Parameter optimization of electro-hydraulic proportional system of PID based on the improved ant colony algorithm

Xiu-fen XU

Electrical and Mechanical Engineering College, Xinxiang Institute, Xinxiang 453000, China

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Parameter optimization of electro-hydraulic proportional system of PID based on the improved ant colony algorithm

Xiu-fen XU?

Electrical and Mechanical Engineering College, Xinxiang Institute, Xinxiang 453000, China

Abstract:VACA is a hybrid algorithm combined with the variable metric algorithm and ant colony optimization algorithm. For the electro-hydraulic proportional control system for PID parameter tuning problem, this paper puts forward the optimization of PID parameters based on VACA, and gives the specific implementation steps: establish mathematical model for electro-hydraulic control system, establish the simulation model of electro-hydraulic proportional control system of VACA-PID by using SIMULINK toolbox, simulation and verification. The results show that: the VACA-PID controller has good static and dynamic performance, can fully meet the electro-hydraulic proportional control system.

Key words:Improved ant colony algorithm, Electro-hydraulic proportional control, PID, Optimization

1.Introduction

Concrete pump truck[1] is a kind of construction machinery with concrete pumps placed in the special purpose vehicle turf, to be able to walk independently and realize transmission and pouring concrete through special boom of high technical content. Pump truck boom is the core part of the electro-hydraulic control system and its dynamic and steady-state performance has far-reaching influences on the vehicle performance. Although traditional Z-N[2-4] setting algorithm can basically meet the requirements, it has some limitations because of the poor stability and low accuracy of setting. So we must adopt measures to improve the control effect. Based on VACA[5] to PID control parameter optimization, the passage forms the intelligent electro hydraulic proportional control system.

Single section control system electro-hydraulic proportion control system is a position closed loop control system, its principle diagram is shown in Figure 1, including the electro-hydraulic proportional valve, valve controlled single rod hydraulic cylinder, conversion link (to convert cylinder expansion amount to boom Angle), obliquity sensor, etc.

Figure 1.The principle diagram of the electro-hydraulic proportional control system

2.The transfer function of the system

Static and dynamic performance of the electro-hydraulic proportional position control system mainly depends on the electro-hydraulic proportional valve and valve control hydraulic cylinder components such as features. Mathematical model of transmission system function is established.

2.1.Transfer function of electro-hydraulic proportional direction valve

According to the actual situation, the transfer function of electro-hydraulic proportional valve can be simplified as the second order oscillation link, its transfer function is:

(1)

In the formula：

X: valve core displacement (m);

Kq: the valve’s flow gain (m3·s-1·A-1);

ωn:the valve’s inherent frequency (rad/s);

ζn:valve damping ratio, usually is 0.5～0.7.

2.2.Transfer function of valve controlled single rod hydraulic cylinder

1) The force balance equation of the hydraulic cylinder and the load

(2)

Y: the hydraulic cylinder piston displacement (m);

Mt: piston and load equivalent to the total mass on the piston(kg);

Bp: the piston and the viscous damping coefficient of load (N·s/m);

FL: effect on the piston as accidental load (N);

2) The flow continuity equation of the hydraulic cylinder:

(3)

In the formula:

βl: effective bulk modulus (Pa);

V0: cavity volume of any hydraulic cylinder (m3);

3) Slide valve flow equation

QL=Q1=KqX-KcPL

(4)

Intheformula:

Kq: valve frontal flow gain (m3·s-1·A-1);

Kc: valve of flow pressure coefficient (m3·s-1·pa-1)

For formula (2), (3), (4), make a Laplace transform, three basic equations can be obtained:

A1PL=mtS2Y+BPSY+FL

(5)

(6)

QL=KqX-KCPL

(7)

Based on the three basic equations, we can get the transfer function expression of valve control hydraulic cylinder

(8)

In the formula:

ωh: valve control hydraulic cylinder natural frequency (rad/s);

ζh: valve control hydraulic cylinder damping ratio;

βe: effective bulk modulus (Pa);

FL: effect on the piston arbitrary load (N);

A1: rodless hydraulic cylinder cavity cross-section area (m2);

A0: hydraulic cylinder rod cavity area (m2);

V0: cavity volume of any hydraulic cylinder (m3).

Take the individual parameters of valve control hydraulic cylinder into the equation above and available valve control cylinder transfer function can be got:

(9)

According to the type of the hydraulic cylinder piston displacement relative proportional valve core displacement and relative to the external load transfer function, it is shown as follows:

(10)

(11)

3.The establishment of the PID algorithm based on VACA

3.1.The PID control parameters setting

PID[6-7] controller is a linear controller, according to the given valuer(t) and the actual output valuey(t) to control deviatione(t), namely:

e(t)=r(t)-y(t)

(12)

Thedeviationoftheratio(P-proportion),integral(I-integral),differential(D-differential),bythelinearcombinationofthecontrolvolume,controlledobject,sothatthePIDcontroller,itscontrollaw(representedbyatransferfunction)for:

(13)

Combining the improved ant colony algorithm and PID together, we can optimize the three parameters of PID controller online. Based on ant colony algorithm of PID control system, structure is shown in Figure 2.

Figure 2.The control program principle diagram of the improved ant colony algorithm

3.2.VACA - PID control servo system model

Under the MATLAB7.0[8] interface, use Simulink to establish the corresponding VACA-PID control system and the module type，as shown in Figure 3.

VACA algorithm process is shown in Figure 4.

(a) Electro-hydraulic proportional system simulation model

(b) the VAC-PID control modules

3.3.The realization of the algorithm

9.10≤KP≤10.0; 100.0≤Ti≤120;

0≤Td≤0.50

Figure 4.VACA flow chart of the algorithm

3.4.The simulation analysis and verification

Improved ant colony algorithm for PID parameters optimization performance indicators are shown in Table 1.

Table 1.PID parameters settings between Z-N optimal and VACA contrast

We can see from the Figure 5, VACA-PID setting of electro-hydraulic proportional system steady state was achieved at 5.6 s and no overshoot. Because of the boom, a process can take a few minutes, and the control accuracy and response time of this system are fully able to meet the requirements.

Figure 5.Two different optimization strategy step response curves

4.Conclusion

The simulation results show that PID parameters optimization method based on improved ant colony algorithm(VACA) can short the setting time and decrease overshoot. VACA control strategy has simple structure, good stability and easy to project implem-entation. It realizes the characteristics of electro-Hydraulic proportional System steady-state performance and dynamic performance optimization.

References

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[3]Yang Jing, Tong Zhixue, Liu Tao. Hydraulic machinery flashlight hydraulic proportion system fuzzy PID control study[J]. machinery science and technology, 2013, 32(6): 834-838.

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基于改進蟻群算法的電液比例系統(tǒng)PID參數(shù)優(yōu)化

徐秀芬?

(新鄉(xiāng)學院 機電工程學院，河南 新鄉(xiāng)453000)

摘要：VACA是變尺度算法融入蟻群優(yōu)化算法中而形成的一種混合算法。針對電液比例系統(tǒng)PID 控制參數(shù)整定問題，提出了基于改進蟻群算法的 PID 參數(shù)優(yōu)化方案，并給出了具體的實現(xiàn)步驟：建立臂架電液控制系統(tǒng)的數(shù)學模型，利用Simulink工具箱建立了電液比例控制系統(tǒng)的 VACA-PID的仿真模型，進行了仿真和驗證。結果表明： VACA-PID 控制器具有良好的靜、動態(tài)性能，完全能達到電液比例控制系統(tǒng)的要求。

關鍵詞：改進蟻群算法；電液比例控制；PID；優(yōu)化

中圖分類號：TM921.51

DOI:10.3969/j.issn.1001-3881.2014.06.025

Received: 2013-09-28

? Xiu-fen XU, E-mail: xxf_xf@163.com