# Optimal Design and Hybrid Control for the Electro-Hydraulic Dual-Shaking Table System
## 3 Control Scheme Design  
Figure 8 shows the fundamental control scheme of one shaking table, which consists of the DOF synthesis matrix \(H_{h}\), DOF decomposition matrix \(H_{f}\), traditional TVC, IFS and GBC control. The control scheme is based on the displacement DOF close-loop using the \(H_{h}\) and \(H_{f}\), which can transfer the control and feedback signals between actuator space and DOF space [18]. TVC controller is used to improve the shaking table system performance using the acceleration, velocity and displacement feedback signals and has been successfully applied in many practical shaking table systems [19; 21; 45]. The gravity balance control is relatively simple, and the force closed-loop control is used for each balanced hydraulic cylinder, whose controller is a proportion controller. To reduce the inner force of the redundant-driven shaking table system due to the inconsistencies of the valve-controlled hydraulic cylinders' performances, the IFS is proposed by [PERSON] and [PERSON] and obtained a better suppression effect [18; 20]. Therefore, to improve the system performance, this paper applies the TVC and IFS as the fundamental control scheme for the platform motion control system, as shown in Figure 8. Note that the velocity signal is synthesized using the acceleration and displacement in practice. Generally, the experiment specimen of the shaking table is the civil engineering structure, which is mostly reinforced concrete structure [5; 6]. As we all know, the reinforced concrete structure specimen is easily damaged when the specimen encounters large deformation. If the attitude control errors of the  
Figure 8: The fundamental control scheme of one shaking table system. shaking tables are large, especially one or both of the shaking tables lose control due to misoperation, which will cause significant deformation to the specimen, even damage. Thus, the synchronization control strategy is needed first to reduce the undesired synchronization error of the shaking tables to avoid the large deformation of the specimen. The synchronization control will keep the shaking tables moving synchronously even though there is large attitude control error or it is out of control. Based on the synchronization control, the tracking control precision also needs to be ensured, thus the feed-forward inverse model is adopted, which has many advantages, such as being independent of the system's stability. However, the identified model errors, designed inverse model errors and some disturbance can still affect the tracking control precision. To improve the control precision further, the disturbance-observer feed-forward inverse model is proposed based on synchronization control, as shown in Figure 9.  
Figure 9 shows the proposed control scheme of the dual-shaking table system. As is shown in the figure, the control system mainly contains the fundamental displacement DOF close-loop control based on Figure 8, synchronization control and tracking control. The cross-coupled synchronization controller ASMC, which can adaptively tune the parameters of the SMC, is proposed to reduce the synchronization error of two shaking tables though compensation control of error to the reference input port of the fundamental close-loop control. On that basis, the feed-forward observer-based inverse model controller combining the inverse model controller and disturbance observer is used to improve the tracking control performance. The proposed compound controller has the advantages of inverse controller and disturbance observer and has a high tracking precision. As can be seen in the figure, the ASMC synchronization controller and observer-based inverse model controller act as an outer control loop of the fundamental close-loop control. Note that this paper mainly studies the synchronization and tracking control, which prefers to obtain the same response performance under the same reference signal, so in the control system the same one reference signal is given to the two shaking tables.