# Robot Joint Vibration Suppression Method Based on Improved ADRC
## 1 Introduction
There is a discrepancy between laboratory environments and real-world scenarios. Most studies validate their methods in ideal conditions, such as constant-temperature and electromagnetic interference-free environments, without considering the multi-variable and multi-disturbance characteristics of industrial sites. The core component of a robot is the robot joint module, as shown in Figure 1, which mainly includes a permanent magnet synchronous motor (PMSM) and harmonic reducer. Figure 1: Robot joint structure. As shown in Figure 1, a high-speed encoder is installed on the motor side of the joint module, and the measured motor angle is \(\theta_{0}\). A low-speed encoder is installed on the side of the harmonic reducer, and the angle of the harmonic reducer is measured as \(\theta_{r}\). The reduction ratio of the harmonic reducer is N. In an ideal state, the output angle of the motor shaft and the output angle of the harmonic reducer can be described as  
\[\theta_{0}=N*\theta_{r} \tag{1}\]  
Equation (1) shows that by controlling the motion angle \(\theta_{0}\) of the PMSM, the motion angle \(\theta_{r}\) of the harmonic reducer can be controlled, thereby controlling the motion trajectory of the robot. The power of robot joints comes from the PMSM. In the control process, the traditional control strategy is to control the motion accuracy of the PMSM, thereby controlling the trajectory of the robot. Due to the fact that the operating angle of the motor is only a 360-degree data loop, the robot needs to read the R values of its joints when powered on to obtain its static posture and prevent collisions after operation. The main contribution of this article is to study the laws of \(\theta_{r}\) and \(\theta_{0}\), extract the vibration disturbance signals of robots, and implement a new method for vibration suppression in the robotics industry. In cases where the resonant frequency of the control system is unknown, the ADRC can provide an effective and practical motion control solution [12]. From the perspective of control algorithms, there still exist underexplored gaps in robot vibration suppression research, which involve profound challenges in control strategies, algorithm design, and system modeling. Robot systems involve multiple nonlinear factors, such as variations in joint damping and the aging of harmonic drives. The interaction of these factors complicates the model. Traditional modeling methods, which are usually based on linear assumptions, fail to accurately capture these nonlinear characteristics. The parameters of nonlinear systems may vary with time or operating conditions and are difficult to measure accurately. To address this issue, an ADRC controller is designed in this article for the vibration suppression of robot joints. The core idea is to estimate and compensate for both internal and external disturbances of the system through the ESO, thereby reducing the dependence on an accurate model. Compared with traditional methods, the ADRC has the advantage of robustness, which does not require precise modeling and is very useful for dealing with the nonlinear parameter variations in robot vibrations. The ADRC is an advanced control method that does not rely on an accurate system model and can actively estimate and compensate for disturbances, thus demonstrating unique advantages in robot vibration suppression. Robot systems involve multiple nonlinear factors that are difficult to model precisely. Therefore, the ADRC theory regards all nonlinear factors and disturbances within and outside the system as \"total disturbance\" (such as the disturbance variations in friction force and other forces you mentioned) and estimates and compensates for them in real time to reduce the dependence on model accuracy. The core is the design of the ESO: the parts that are not modeled, the nonlinear friction, external disturbances, etc., are all regarded as total disturbance, and the total disturbance value is estimated in real time through the state observer.