# Optimal Design and Hybrid Control for the Electro-Hydraulic Dual-Shaking Table System
## 4 Experimental Results  
To verify the effectiveness of the proposed control scheme in this paper, the dual-shaking table host-to-target real-time control experiment system shown in Figure 13 is built based on a rapid prototype technique and a variety of experiments are performed. The control system mainly contains several parts: task management unit, hydraulic power supply management unit, hydraulic power supply unit, servo motion control unit, signal conditioning unit, signal acquisition unit, shaking tables and the test specimen. The target PC is the National Instrument computer PXI-1044, including the controller PXI-8119, the A/D cards PXI-6259, D/A cards PXI-6733, digital I/O card PXI-6508. The task management unit monitors and controls the servo motion control unit through the TCP/IP communication protocol, respectively. The proposed control strategy is programmed using the Matlab/Simulink and then complied to target PC for real-time control execution. The control signals from motion control unit will be processed in the signal conditioning unit and then are sent to the servo valves in the form of input current to control the motion of hydraulic cylinders, which in turn drive the dual-shaking table to move with desired trajectory. The sample time of real-time controller is 1 ms.  
The experiment tests mainly contain four parts: servo valve tests, IFS and GBC tests, synchronization control tests and tracking control tests. Note that although the shaking table has six DOFs, whose structure is to realize the three translations and reduce the coupling action of the three directions, the experiment tests are generally performed only in three translation directions. It is because the earthquake waveform and anti-earthquake research are both only in the three translation directions, which has been shown in many practical applications [7; 49; 50]. Thus, the experiment tests in this paper are performed in \(X/Y/Z\) translation directions. Note that the TVC mentioned in Section 3 runs in the displacement control and all the experiment tests except for the servo valve tests in this paper are performed with the specimen described in Section 2.1.  
Figure 13: The dual-shaking table experiment system. (**a**) Real-time control system; (**b**) Built experiment system.  
The DOF synthesis matrix \(H_{h}\) in Figure 8 is obtained according to a geometrical relationship  
\[H_{h}=\left[\begin{array}{cccccccc}0.5&0&-0.5&0&0&0&0&0\\ 0&0.5&0&-0.5&0&0&0&0\\ 0&0&0&0&0.25&0.25&0.25\\ 0&0&0&0&-0.018&-0.018&0.018\\ 0&0&0&0&-0.018&0.018&-0.018\\ -0.11&-0.11&0.11&0&0&0&0\end{array}\right] \tag{40}\]  
The DOF decomposition matrix \(H_{f}\) in Figure 8 is the pseudo-inverse of \(H_{h}\)  
\[H_{f}=\textit{pinv}(H_{h})=\left[\begin{array}{cccccccc}1&0&0&0&0&-22.32\\ 0&1&0&0&0&-22.32\\ -1&0&0&0&0&22.32\\ 0&-1&0&0&0&22.32\\ 0&0&1&-13.5&-13.5&0\\ 0&0&1&-13.5&13.5&0\\ 0&0&1&13.5&-13.5&0\end{array}\right] \tag{41}\]  
The inner force matrix is derived as [20]  
\[H_{if}=I-H_{h}^{T}H_{f}^{T}=\left[\begin{array}{cccccccc}0.25&0.25&0.25&0.25& 0&0&0&0\\ 0.25&0.25&0.25&0.25&0&0&0&0\\ 0.25&0.25&0.25&0.25&0&0&0&0\\ 0&0&0&0&0.25&0.25&-0.25&-0.25\\ 0&0&0&0&-0.25&-0.25&0.25\\ 0&0&0&0&-0.25&-0.25&0.25\\ 0&0&0&0&-0.25&-0.25&0.25\\ 0&0&0&0&-0.25&-0.25&0.25\end{array}\right] \tag{42}\]