Design and Simulation of Fuzzy-PID Controller Based on Mixed Injection Molding Machine

Jianming DU

College of Mechatronics and Control Engineering Shenzhen University

Shenzhen Guangdong China djm33@szu.edu.cn

Yixing LUO College of Mechatronics and Control Engineering

Shenzhen University Shenzhen Guangdong China batistar007@yahoo.com.cn

Abstract— The mixed injection molding machine driven by PMSM control system was established and a Fuzzy-PID controller based on the Fuzzy-PID control method was designed according to the characteristic of melting and plasticizing action. In the Simulink environment the Fuzzy-PID control system was simulated. The results of simulation indicated that the Fuzzy-PID system has the better performance in comparison with traditional PID control system.

Keywords- Fuzzy-PID controller; fixed injection molding machine; PMSM; Simulink

I. INTRODUCTION As the main molding equipment, injection molding

machine makes different shapes of plastic products which made of thermoplastic or thermosetting materials. The melting plastic process is one of the most important actions in the injection molding cycle. It impacts the final quality of the product. Nowadays, the hydraulic driving system was applied to most of injection molding machines, such as hydraulic motor that drives the plasticizing screw to melt. However, there are some disadvantages such as high energy consumption, slow-response, low-precision, oil leakage, noisy and so on in hydraulic driving system and every action of injection molding cycle can only be carried out orderly [1]. Aiming at these problems, a new solution of mixed injection molding machine driving system was proposed. The main pump and plasticizing screw are driven by PMSM respectively. The mixed driven system can not only enhance the plasticizing quality but also shorten the injection molding cycle of some product effectively by making the optimization design and synchronizing some technological actions. Moreover, especial power transmission technology by transmitting the breaking energy of two PMSMs can achieve the goal of further energy saving [2].

The plasticizing screw rotating and shearing with plastic generates energy which is the main source for melting plastic. The rotation speed of plasticizing screw can determine the quality of melting plastic action. Therefore, the plasticizing screw should be controlled accurately and steadily rotating at the setting velocity. The traditional PID control method has been widely used, but the accurate model of the controlled object should be known firstly. The PID controller controls the system according to the setting parameters of

Proportional, Integral and Differential, but the melting plastic mechanism is so complicated and changeful that model of system can not be described easily. Therefore the Fuzzy-PID control method is selected to control plasticizing screw rotating. The Fuzzy-PID controller not only has the advantages of traditional PID control method but also has small overshoot and fast response, and moreover it is not necessary to know the accurately model of the controlled object [3]. The model of the melting plastic mechanism based on the PT160 injection molding machine from L.K Group was established under the Simulink environment of Matlab. The dynamic simulations of melting plastic mechanism were performed using the PID and Fuzzy-PID control method, and the results of simulation were analyzed.

II. MELTING PLASTIC SYSTEM MODELING AND FUZZY-PID CONTROLLER

Melting plastic action has the characteristics of low-speed and high-torque. The model of melting plastic of PT160 injection molding machine produced by L-K Group was established. Hydraulic motor was substituted by PMSM and motor shaft connects directly with screw by the way of using splined shaft. The melting plastic mechanism is shown in Fig.1:

Fig.1 Schematic diagram of melting plastic mechanism

Melting plastic mechanism is the closed-loop system

including the current loop and speed loop. The speed feedback signal comes from the encoder of PMSM encoder and the current feedback signal comes from the driver. System control structure is shown in Fig.2:

Project of Science and Technology Plan of Shenzhen (No.08CXY-47)

978-1-4244-5874-5/10/$26.00 ©2010 IEEE

Fig.2 Block diagram of melting plastic control system

The mathematical model of PMSM is so complex that the model was established under the rotor based synchronously rotating reference frame (d-q-0 coordinate system). The coordinate transformation from d-q-0 to a-b-c can make the diagonalization of impedance and eliminate the rotary coupling between stator and rotor, and thus achieve the purpose of simplification of the model [4]. The mathematical model of PMSM under the d-q-0 coordinate system is given as follow:

dd S d d n m q q

diu R i L P L i

dt= + − ω (1)

qq S q q n m d d n m f

diu R i L P L i P

dt= + − ω + ω ψ (2)

em n d q q dT P ( i i )= ω − ω (3)

em n f q d q d qT P [ i (L L )i i ]= ψ − − (4)

me m l

dT J R Tdt ωω= + ω + (5)

Where the symbol Ud is d-axis voltage, Uq is q-axis voltage, id is d-axis current, iq is q-axis current, Ld is d-axis inductance, Lq is q-axis inductance, Pn is pairs of poles, Ψf is flux induced by magnets, J is rotor moment of inertia, Te is electromagnetic torque, and Rω is coefficient of friction. The product of ωm and current of d-axis and q-axis implies that there are interference and coupling between these parameters. Therefore, making sure id=0 is the way to eliminate the interferes between id and iq and achieve steady state decoupling control [4]. In addition, the d-axis and q-axis have the same inductance Ld=Lq due to that the permeability of permanent magnet rotor is close to air.

The general expression of traditional PID controller can be stated as:

t

p i d0

de(t)u(t) K e(t) K e( )d Kdt

= + τ τ +∫ (6)

The structure of PID controller is shown in Fig.3, where the error value e is the deviation of input and feedback values. The controller regulates the output according to the PID parameters.

Fig.3 Block diagram of PID controller

Fuzzy-PID controller is the two-dimensional structure.

The controller has two inputs. One is denoted by e, i.e. the deviation of input and feedback values. Another is the change rate of deviation denoted by ec. The output is the increment of the controlled value. Firstly, the fuzzy processing of input is carried on according to the fuzzy membership table. Secondly, the controller adjusts the PID parameters on-line according to the fuzzy control rule table and quantifies the

output. Finally, the dynamic control is achieved [5]. The structure of Fuzzy-PID controller is shown in Fig.4:

Fig.4 Block diagram of Fuzzy-PID controller

According to block diagram of Fuzzy-PID controller, the

fuzzy domain of input is [-300,300], and the fuzzy domain of output is [-10, 10]. In the output Kp fuzzy control rule table, the velocity deviation was divided into 8 membership degrees and the deviation variation rate was divided into 7 membership degrees. The division of input and output’s membership degrees is shown in Table 1, Table 2 and Table 3:

TABLE 1. OUTPUT Kp FUZZY CONTROL RULE TABLE △Kp e

NB NM NS NZ PZ PS PM PB

ec

NB PB PM PM PS NB NM Z Z NM PB PM PS PS NM NS Z PS NS PB PS PS Z Z Z PS PB Z PB PS Z Z Z Z PM PB

PS PM PS Z Z Z PS PM PB PM PS Z NS NM PS PS PB PB PB Z Z NM NM PB PB PB PB

TABLE 2. OUTPUT Ki FUZZY CONTROL RULE TABLE △Ki e

PB PM PS Z NS NM NB

ec

NB Z Z NM NM PB PB PB NM PS Z NS NS PM PB PB NS PM PS Z Z PS PM PB Z PB PM PS Z PS PM PB

PS PB PM PS Z Z PS PM PM PB PB PM NS NS Z PS PB PB PB PB NM NM Z Z

TABLE 3. OUTPUT Kd FUZZY CONTROL RULE TABLE △Kd e

NB NM NS Z PS PM PB

ec

NB PB PM PB PB PB Z NB NM PM PS PM PM PM NS NB NS PS Z PS PS PS NM NM PS NM NB PS PS PS Z PS PM NB NS PM PM PM PS PM PB NB Z PB PB PB PM PB

III. SIMULATION MODEL AND RESULTS The dynamic simulation model of melting plastic

mechanism based on Fuzzy-PID control system was established under the Simulink environment of Matlab. The close-loop control system consists of the internal current loop and external speed loop. The difference value of setting speed and feedback speed is processed by Fuzzy-PID controller, and the control current based on the d-q-0 coordinate system is output. Then the coordinate converter module outputs the

three-phase control current based on a-b-c coordinate system. Finally, PWM inverter module outputs the three-phase control voltage to PMSM and melting plastic mechanism is driven by PMSM.

Parameter settings for simulation are as follows: the setting speed 300rmp, the initial values of Kp, Ki and Kd are 1.2, 9.1 and 0.01, the practical quantization factors are 0.5, 0.5, and 0.001. PMSM parameter settings are as follows: phase resistance 0.0918ohm, d-q inductance 0.000975H, flux induced by magnets 0.1688wb, rotor moment of inertia 0.003945kgm2, friction factor 0.0004924, pairs of poles 4, the variable step-size ode23s (stiff/Mod.Rosenbrock) algorithm, simulation time 0.06s. The simulation results are shown in Fig.5 and Fig.6.

In Fig.5 and Fig.6 the solid line represents the speed curve controlled by Fuzzy-PID control method and the dashed line represents the speed curve controlled by traditional PID control method. Simulation results show that the Fuzzy-PID controller has faster response ability, lower overshoot and steady state error in comparison with traditional PID control method.

Fig.5 The simulate output of speed curve

Fig.6 The partial enlarged view of speed curve

IV. CONCLUSION The new plan of mixed injection molding machine has

been proposed in order to implement precision injection, the better control ability saving energy. The main pump motor and hydraulic motor was replaced by two PMSM. The model of melting plastic system is complex and changeful. Therefore

the Fuzzy-PID controller based on parameter self-tuning was designed to control the melting plastic mechanism. The controller can adjust the PID parameters real-timely according to parameter estimation and accomplish the accurate control to complex system. The results of dynamic simulation by Simulink indicate that the Fuzzy-PID control method can improve the working performance of melting plastic mechanism in comparison with traditional PID control method.

REFERENCES

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