# Constant Force Control of Centrifugal Pump Housing Robot Grinding Based on Pneumatic Servo System
## 7 Conclusions  
In this paper, we studied the compliance of the grinding robot with the inner circle of the centrifugal pump shell. The macro-micro manipulator structure was adopted, the industrial manipulator realized the position control, and the pneumatic servo system was adopted for controlling the contact force in the grinding process with the end actuator. At the same time, the compressibility of gas was used to realize the compliance of the end effector. The relationship between the constant force control performance of the end effector and the structural parameters of the cylinder was analyzed in detail. The PID control algorithm was used to realize the fast response and stable control of the displacement and force output of the pneumatic servo system. The corresponding relationship between the PID gain and the structural parameters of the cylinder was obtained to carry out the simulation experiment. The simulation results show that the PID control improved the response speed and steady-state accuracy of the system, reduced the impact and oscillation of the system contact force, and effectively suppressed the influence of load interference, so that the average steady-state error decreased from 5.95% to 0.785%. The average steady-state error with load interference is 0.785% and the steady-state error without interference is 0.042% when the cylinder diameter D = 80 mm, the piston rod diameter d = 25 mm, and the stroke L = 100 mm with PID control. It realized the constant control of the contact force in the robot grinding process, so as to realize the stable, accurate, and fast response control of the grinding force. The uncertainty and complexity of force control in the grinding process of an industrial robot were resolved. The control strategy proposed in this paper is based on a simplified mathematical model of the pneumatic servo system. In the derivation process, it was assumed that the gas is ideal and the working pressure of the cylinder is constant. Therefore, the mathematical model established in this paper has certain limitations. Using intelligent control algorithms to study the constant force control of robots in the presence of interference, achieving the self-adaptive adjustment of control parameters, and verifying constant force control through experiments will be the focus of a future study.  
Conceptualization, X.S. and L.S.; methodology, X.S., Y.X. and L.S.; software, X.S.; validation, X.S., Y.X. and L.S.; formal analysis, Y.X. and B.J.; investigation, Y.X. and B.J.; resources, X.S.; data curation, X.S. and L.S.; writing--original draft preparation, X.S. and Y.X.; writing--review and editing, X.S. and L.S.; visualization, X.S. and L.S.; supervision, B.J.; project administration, X.S.; funding acquisition, X.S. All authors have read and agreed to the published version of the manuscript.  
Figure 19: Force response curves with interference. (**a**) Interference signal; (**b**) Force response curves with interference; (**c**) Error curves with and without PID control; (**d**) Comparison of PID control response curves with and without interference.  
**Funding:** Financial support from the Key Project of Natural Science Research in Colleges and Universities of Anhui Province, Grant Number kj2019a0147.  
**Data Availability Statement:** Please contact the first author: [EMAIL_ADDRESS].  
**Conflicts of Interest:** The authors declare no conflict of interest.