# Linear System Identification and Vibration Control of End-Effector for Industrial Robots
## 1 Introduction  
The problem of vibration suppression has traditionally been a research hotspot of scholars, and studies on vibration control are increasing year by year [1]. Due to the advantages of lightweight, large output, fast response speed and high strain sensitivity, piezoelectric materials have been widely used for vibration control and other occasions [2].What is more, a piezoelectric patch can be easily attached to the cantilever structure which is the most used mechanism in the area of industrial robots and the most easily simplified model for transportation robots [3, 4]. Therefore, using piezoelectric materials for vibration suppression of beam structures has been widely studied. Piezoelectric material was introduced into the beam vibration by [PERSON] and [PERSON] [5] for the first time, and subsequently, it was widely used in robot structure. Some scholars use the positive piezoelectric effect and the inverse effect to design sensor and actuator for robot. It achieved the collection of the vibration signal through a sensor and gave a reverse vibration by the actuator in order to achieve the mechanism vibration suppression, e.g., [PERSON] et al. [6, 7], [PERSON] et al. [8], [PERSON] [9] and [PERSON] [10]. However, soon the hysteresis characteristic of piezoelectric materials and the interference between electrical signals appeared. [PERSON] [11] found the influence of the time-delay effect of piezoelectric materials on vibration suppression and started to study the hysteresis characteristics, as well as [PERSON] [12], [PERSON] [13], and so on. In addition, some scholars focused on separation of control signals. Another research direction is only using piezoelectric materials as actuators. [PERSON] [14] used a piezoelectric (PZT) patch as actuator which is bonded on the surface of the flexible beam to suppressresidual vibration. [PERSON] et al. [15] gave a vibration suppression method of two bending modes and two torsional modes. At the background of this research direction, [PERSON] et al. [16] discussed using an auxiliary piezoelectric actuator to control vibration for high-speed linear robots. Because of the minute output of piezoelectric material, it is often used in many pieces to achieve the precise vibration suppression of robots. [PERSON] et al. [17], [PERSON] [18] and [PERSON] et al. [19]. [PERSON] et al. [20] studied the accurate models of a flexible link and two surfaces bonded with piezoelectric patches, where the link and the piezoelectric patches will be modelled through the use of Euler-Bernoulli beam theory (EBT). When using PZT patch as actuator, in order to achieve vibration suppression, some people have studied the model identification of the system. [PERSON] [21] carried out detailed research on system identification and real-time control of dynamic systems, and realized adaptive control of nonlinear systems. People of the same range studied the identification method based on dynamic system, e.g., [PERSON] [22], [PERSON] [23; 24; 25]. [PERSON] [26] of Rockwell International Science Center established a self-learning double-layer back propagation (BP) neural network control system for unknown characteristics and dynamic model systems, while [PERSON] [27] established neural network discrimination. [PERSON] et al. [28; 29] studied an adaptive method and gave the relationship between the proportion of low frequency components and the modal order. Some identification models came from experiments, such as [PERSON] et al. [30]. The existing research on vibration control of beam structure lacks the research on industrial robot with low frequency vibration. At the same time, under this working condition, most adaptive control systems or feedback compensation systems cannot provide the feedback signals needed by the system in real time. Therefore, a vibration controller based on linear system identification is proposed to solve the problem of low frequency oscillation. The remainder of this paper is organized as follows.