**1. Introduction**

Mechanical vibration exists in various machines in working conditions, such as precision machine tools, aircrafts, ships, etc. Strong vibration will affect the accuracy and stability of mechanical parts. In severe cases, it will also lead to fatigue failure and shorten the life of the structure or cause resonance to damage the structure. Therefore, suppressing the unfavorable vibration response has become an urgent problem to be solved in the industry.

The passive vibration suppression system commonly used in the engineering field achieves the purpose of vibration suppression by installing elastic damping elements to consume and absorb vibration energy. The system has high reliability but cannot adjust the vibration suppression characteristics and cannot adapt to changes in the external environment. Therefore, the active vibration suppression system with active adjustment capability and wide adaptive frequency range has become a research hotspot.

The active vibration suppression system is composed of sensors, actuators, and control systems, so the current research mainly focuses on two directions. One is the study of active control strategies; the other is the study of new materials and corresponding actuators. The active control strategies currently used in the field of

vibration suppression include PID control [1], adaptive control [2, 3], intelligent control [4, 5], and so on. The actuator is one of the key elements that affect the vibration suppression performance of the entire active vibration suppression system. In recent years, the development of smart material structures has provided conditions for the development of actuators, which has greatly promoted the research and application of active vibration control technology. At present, the smart materials used in the design of active vibration suppression actuators mainly include electro/magnetorheological fluids [6, 7], shape memory alloys [8, 9], magnetostrictive materials [10, 11], piezoelectric materials [12], and so on. Among them, the piezoelectric materials can be used as both actuators (inverse piezoelectric effect) and sensors (positive piezoelectric effect) due to their positive and inverse piezoelectric effects. As actuators, they have many advantages such as fast frequency response, wide control frequency range, high displacement resolution, small size, easy integration, no mechanical friction, and so on [13]. They have been widely used in active vibration suppression systems.

Most of the active suppression methods based on piezoelectric actuators reduce the vibration by directly suppressing the excitation force. That is, when the piezoelectric actuators are arranged, the direction of the output force/displacement of the actuators is consistent with the direction of the system vibration. In order to improve the vibration suppression effect, it is usually required that the piezoelectric actuator can output a sufficiently large displacement and control force at the same time, but its realization is limited by the electromechanical coupling characteristics of the piezoelectric actuator. This chapter discusses an active-passive composite vibration suppression system based on piezoelectric actuators. The active control element adopts a piezoelectric stack actuator with a mechanical displacement amplifying mechanism. The piezoelectric stack actuator has the advantages of high energy conversion efficiency, low operating voltage, and large output force. The mechanical displacement amplifying mechanism has a compact structure and can effectively amplify the displacement of the actuator. The second section of the chapter will analyze the driving characteristics of the piezoelectric actuator and the magnification of the displacement amplifying mechanism in the active control element, and discuss the compensation of hysteresis that affects the control accuracy of the piezoelectric actuator. Section 3 will analyze and construct the structure of the active-passive composite vibration suppression system based on the piezoelectric actuator, and establish its dynamic model. Section 4 will analyze the vibration control theory of the active-passive composite vibration suppression system using different control algorithms and control loops on the basis of the system dynamics model, and simulate the effectiveness of the algorithms. Section 5 will build an experimental platform to verify the active vibration suppression effect of the active-passive composite vibration suppression system based on the piezoelectric actuator. Section 6 is the conclusion, which will summarize the content of this chapter.
