# Fuzzy PID Control of the Three-Degree-of-Freedom Parallel Mechanism Based on Genetic Algorithm
## 1 Introduction  
In the packaging industry of industrial production, it is usually necessary to complete the classification, inspection, packaging, and other operations of light and small objects at a faster speed to improve work efficiency. It is difficult to complete the precise operation with high strength and high speed for a long time using the traditional manual operation method. Compared with the series mechanism [1, 2], the parallel mechanism (PM) has high stiffness, small dead weight load ratios, a strong bearing capacity, high precision, and a compact structure. The PM is suitable for applications with a small working space and large load strength, and it is widely used in machine tool processing, aircraft manufacturing, and medical treatment. Artificial intelligence is used to store mathematical models and operation experience in the computer with the development of computer technologies. The established control system model aims to control the whole mechanical system easily. Proportional-integral-derivative (PID) controllers are still widely used in the industrial process control. Engineers can tune these three gains through experience or simple principles such as classical tuning rules proposed by [PERSON] [3]. There are many factors in the control system of PMs, such as uncertainty, nonlinearity, and external disturbance. The conventional PID controller has some problems, such as poor parameter settings and poor adaptability to variable working conditions. The combination of fuzzy control and PID control theory can solve these problems. [PERSON] [4] proposed a novel fuzzy logic controller (FLC) for the gap between the time response and the rule base. It performs well in both transient and steady states withoutusing multiple decision tables. [PERSON] [5] presented a new fuzzy PID control method for nonlinear systems that are structurally difficult to model. [PERSON] [6] used two kinds of fuzzy inference engines to construct an adaptive fuzzy PID controller, which achieves a fast convergence time and high performance. [PERSON] [7] proposed an orthogonal fuzzy PID control method to control the manipulator, which improves system accuracy and reduces the oscillation process near the steady state. [PERSON] [8; 9] studied some qualitative properties of fuzzy PID control systems in fuzzy number space. HuKuhara differentiability and fuzzy second-order differential equations are used to solve the multi-boundary problem, which proves the existence and uniqueness of the solution of the differential equation. [PERSON] [10] proposed a cascading predictive fuzzy PID (FPID) controller with weight and used the fastest descent method to calculate weight and improve the accuracy of trajectory tracking. The quantization factor and scale factor affect the control effect of the fuzzy controller. Traditional selection methods are mostly based on expert experience and industrial knowledge, which will make the control effect unsatisfactory. Therefore, the optimization algorithm is introduced to optimize PID control parameters quickly and accurately using its global optimization ability. [PERSON] [11] proposed a novel adaptive PID control method--using predictive control and outputting recursive fuzzy wavelet neural networks to process a set of nonlinear digital delayed dynamic systems. [PERSON] [12; 13; 14] previously studied the use of the GA and neuro-fuzzy techniques to design optimal control systems. The results can be used as benchmarks to compare with the proposed design. [PERSON] [15] compared various controllers. The PID controller optimized by the GA has a shorter rise time, and smaller steady-state error, but higher theoretical complexity. The proposed fuzzy PID controller was applied to the servo control system [16], showing that the fuzzy PID controller optimized by a GA has good speed control and anti-jamming ability. [PERSON] [17; 18] proposed that the membership function should be adjusted by nonlinear factors, which greatly improves the GA and verifies its feasibility.