# Optimal Design and Hybrid Control for the Electro-Hydraulic Dual-Shaking Table System
## 1 Introduction
[PERSON] [28] researched feed-forward inverse control for the time waveform replication of the shaking table. [PERSON] [29] presented an optimal control for electro-hydraulic systems by adopting a combination of feed-forward inverse and feedback controllers. The common system parameter identification algorithms are mainly LMS and RLS and the latter has a better convergence velocity and stability than the former [30]. Generally, the identified system model is always a non-minimum phase system and the direct inverse model as a feed-forward controller is unstable [31]. The system parameter uncertainty, nonlinearity, cross-coupled characteristic, disturbance and noise signals may affect the identified precision of the system model [32]. First, to compensate the absence, this paper introduces the design and optimal method of the shaking tables system built by the Harbin Institute of Technology (HIT) in detail. To improve the system performance, the servo valves with parameter-tunable valve controllers are designed and the gravity balance control (GBC) is proposed to reduce the output forces of vertical hydraulic cylinders and to improve the asymmetric performance in the vertical direction. The DOF control method is used and the TVC and IFS control schemes are adopted as the basic control to realize the motion control. Furthermore, the advanced synchronization and tracking control method is proposed to improve the control precision. The parameters of traditional SMC are constant and unchangeable, which leads to poor control performance. To improve the problem, this paper proposes a novel ASMC, which can adaptively tune the parameters of the SMC, to markedly improve synchronization performance while eliminating the chatting phenomenon. The RLS algorithm is applied to identify the system model and the ZPETC proposed by [PERSON] [33] is applied to obtain the system inverse model. The observer-based compensation scheme, which combines the feed-forward inverse model controller and disturbance observer, is proposed to further improve the control system performance. It cannot only compensate the disturbance and noise signals, but also can compensate the estimated model error and the designed system inverse model error. The contributions of this study are: (i) the system parameters are designed and optimized; (ii) the ASMC is proposed to improve the synchronization performance; (iii) the observed-based inverse model controller is proposed to improve the tracking performance; and (iv) that the combination of the ASMC and observed-based inverse model controller is proposed to improve the synchronization and tracking performance of the dual-shaking table system. The remainder of this paper is organized as follows. In Section 2, the dual-shaking table system parameters are designed and optimized; The ASMC designed for the cross-coupled synchronization controller is proposed in Section 3; Section 3 presents the designed tracking controller based on feed-forward inverse controller and the observer-based compensation scheme; The test experiments are performed to verify the performance of the designed controller in Section 4; followed by Section 5, which briefly concludes the paper.