# Optimal Design and Hybrid Control for the Electro-Hydraulic Dual-Shaking Table System
## 4 Experimental Results
### IFS and GBC Tests  
This part will test the IFS and GBC. To make the verification adequate, various experimental tests are performed using different control strategies. The experimental results are approximately identical for the two shaking tables, so only the results of the first one are listed in the figures and tables for simplicity.  
For different control strategies, Figures 15 and 16 show the output forces and inner forces of hydraulic cylinders when the shaking table is static at the 0 position and under the random signal excitation, respectively. Each figure is divided into three phases: the first phase is without IFS and without GBC, the second phase is with IFS and without GBC and the third phase is with both IFS and GBC, and each phase lasts 30 s. The detailed data comparisons of inner forces and output forces are tabulated in Tables 2 and 3, which counts the maximum values. Note that the output forces in the figures and tables are used to demonstrate the validity of the designed GBC, which is used to reduce the output forces of vertical hydraulic cylinders by balancing the gravity of table and load. The inner forces of hydraulic cylinders are the partial output forces not making any real contribution to the shaking table's motion. Also, the inner forces are obtained according to the output forces and inner force matrix Equation (42). The inner forces of hydraulic cylinders in the figures and tables are used to demonstrate the validity of the adopted IFS.  
Figure 14: The frequency characteristics before and after tuning valve controllers. (**a**) Magnitude frequency characteristics before; (**b**) Phase frequency characteristics before; (**c**) Magnitude frequency characteristics after; (**d**) Phase frequency characteristics after.  
Figure 16: The output forces and inner forces under random signals. (**a**) The horizontal output forces; (**b**) The vertical output forces; (**c**) The horizontal inner forces; (**d**) The vertical inner forces.  
Figure 15: The output forces and inner forces with different controllers at 0 position. (**a**) The horizontal output forces; (**b**) The vertical output forces; (**c**) The horizontal inner forces; (**d**) The vertical inner forces.  
From Figures 15 and 16 and Tables 2 and 3, it can be seen that without IFS and GBC the inner forces and output forces of the hydraulic cylinders are both very large (2.2 \(\times\) 10\({}^{4}\)-2.7 \(\times\) 10\({}^{4}\) N, 2.5 \(\times\) 10\({}^{4}\)-4.8 \(\times\) 10\({}^{4}\) N) due to the inevitable offset of the servo valves, electronic system and mechanical assembly, etc. After using the IFS, the output forces and inner forces of hydraulic cylinders are reduced significantly (200-2000 N, 500-1.4 \(\times\) 10\({}^{4}\) N), which indicates that the adopted IFS control strategy can reduce the output forces and inner forces effectively under the same condition and thus reduce the energy consumption and the forces acting on the table. However, the output forces of vertical hydraulic cylinders are still relatively large because of the gravity of the table and load. After using the GBC, the forces are reduced from 1.4 \(\times\) 10\({}^{4}\) N to about 1200 N, which indicates that the GBC can balance the gravity of the table and load and reduce the output forces of the vertical hydraulic cylinders. From the above, it can be concluded that the IFS and GBC control strategies are feasible and effective.