# Vibration Suppression of Collaborative Robot Servo with Dual Encoders
## 9 Conclusions  
Due to the presence of elastic structures such as reducers and linkages in collaborative robots, even if the speed of the motor side is well controlled, vibrations will still be transmitted to the end effector. Installing an encoder on the reducer side and incorporating its measured speed into the control process has a positive impact on suppressing vibration. Depending on the actual working conditions, dual encoders can be added to the second and third axes, where the moment of inertia changes the most and is the most difficult to control. This approach achieves both cost savings and vibration suppression effects. The  
Figure 14: The cooperative robot with dual encoders. ratio of encoder control between the motor and the reducer should be chosen appropriately and can be adjusted based on the actual vibration suppression effect. Typically, the ratio k1 of motor encoder control should be greater than or equal to 0.5, while the ratio k2 of reducer encoder control should be less than or equal to 0.5. Otherwise, a slow response may lead to other issues. Good results can be achieved when the motor encoder coefficient k1 is in the range of 0.5-0.8 and the reducer encoder coefficient k2 is in the range of 0.5-0.2. This study adjusted the relevant parameters and achieved satisfactory results. Additionally, it should be noted that there are significant differences in control parameters between dual-encoder control systems and single-encoder control systems, so adjusting control parameters based on actual effects is crucial. This article has implemented the function of automatically obtaining parameters k1 and k2. The quantitative indicator of vibration reduction is mainly reflected by the speed fluctuation on the reducer side. The smaller the speed fluctuation measured by the reducer, the smaller the vibration. From the waveforms of the startup phase, steady phase, and deceleration phase, it can be seen that after adding control to the speed on the reducer side, the fluctuation on the reducer side is significantly reduced. The maximum speed fluctuation of 10% is controlled within 4%. If the encoder on the reducer side is not added to the control during the steady phase, the speed fluctuation on the reducer side will reach +\(-\)10 PRM or more. After adding control, the speed fluctuation on the reducer side during the steady phase is within +\(-\)4 RPM. Compared to the single-encoder configuration, the dual-encoder system incurs additional costs, including an extra encoder, a BiSS signal processing chip, and various passive components such as resistors, capacitors, inductors, and TVS diodes. However, the substantial performance improvement achieved through this implementation justifies the increased expenditure, making it a cost-effective solution in terms of performance enhancement versus additional investment. The incorporation of an additional encoder introduces a system latency of 12.8 \(\upmu\)s. However, when operating with a sampling clock frequency of 10 MHz, this latency is reduced to 3.2 \(\upmu\)s. Considering a control cycle of 100 \(\upmu\)s, this additional latency represents only a 3.2% increment in the cycle time, which is negligible in terms of overall system performance impact. Conceptualization: Q.X., C.C. and Y.J. ; methodology: Q.X. ; software: Q.X. ; validation: Q.X., C.C. and Y.J. formal analysis: Q.X. ; investigation: Q.X. ; resources: Q.X. ; data curation: Q.X. ; writing--original draft preparation: Q.X. ; writing--review and editing: Q.X. ; visualization: C.C. ; supervision: C.C. ; project administration: Q.X. ; funding acquisition: C.C. All authors have read and agreed to the published version of the manuscript. This research was funded by Research on Servo Jitter Suppression in Industrial Robots Based on Inertial Sensors: An Industry-Academia Collaboration Project (Grant No. 230606). Not applicable. The original contributions presented in this study are included in this article; further inquiries can be directed at the corresponding author.