# Pneumatic Rotary Actuator Position Servo System Based on ADE-PD Control
## 7 Conclusions  
In this paper, the pneumatic rotary actuator position servo system is studied and analyzed, and an experimental platform is set up. The motion laws of the rack and pinion pneumatic rotary actuator and the proportional directional control valve are analyzed. Starting from the flow of gas flowing through the proportional directional control valve and the motion state of the pneumatic rotary actuator, the basic equations of the actuator controlled by the valve are obtained and linearized near the middle position, and the mathematical model of the pneumatic rotary actuator is deduced.  
Figure 16: Tracking curves when moment of inertia is 3.2 \(\times\) 10\({}^{-4}\) kg\(\cdot\)m\({}^{2}\): (**a**) Rotation position tracking fixed value; (**b**) Error tracking fixed value; (**c**) Rotation position tracking sinusoidal signal; and (**d**) Error tracking sinusoidal signal.  
Figure 17: Tracking curves when moment of inertia is 4.5 \(\times\) 10\({}^{-4}\) kg\(\cdot\)m\({}^{2}\): (**a**) Rotation position tracking fixed value; (**b**) Error tracking fixed value; (**c**) Rotation position tracking sinusoidal signal; and (**d**) Error tracking sinusoidal signal.  
Then the mathematical model of the whole system is obtained. The establishment of this model lays a foundation for the research of theory and experiment.  
An Adaptive Differential Evolution (ADE) algorithm is proposed in this paper. In the process of individual variation, the values of scaling factor and crossover probability are adjusted by a decreasing concave function and an increasing convex function, respectively, which improves the accuracy and the speed of algorithm optimization. The ADE-PD controller is designed to control the pneumatic rotary actuator position servo system, and the experimental platform is used to select parameters, compare the controller with DE algorithm, and compare with PID controller by changing input signals. Finally, the characteristics of the system are discussed by increasing the inertia load. The conclusions obtained from experiments can be summarized as follows:  
1. Different values of \(F\) and \(CR\) can change the stability of the control. Rotation position controlled by ADE-PD has smaller overshoot and fluctuation than others controlled by DE-PD when \(F_{\text{max}}\) = 1.5, \(F_{\text{min}}\) = 1.0, \(CR_{\text{max}}\) = 0.9, \(CR_{\text{min}}\) = 0.6.
2. The control precision of the system becomes worse with the increase of the frequency of sinusoidal wave. And there are persistent fluctuations in steady state because of stickiness in the actuator when changing the direction of motion. The system based on ADE-PD control can reduce the occurrence of stickiness, and has greater position precision and faster response than NCD-PID control.
3. Increasing the moment of inertia will reduce natural frequency and damping ratio, and make the error increase and even deviate from center. Even so, the system has relatively stable trajectories and tiny errors, which shows great robustness.
4. Although a resonance is expected by the compressibility and the friction could cause a small displacement instability, a reasonable control can be obtained.  
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).  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments and [PERSON] analyzed the data; [PERSON] wrote the paper and [PERSON] modified the manuscript.  
The authors declare no conflict of interest.