# Fuzzy PID Control of the Three-Degree-of-Freedom Parallel Mechanism Based on Genetic Algorithm
## 7 Conclusions  
1. The PM is a highly nonlinear, strongly coupled, and time-varying control system. It is difficult to obtain the ideal control effect with the traditional control method. In the trajectory tracking control of 3-DOF PM, the PID control was combined to improve the control accuracy. Without relying on the exact mathematical model of the controlled object, the fuzzy control method was used to approximate the nonlinear system. Through the combination of the fuzzy controller and PID controller, a fuzzy PID controller was designed, which could self-tune PID parameters online in the control process. In view of the problem that the design of the fuzzy control system needs expert knowledge and experience to obtain the best control effect, the fuzzy PID controller was optimized by a genetic algorithm. 2. The traditional PID control, fuzzy control, fuzzy PID control, and fuzzy PID control optimized by the GA were carried out to simulate signal-tracking and to verify the effectiveness of the optimized controller. The simulation showed that the servo system under the fuzzy PID control based on the GA had significantly improved dynamic response characteristics and steady-state accuracy, with a better trajectory-tracking effect. The ideal control performance of the PM in trajectory tracking control depended on the design of the control system. Through the reasonable selection and design of the control strategy, the control deviation of the joint angle and angular velocity of the PM could be reduced. Thus, the response speed and stability of the system were improved, which is of great significance to the application of PM. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Controller Type** & **Joint Q1** & **Joint Q2** & **Joint Q3** \\ \hline PID & 0.0655 & 0.057 & 0.057 \\ FUZZY & 0.1568 & 0.1667 & 0.1667 \\ FPID & 0.0388 & 0.0319 & 0.0319 \\ GAFPID & 0.0265 & 0.0197 & 0.0197 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ITAE values. Figure 14: Joint trajectory Q3: (**a**) tracking response; (**b**) local enlarged view. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Controller Type** & **Joint Q1** & **Joint Q2** & **Joint Q3** \\ \hline PID & 0.0436 & 0.042 & 0.042 \\ FUZZY & 0.1094 & 0.1196 & 0.1196 \\ FPID & 0.0237 & 0.0235 & 0.0235 \\ GAFPID & 0.0147 & 0.0144 & 0.0144 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: IAE values. 3. The optimization of other intelligent algorithms and the combination of each other's advantages will be further considered in the future to greatly adapt to more complex regulatory processes. The neural network fuzzy control was considered. Neural networks can adequately approximate arbitrary complex nonlinear relationships. It can learn and adapt to the dynamic characteristics of uncertain systems. The adaptive fuzzy control system was introduced, which can identify system parameters and adjust control parameters online. The expert intelligent self-tuning PID controller was used to recognize the system error pattern when the closed-loop system was disturbed. The key problems to be solved in the above control strategy were online parameter identification, parameter adaptive adjustment, the establishment of an expert system, and the combination of a neural network and fuzzy control. The above needs to be studied in further research work. Conceptualization, Z.Z. and Y.L. ; methodology, Y.H. ; software, W.W. and Y.L. ; validation, Y.L., H.W., Z.Z. and C.H. ; formal analysis, Y.L. ; investigation, Z.Z. ; resources, H.W. ; data curation, Z.Z., Y.L. and B.Y. ; writing--original draft preparation, Y.L. and Y.H. ; writing--review and editing, Z.Z. and Y.L. ; visualization, B.Y. ; supervision, H.W. and C.H. ; project administration, B.Y. ; funding acquisition, Z.Z. and B.Y. All authors have read and agreed to the published version of the manuscript.