Design of electro-hydraulic proportional system for loader working device based on fuzzy adaptive PID

Xiu-fen XU

(Electrical and Mechanical Engineering College of Xinxiang University, Xinxiang 453000, China)

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Design of electro-hydraulic proportional system for loader working device based on fuzzy adaptive PID

Xiu-fen XU*

(Electrical and Mechanical Engineering College of Xinxiang University, Xinxiang 453000, China)

Taking ZL40G as the object of the loader, this paper builds the math models on the basis of the structure of the Electric proportional, and designs the position controller by the fuzzy self-tuning PID parameter method. By using Matlab/Simulink module, the simulation study was conducted and the results showed that the load disturbance could be eliminated by using this approach and the steady state characteristics could be improved to a better self-adaptive capacity.

Loader, Working device, Fuzzy control, PID, Position control, Simulation

1 Introduction

At present, the domestic loader [1] has basically realized the electro-hydraulic proportional pilot control of working device. In order to improve the operation stability of loader, it is necessary to improve the response speed and control precision of the electro-hydraulic proportional system for the final actuator. The electro-hydraulic proportional system is a typical nonlinear and time-varying system, the general control methods can not meet the performance requirements. Therefore, the fuzzy PID control method and the PID parameters on-line by fuzzy controller are adopted in the real applications. In order to verify the control effect of fuzzy PID control of electro hydraulic proportional position system, mathematical model of the system was established, and the dynamic performance was simulated by using Matlab/Simulink [2-3].

2 The principle of control system

The loader working device is a mechanism with two degrees of freedom, which is an important part of loader. Control system of working device is composed of a working mechanism, operation system, hydraulic system and control system. The position and angle of the bucket will be determined by the boom cylinder and the rotating bucket cylinder, the main control arm of oil cylinder lifting positions of the moving arm, rotating bucket cylinder mainly control the bucket through the comparison with the boom angle. Actual operation as long as the detection of moving arm lift angle and the angle of the bucket and boom, it can judge the position and angle of the bucket. Therefore, the control system should have the requirements of reliable work, flexible operation, high work efficiency, and smooth running characteristics.

The basic components of digital electro hydraulic proportional control system have a digital controller, digital amplifier, servo valve, proportional valve, hydraulic actuator, and detection feedback components. The working principle of the electro-hydraulic proportional control is as follows: the detection element will feedback the controlled amount of the actual value, and give a comparison control signal, through the deviation signal to adjust the deviation signal by the power amplifier to control the proportional electromagnet, opening amount and the direction of the control valve[4]. Schematic representation is shown in Fig.1.

Fig.1 Electro-hydraulic proportional control system block diagram

3 The mathematical model of the hydraulic system of working device

3.1 Mathematical models of high-speed on-off valve

Ignoring the quality of the main spool valve, the transfer function in a period of high speed on-off valve could be obtained as follows:

(1)

In the above formula：Ahis valve spool end area，m2；Bis fluid viscous damping coefficient，N·s/m；Kqis zero flow gain high speed on-off valve；khis the elastic coefficient of spring in the valve spool，N/m；xhis the reversing valve spool displacement, m.

3.2 The mathematical model of digital multi way direction valve

The flow continuous equation of main valve port is as follows：

(2)

In the above formula：Kq1is reversing valve zero flow gain，m2/s；Kc1is valve flow pressure coefficient, m5/N·s.

Ignoring the friction loss, pipeline fluid quality influence and pipeline dynamic, the continuity equation of hydraulic cylinder could be written as follows:

(3)

In the above formula：Apis the average area of piston cylinder，m2；yis piston displacement，m；Cis cylinder leakage coefficient，m5/(N·s)；Veis cylinder equivalent volume，m3；βis the effective elastic coefficient of the liquid in the solvent system，Pa.

Based on the formula (2) and (3), make a Laplace transform, the basic equations can be obtained:

(4)

Put the formula (1) into (4), one could obtain the transfer function of the high-speed switch valve and multi valve as follows:

(5)

3.3 The force balance equation for hydraulic cylinder and load

Ignoring the Coulomb friction load and oil quality, according to Newton’s second law, the Laplace transform could be obtained:

(6)

Put the formula (5) into (6), the system transfer function could be obtained:

(7)

4 Design of fuzzy adaptive PID contro-llerl

4.1 Structure of fuzzy adaptive PID controller[5]

The PID parameter fuzzy adaptive system is mainly composed of adjustable parameter PID and fuzzy control system, the structure is shown in Fig.2. On the basis of the conventional PID controller, taking errorEand error rate of change EC as input, use the fuzzy inference method to tune the PID parameters ofKp,KiandKdto meet the different requirements of theEandECparameters of the controller, and the object will obtain a good dynamic and static performance [6].

Fig.2 Parameter adaptive fuzzy PID control system structure diagram

4.2 Determination of membership function and control rules[7-8]

Fuzzy subset ofE,ECandVare divided into 7 levels, respectively, they are: {NB, NM, NS, ZO, PS, PM, PB}[9], a subset of elements corresponding to the large, negative, negative in the negative, zero, small is small, Manaka, zhengda.E,ECandVdomain {-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6},E,ECandVare in the state of NB and PB by fuzzy triangular membership functions (trimf), the rest of the fuzzy state chooses Gauss membership function (gaussmf). Ultimately, theEandECmembership functions [10] are shown in Fig.3, the membership function ofKp,KiandKdare shown in Fig.4 as well.

(8)

The control rule [11-12] can use If (condition), Then (results) statement, such as If (Eis NB) and (ECis NB) Then (Kpis PB) (Kiis NB) (Kdis PS). In the rule table, each statement decides a fuzzy relation. According to the relationship of fuzzy reasoning, for the parameters ofKp, formula (8) can be obtained

According to the different moments of E and EC input, we can calculate theKp[13-14], the calculation formula is as follows:

(9)

In the formula (9)：

eTisefor vector transpose [15].

Kp,KiandKdare the control parameters of the control rules and they are shown in Table 1.

Fig.3EandECmembership function diagram

Fig.4Kp,Ki,Kdmembership function diagram

Table 1 TheKp,Ki,Kdfuzzy control rule table

e/ecNBNMNSZOPSPMPBNBPB/NB/PSPB/NB/NSPM/NM/NBPM/NM/NBPS/NS/NBZO/ZO/NMZO/ZO/PSNMPB/NB/PSPB/NB/NSPM/NM/NBPS/NS/NMPS/NS/NBZO/ZO/NSNS/ZO/ZONSPM/NB/ZOPM/NM/NSPM/NS/NMPS/NS/N,MZO/ZO/NSNS/PS/NSNS/PS/ZOZOPM/NM/ZOPM/NM/NSPS/NS/NSZO/ZO/NSNS/PS/NSNM/PM/NSNM/PM/ZOPSPS/NM/ZOPS/NS/ZOZO/ZO/ZONS/PS/ZONS/PS/ZONM/PM/ZONM/PB/ZOPMPS/ZO/PBZO/ZO/NSNS/PS/PSNM/PS/PSNM/PM/PSNM/PB/PSNB/PB/PBPBZO/ZO/PBZO/ZO/PMNM/PS/PMNM/PM/PMNM/PM/PSNB/PB/PSNB/PB/PB

Similarly, the values ofKiandKdcould be evaluated.

According to the fuzzy subset membership function of each fuzzy variable and each parameter control model, the application of fuzzy synthesis theory of fuzzy matrix design parameters of PID could use the following formula:

(10)

5 Simulink simulation and analysis of fuzzy adaptive PID control [8]

5.1 Fuzzy adaptive PID control system simulation model

Based on the fuzzy adaptive PID control algorithm, the system could obtain the open-loop transfer simulation model, as shown in Fig.5. According to the actual condition of work device, the range ofEfor [-100 mm, 100 mm] and the range ofECfor [-0.5 mm, 0.5 mm] could be obtained.Kp,KiandKdare in the following range of [0.1, 16], [0.1, 6] and [0.3, 3.5], respectively. The simulation model of PID control algorithm (as shown in Fig.6) could be used for comparison. In accordance with the tuning method of PID parameters, the PID control parameters could be ultimately determined as follows:kp=10,ki= 0.03 andkd=0.25.

Fig.5 Fuzzy PID control simulation system structure diagram

Fig.6 The conventional PID control simulation system structure diagram

5.2 Simulation results and analysis

Input a step signal and run the simulation model, the simulation results could be obtained, as shown in Fig.7 and Fig.8.

Based on the simulation results, one could conclude that: the fuzzy adaptive PID control step under the above mentioned condition has no overshoot, and the adjusting time is much shorter than that of the conventional digital PID controller, and it could improve the system steady-state characteristics; According to the displacement error and the change of error, the actual operating conditions could automatically carry out the adjustment of PID Parameters. Therefore, the controller of Fuzzy Adaptive PID has a good adaptive capability.

Fig.7 The conventional PID control the system step

response

Fig.8 Fuzzy PID control system curve step response

curve

In order to further test the fuzzy and PID dynamic performance and steady-state performance, the sinusoidal signal could be tracked and the simulation results are shown in Fig.9 and Fig.10.

Fig.9 The conventional PID control system sine response curve

Fig.10 The fuzzy PID control system for sineresponse curve

Compare the results of Fig.9 and Fig.10, one could observe that: the output system of conventional PID control has obvious lag characteristics, and the output fuzzy PID control system can follow the input. Therefore, the fuzzy PID control has better advantages than the conventional PID control in terms of fast response or steady state accuracy.

6 Conclusions

The electro-hydraulic proportional system of working device of loader has some characteristics such as nonlinear, time-varying and load disturbance, and the general PID control algorithm is difficult to meet all the performance requirements. Therefore, the introduction of the fuzzy set theory, which is established on the fuzzy PID controller, the PID parameters according to the error and error change rate of the size and the dynamic changes of debugging, could avoid the complicated parameter adjustment ability, and the system is adaptive. Therefore, it could be well adapted to the different environment, and the reliability could be enhanced as well.

Acknowledgement

This work is supported by Natural Science Foundation of Education Department in Henan Province (No. 2012B46002).

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裝載機工作裝置模糊自適應PID電液比例系統設計

徐秀芬*

新鄉學院 機電工程學院，河南 新鄉453000

以 ZL40G 裝載機為研究對象，根據裝載機工作裝置電液比例控制系統的結構建立其數學模型；采用模糊自整定 PID 參數法設計了位置控制器，運用 Matlab/SIMULINK 模塊進行了仿真研究；通過與普通 PID 算法的仿真結果進行比較，結果表明：采用模糊自整定 PID 參數法能消除系統負載干擾，可顯著提高穩態特性，具有較好的自適應能力。

裝載機；工作裝置；模糊控制；PID；位置控制；仿真

5 October 2014; revised 16 December 2014;

Xiu-fen XU, Lecturer.

E-mail: xxf_xf@163.com

10.3969/j.issn.1001-3881.2015.18.019 Document code: A

TH243

accepted 2 March 2015

Hydromechatronics Engineering

http://jdy.qks.cqut.edu.cn

E-mail: jdygcyw@126.com