## 6 Conclusions  
In order to improve the position accuracy of the pneumatic rotary actuator servo system, the modeling of the system and the design of the evolutionary algorithm-based friction feedforward compensation control architecture were carried out and verified by the experiments. Firstly, basic equations of the valve-controlled actuator were derived and linearized in the middle position, and the transfer function of the system was further obtained. Then, the evolutionary algorithm-based friction feedforward compensation control architecture was designed, which includes the optimization of the controller coefficients and the identification of the friction parameters. Finally, in the position tracking experiment, the positioning experiment and the stability experiment with load, the control performances of four control strategies (the traditional PD control, the PD control with friction feedforward compensation without evolutionary algorithm tuning, the PD control with friction feedforward compensation based on the DE algorithm and the PD control with friction feedforward compensation based on the GA) were contrasted and analyzed, and the following conclusions were obtained:  
1. The PD control with friction feedforward compensation without evolutionary algorithm tuning can reduce the system error to a certain extent. However, since the controller parameters and friction parameters were not optimized, the error values were still relatively large.
2. The friction feedforward compensation based on evolutionary algorithm greatly improved the position tracking performance for the sinusoidal signal, and the DE-based case had better control accuracy and smaller velocity fluctuations.
3. The friction feedforward compensation based on evolutionary algorithm greatly improved the positioning performance when the input angle was a constant, and the DE-based case achieved higher accuracy.
4. Although the existence of the load affected the tracking and positioning effects, the system with the evolutionary algorithm-based friction feedforward compensation still maintained high accuracy and strong stability.  
Conceptualization, K.L. and Y.Z.; Data curation, S.W. and H.Y.; Funding acquisition, Y.Z.; Investigation, K.L.; Project administration, Y.Z.; Supervision, S.W.; Writing--original draft, K.L.; Writing--review & editing, K.L., Y.Z. and H.Y.  
The research reported in the article was funded by the Fundamental Research Funds for Henan Province Colleges and Universities (Grant No. NSFRF140120); Henan Province Science and Technology Key Project (Grant No. 172102310674); the Doctor Foundation of Henan Polytechnic University (Grant No. B2012-101); the Science and Technology Research Projects of Education Department of Henan province (Grant No. 14B460033); The Construction Project of the Case Library Course for Graduate Students of Henan Polytechnic University (Grant No. 2016 YAL09).  
Figure 17: Angle errors under different loads. (**a**) Position tracking error; (**b**) positioning error.  
**Acknowledgments:** The authors would like to thank Henan Polytechnic University for its support. The authors are sincerely grateful to the reviewers for their valuable review comments, which substantially improved the paper  
**Conflicts of Interest:** The authors declare no conflicts of interest.