# Linear System Identification and Vibration Control of End-Effector for Industrial Robots
## 2 Materials and Methods--Structure Design of Cantilever Beam  
Since the first generation of industrial robots came out in 1945, the application of industrial robots has gradually become more and more widespread [31]. More and more industrial robots replace human to complete industrial tasks with unusual or difficult requirements. People have higher and higher requirements for the quality of industrial robots. This paper mainly studies the transport robot for glass substrate shown in Figure 1. Due to the heavy weight, large area and easy damaging of the glass substrate, the position accuracy of the end-effector of the transport robot is required to be high. In practice, the vibration of the end-effector is the lead cause of glass substrate damage. Therefore, based on the end-effector of a glass substrate handling robot, a cantilever structure is designed for system identification and vibration control.  
Figure 1: Glass transport robot.  
The end execution structure of the existing glass substrate handling robot is illustrated in Figure 2. The overall structure is a rod-shaped structure with uniform mass distribution, large span and relatively thin thickness. The upper surface is the contact surface of the glass substrate which is connected by the glass substrate absorber. The end-effector is usually fixed to the arm by riveting or screw insertion into the arm mounting hole. Most substrates are composed of rubber while the material of the end-effector is steel and carbon fiber. Therefore, the structure can be simplified as a cantilever beam model, as shown in Figure 3.  
From Figure 3, it can be found that the absorber is omitted after comparing the mass so that we can simplify the end-effector into a thin cantilever beam. According to the actual length, width, and height of the end-effector, we reduced in equal proportion. The structural parameters of the cantilever beam designed and processed for system identification are \(250\times 2\times 25\) in mm. Additionally, on the left there are 30 mm left to fix the end which is called exposed core. The specific structure is shown in Figure 4. The parameters of the pasted piezoelectric ceramics are shown in Table 1.  
Figure 4: Structure of the cantilever beam.  
Figure 3: The model of end-effector.  
Figure 2: Structure of end-effector.  
In this paper, the excited signal of the end-effector comes from the contacting end with the arm of the robot. In order to restore the excitation of the end-effector as realistically as possible, we pasted a piezoelectric sheet as close to the exposed core as we can in order to excite the vibration. The maximum strain of a cantilever beam is at the clamp, so we pasted the other piezoelectric sheet near the excited one to control the vibration. Expressing the actual output vibration characteristics of the system called displacement acquisition point is 10 mm relative to the other end. The response of 0-300 Hz sinusoidal sweep excitation signal of the cantilever beam is carried out by fast Fourier transform. As shown in Figure 5, the first-order natural frequency of the structure is about 32.8 Hz, and the second-order natural frequency is about 195 Hz. The two natural frequencies have a large distance on the horizontal axis. The frequency domain response amplitude difference is