## 1 Introduction
The control of civil engineering structures has been an active research area for recent years, with the goal of protecting structures from dynamic loading due to earthquakes, wind, and other sources [15; 16; 17]. There are three major categories of control methods for structures: passive, semi-active, and active [18]. Passive structural control techniques are the most straightforward, with no energy input and constant parameters, and are the focus of this paper. In passive vibration control, the tuned mass damper (TMD) is a popular structural control device [19]. It provides precise tuning control, especially for structures with a single frequency. The effective use of TMDs for vibration response control of structures subjected to earthquake and wind excitations was shown by [PERSON] and [PERSON] [20] and [PERSON] et al. [21]. The multiple tuned mass damper (MTMD) was demonstrated to be more effective than the single tuned mass damper (STMD) in the dynamic response control of structures [22]. Improved structural vibration control was demonstrated by using the damper with optimal parameter values. [PERSON] induced random and sinusoidal excitation on a wooden three-layer TMD structure model via shaking table experiments, and the results demonstrated that TMD could effectively decrease the model response [23]. [PERSON] designed a TMD for decreasing the resonance effect of the bottom layer of the structure due to several vibrations via a theoretical and experimental comparison of vibrational responses to the three-layer structure [24], and conducted a numerical analysis and an experimental evaluation of the dynamic characteristics of the entire mechanical system and its stability. [PERSON] proposed a multi-double-tuned mass damper control strategy and demonstrated by numerical analysis that it had higher effectiveness and robustness [25]. The above research mainly used TMDs to control the structural low-frequency response caused by an earthquake or wind vibration and investigated various TMD control strategies. The vibration control problem of structures with high frequency has yet to be studied. Moreover, the research is mainly based on numerical analysis, and the performance of a physical model of TMD damping remains to be verified. Therefore, it is necessary to evaluate the control performance of TMD on high-frequency vibration via a physical model. The key steps in reducing the high-frequency vibration of the structures of PSPPs are to design a high-frequency TMD and implement a control method for high-frequency vibration. In contrast to low-frequency control, the vibrational response of the top structure is typically the strongest, and the TMD can be effectively controlled by arranging it on the top of the structure. High-frequency vibration often causes higher-order modal vibration of the structure, and the maximum response does not always occur at the top of the structure, hence the damping effect of traditional control strategies is not significant. In view of the shortcomings of previous research, this investigation is the first to consider the combined effects of passive structural control and water pressure pulsation and use the modal analysis method and fixed-point theory to derive the optimal tuning relationship for a certain mode of a multiple-degree-of-freedom system. Based on the high-frequency characteristics of the superstructure of a pumped storage power plant, a vibration control method of the plant structure is proposed and a TMD device with a high-frequency tuning function is designed, then physical model tests are conducted to evaluate the damping effects of various TMD control strategies. The feasibility of the proposed method is further verified by numerical simulations, and the vibration damping performance of different control strategies is analyzed more comprehensively from the frequency domain perspective.