved.  
For the BN1 controller, the control current is so small, as shown in Table 4, that the damping force generated by the MREA is also lower than its optimal value (Figure 13a). In this case, the hammer has a non-zero velocity when it arrives at the available stroke of 10 cm and comes to a rest at the stroke of 13.2 cm at the end. The soft landing