## 5 Verification of Real-time Hybrid Control System
### Three-DOF Structural Dynamic Test with Concrete Structure
#### 5.2.2 Non-Linear Dynamic Test with Real-Time Hybrid Control System  
To ensure the response in the nonlinear dynamic test before the multiple degree of real-time hybrid test, the preliminary test was conducted with concrete specimens as shown in Figure 19. For the feasible nonlinear dynamic behavior, the wave-like displacement input was used as shown in Figure 19a. The wave acceleration was gradually increased from linear range to about 70 mm in order to show the variation between linear behavior and nonlinear one and to predict the maximum displacement and load of the concrete structure. Figure 19 graphically shows the displacement versus time history and displacement-load results and the total time was about 200 s. As a result, the absolute maximum displacement value was about 30 mm and the maximum load was 35 kN.  
After verifying the feasibility through preliminary tests, a real-time hybrid test was performed for the concrete structure. Figure 20 describes the comparison of the results of FEAPH numerical analysis and the RTHT under the same condition. To analyze the reliability and applicability, Figure 21 shows the result of comparing the real-time hybrid test and shaking table experiment. Table 2 describes the comparison of maximum displacement error and root mean square (RMS) error. RMS error is derived from Equation (15) and the evaluation of the error value can be more accurate as close to zero (0) [33].  
\[RMS\ error=\sqrt{\frac{\sum_{i}\sum_{j=1}^{n}\left(d_{i}^{\left(j\right)}-d_{ i}^{\left(j\right)}\right)^{2}}{\sum_{i}\sum_{j=1}^{n}\left(d_{i}^{\left(j \right)}\right)^{2}}} \tag{15}\]  
In Figure 20, the maximum displacement from the numerical analysis is about 60 mm. The maximum displacement by the real-time hybrid test was about 52 mm, which was reduced by about 13% as shown in Table 2. This is because the material nonlinear model of concrete and reinforcement used in the numerical analysis contains a lot of errors, which seems to be somewhat different from the actual behavior. On the other hands, the real-time hybrid test was almost in agreement with the results of the shaking table test. The peak displacement error and RMS error were good evidence in Table 2. This is because the real-time hybrid test can consider the actual material property. That is, the measured displacements and loads obtained from the feedback of the actuators can be applied to the numerical model, so that the next command displacement can be corrected.  
Figure 22 also shows the relationship between the displacement and the load occurring at the top of the specimen. Over time, cracks develop in the concrete, which results in a non-linear behavior with sudden changes in displacement and a sharp decrease in strength as the load increases. This resulted in many cracks and peelings as the steel thickness in the upper and lower right corners (see Figure 23c). Figure 24 shows the strain over time measured by installing a strain gauge on the rebar in concrete. This is the result measured at the position where Figure 23c breakage occurred. Afterward 200 s in Figure 10, the reinforcing bars suddenly shifted and then about 4000 microstrains remained as residual strain. The reinforcement concrete specimens show the sudden large displacement and load. Therefore,  
Figure 18: Northridge ground acceleration.  
Figure 23: 3-DOF hybrid test for concrete frame; (**a**) Accelerator (**b**) Strain gauges (**c**) Fracture shape.  
Figure 24: Strain on top of the concrete specimen.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & **FEAPH\_Num (A)** & **Shake Table Test (A)** \\ \cline{2-3}  & **Real-Time Hybrid Test (RTHT) (B)** & **Real-Time Hybrid Test (RTHT) (B)** \\ \hline Peak displacement error (\%) 1 & 13.3 & 2.3 \\ \hline RMS (Root Mean Square) error & 0.799 & 0.203 \\ \hline \hline \end{tabular}  
* Peak displacement error = (A –B)/B × 100.  
\end{table}
Table 2: Comparison of peak displacement value error and root mean square (RMS) error.  
Figure 22: Force and displacement at the top of the specimen.