Analyze the characteristics of electro-hydraulic servo system’s position-pressure master-slave control

Abstract

For electro-hydraulic system of large flow and overloading, established position and pressure closed-loop control in accordance with the conventional hydraulic servo system theory that system control algorithm is complicated and difficult to implement. This article presents a method which gives priority to position closed-loop control and establishes the corresponding relation between pressure of hydraulic cylinder and load by collecting the pressure signal from rear cavity and rod cavity of hydraulic cylinder; meanwhile, applied position-pressure conversion formula will turn dynamic pressure signal into position signal and compensate the transformed position signal to the master position closed loop of the electro-hydraulic servo system which could achieve the position-pressure master-slave control. The simulation results show that the control method is correct, effective, and feasible. The results indicate that the method can achieve online converting between position and pressure which are different variables and improve the response speed and control precision of the system.

Keywords

Hydraulic transmission and control system electro-hydraulic servo system position-pressure master-slave control conversion equation hydraulic

Introduction

Large-flow, heavy-load, and pressure-position electro-hydraulic servo system with the advantages of fast-response high control precision and high output power is widely used in heavy-duty equipment. It is considered to be the most promising choice for modern industry and has become an indispensable control method in the metallurgical industry, mechanical manufacturing, construction machinery, and defense industries’ sophisticated equipment.

In order to improve the control precision of conventional electro-hydraulic servo systems for large-flow, heavy-duty, high-precision, and multi-degree-of-freedom (DOF) in conventional metallurgical equipment. L Quan et al.,¹ based on the position and pressure control, conclude that only the closed-loop position and the pressure closed-loop structure are used, and the pressure and position controllers will not affect each other. Asymmetrical valves control asymmetric cylinders is a trend, especially in large systems with large load changes and high system accuracy requirements, and the establishment of asymmetric servo valve control servo cylinder models^2,3 and asymmetric valve control asymmetric cylinder can improve the control accuracy, reduce the requirements of the servo valve and the oil on the equipment, and reduce the use cost.^4,5 At the same time, the influence of different algorithms of proportional–integral–derivative (PID) adaptive fuzzy control on the control precision and the research of the function of adaptive fuzzy control on the system defect have been greatly developed.^6–8 Zulfatman⁹ applied PID controllers to the identification of industrial hydraulic drive systems to improve the control accuracy of electro-hydraulic servo systems. JB Lei et al.¹⁰ studied the proposed sliding-mode controller over a PID controller when the load varies within a certain range. HY Han et al.^11,12 proposed a new type of composite link rolling shear and established the motion and balance equations to calculate the data of the shearing mechanism’s motion curve and cylinder position and pressure. YH Bai and L Quan.¹³ adopted a dual-flow valve control scheme and specifically used a fast-response servo valve for flow compensation. The maximum dynamic error using this solution can be reduced by 75%. G Shen et al.^14,15 proposed a new controller and hybrid controller combining offline designed feedback controller (ODFC) and online adaptive compensator, which effectively improved the control accuracy of the electro-hydraulic proportional system. With the continuous development of technology and the continuous improvement of the control precision requirements, in the large-flow, heavy-load, high-precision, and multi-DOF electro-hydraulic servo system should not only ensure the position control accuracy but also solve the problem which high strength load to the system’s shock and the position deviation of the hydraulic cylinder, while considering pressure deviation impact on the equipment. This requires high-precision control of position meanwhile achieves precise control of pressure. The control mechanism has obvious difference between position closed-loop and pressure closed-loop, the control variable need to be converted and unified in order to achieve the simultaneous reasonable online control between position and pressure in one process.

In order to meet the above requirements, this article proposed a position-pressure master-slave control method of electro-hydraulic servo system as shown in Figure 1. The specific approach is that in the low pressure and a certain range, the system is only controlled by position closed loop, which is due to electro-hydraulic servo valve opening range and closed-loop gain value of the entire electro-hydraulic control system are large, and the response of the whole system is relatively stable in a situation of position closed-loop control. When the pressure reaches a certain high-pressure range, the corresponding relation between pressure of hydraulic cylinder and load by collecting the pressure signal of rear cavity and rod cavity of hydraulic cylinder could be established, meanwhile applying position-pressure conversion formula will turn dynamic pressure signal into a position signal, then, compensating the transformed position signal to the master position closed loop of the electro-hydraulic servo system to achieve the position-pressure master-slave control. This method not only simplifies the control process but also guarantees the control precision and stability of the position and pressure at the same time to make the two control variables of position and pressure reasonably in the same control process to achieve the dynamic compensation and coordination control.

Figure 1.

Master-slave control theory diagram.

Mathematical model of electro-hydraulic servo system

The simplified model of the common electro-hydraulic servo system is shown in Figure 2, which includes proportional servo valve and asymmetric hydraulic cylinder. The servo valve flow equation, hydraulic cylinder flow continuity equation, and the force-balance equation of the hydraulic cylinder with load need to be deduced in order to deduce the mathematical model of electro-hydraulic servo system.

Figure 2.

The servo valve control servo cylinder schematic.

Building the mathematical model of position master control of valve control cylinder

The flow equation of servo valve

When the servo valve control servo cylinder is stable, it satisfies the stable equilibrium equation

p_{1} A_{1} - p_{2} A_{2} = F_{L}

(1)

where $p_{1}$ is the pressure of rear cavity of cylinder (Pa); $p_{2}$ is the pressure of rod cavity of cylinder (Pa); $A_{1}$ is the effective action area of the rear cavity of the cylinder (mm²); $A_{2}$ is the effective action area of the rod cavity of the cylinder (mm²); and $F_{L}$ are the loads of cylinder (N).

The direction of piston rod of the servo cylinder stretched out is a positive direction, the pressure of loads is $p_{L}$ , and the load-flow is $q_{L}$ .

From equation (1), we get

p_{L} = \frac{F_{L}}{A_{1}} = \frac{p_{1} A_{1} - p_{2} A_{2}}{A_{1}} = p_{1} - \frac{A_{2}}{A_{1}} p_{2}

(2)

For the cylinder, set $λ = A_{2} / A_{1}$ , hence we can get

p_{L} = p_{1} - λ p_{2}

(3)

The output power of the cylinder is

N = p_{1} q_{1} - p_{2} q_{2} = (p_{1} - \frac{A_{2}}{A_{1}} p_{2}) q_{1} = p_{L} q_{1}

(4)

Then the load-flow is $q_{L} = q_{1}$

q_{L} = C_{d} w_{1} x_{v} \sqrt{\frac{2 (p_{s} - p_{1})}{ρ (1 + λ)}}

(5)

where $C_{d}$ is flow coefficient; $w_{1}$ is the valve orifice area gradient; $x_{v}$ is the displacement of servo valve spool; $p_{s}$ is the pressure of oil source of system; $ρ$ is the density of the hydraulic oil; Set $λ = A_{2} / A_{1}$ .

In order to better analyze and study the performance of the leveler press control system formula (5) is linearized, and based on the Tailor formula, a first-order Tailor series expansion is performed near a certain operating point $q_{LO} = f (x_{vO}, p_{LO})$ , we get

q_{L} = q_{LO} + \frac{\partial q_{L}}{\partial x_{v}} |_{O} Δ x_{v} + \frac{\partial q_{L}}{\partial p_{L}} |_{O} Δ p_{L}

(6)

Linearized equation of servo valve incremental form is as follows

q_{L} - q_{LO} = Δ q_{L} = \frac{\partial q_{L}}{\partial x_{v}} |_{O} Δ x_{v} + \frac{\partial q_{L}}{\partial p_{L}} |_{O} Δ p_{L}

(7)

K_{q} = \frac{\partial q_{L}}{\partial x_{v}} = C_{d} w_{1} \sqrt{\frac{2 (p_{s} - p_{1})}{ρ (1 + λ)}}

(8)

K_{c} = - \frac{\partial q_{L}}{\partial p_{L}} = \frac{C_{d} w_{1} x_{v}}{\sqrt{2 ρ (1 + λ) (p_{s} - p_{1})}}

(9)

where $K_{q}$ is the flow gain of the valve; $K_{c}$ is the flow-pressure coefficient of the valve.

In order to simplify the operation equation (7), it can be written as

q_{L} = K_{q} x_{v} - K_{c} p_{L}

(10)

The flow continuity equation of servo cylinder

In order to deduce the flow continuity equation of servo cylinder, this article assumes that the ideal conditions are as follows: the pipeline loss and the dynamics of the pipeline can be neglected; the oil bulk modulus and the temperature can be regarded as constants, the internal and external leakage of servo cylinders are laminar flow. Flow continuity equation of servo cylinder can be got

q_{L} = A_{1} \frac{d x_{p}}{dt} + C_{tp} p_{L} + \frac{V_{t}}{2 (1 - λ^{2}) β_{e}} \frac{d p_{L}}{dt}

(11)

where $x_{p}$ is piston displacement; $β_{e}$ is the comprehensive bulk modulus of hydraulic oil, $β_{e} = 1.0 \times 10^{9} N / m$ ; $C_{tp}$ is total leakage coefficient of servo cylinder as

C_{tp} = \frac{1 + λ}{1 - λ^{2}} C_{ip} + \frac{1}{1 - λ^{2}} C_{ep}

(12)

where $C_{ip}$ is the internal leakage coefficient of the hydraulic cylinder; $C_{ep}$ is the external leakage coefficient of the hydraulic cylinder.

The equilibrium equation between servo cylinder and load

The dynamic characteristics of hydraulic power component are affected by load characteristic. Load force generally includes an inertial force, viscous drag, the elastic force, and any external load force.

The dynamic equilibrium equation of the cylinder and loads is

A_{1} p_{L} = m_{t} \frac{d^{2} x_{p}}{d t^{2}} + B_{p} \frac{d x_{p}}{dt} + K x_{p} + F_{L}

(13)

where $m_{t}$ is the mass piston and load converted to the piston; $B_{p}$ is the viscous damping coefficient of piston and loads; $K$ is the spring stiffness of the loads, and $F_{L}$ are the loads.

The transfer function of servo valve control servo cylinder

By using Laplace transform to the equations (10), (11), and (13), we can get

Q_{L} = K_{q} X_{v} - K_{c} P_{L}

(14)

Q_{L} = A_{1} s X_{p} + C_{tp} P_{L} + \frac{V_{t}}{2 (1 - λ^{2}) β_{e}} s P_{L}

(15)

A_{1} P_{L} = m_{t} s^{2} X_{p} + B_{p} s X_{p} + K X_{p} + F_{L}

(16)

According to equations (14)–(16), we get the servo cylinder piston displacement calculation formula (as shown below) under the action of the servo valve spool displacement and load.

At the same time, we get the transfer function of master control of position as follows

\begin{matrix} \frac{X_{p}}{X_{v}} = \frac{\frac{A_{1}}{K K_{ce}}}{(1 + \frac{s}{ω_{h}}) (\frac{s^{2}}{ω_{0}^{2}} + \frac{2 ξ_{0}}{ω_{0}} s + 1)} \\ X_{p} = \frac{\frac{K_{q}}{A_{1}} X_{v} - \frac{K_{ce}}{{A_{1}}^{2}} (1 + \frac{V_{t}}{2 (1 - λ^{2}) β_{e} K_{ce}}) F_{L}}{\frac{m_{t} V_{t}}{2 (1 - λ^{2}) β_{e} {A_{1}}^{2}} s^{3} + (\frac{K_{ce} m_{t}}{{A_{1}}^{2}} + \frac{V_{t} B_{p}}{2 (1 - λ^{2}) β_{e} {A_{1}}^{2}}) s^{2} + (1 + \frac{B_{p} K_{ce}}{{A_{1}}^{2}} + \frac{K V_{t}}{2 (1 - λ^{2}) β_{e} {A_{1}}^{2}}) s + \frac{K K_{ce}}{{A_{1}}^{2}}} \end{matrix}

(17)

where $ω_{h}$ is first-order frequency; $ω_{0}$ is second-order natural frequency; and $ξ_{0}$ is the damping ratio

\begin{matrix} ω_{h} = \frac{K K_{c}}{A^{2} (1 + \frac{K}{K_{0}})} \\ ω_{0} = \sqrt{\frac{2 (1 - λ^{2}) β_{e} {A_{1}}^{2}}{V_{t} m_{t}}} \sqrt{1 + \frac{K}{K_{0}}} \\ ξ_{0} = \frac{1}{2 ω_{0}} (\frac{2 (1 - λ^{2}) β_{e} K_{c}}{V_{t} (1 + \frac{K}{K_{0}})} + \frac{B_{p}}{m_{t}}) \end{matrix}

Building the mathematical model of pressure valve control of valve control cylinder

This article defined a position-pressure conversion formula expressed with $K_{f}$ which can achieve unified control between two different control variables easily and feasibly in the electro-hydraulic servo system meanwhile optimize the original control model so as to achieve the better control effect. Pressure conversion computation formula is as follows

Kf = | \frac{Δ X}{Δ P} | = | \frac{X_{t} - X_{t - 1}}{P_{t} - P_{t - 1}} |

(18)

where $K_{f}$ is pressure conversion formula; $Δ P$ is the differential pressure signal of hydraulic cylinder by online real-time measured between the adjacent time; $Δ X$ is the differential displacement signal of hydraulic cylinder by online real-time measured between the adjacent time periods; $X_{t}$ is the displacement signal of hydraulic cylinder at the time of t; $X_{t - 1}$ is the displacement signal of hydraulic cylinder at the time of t–1; $P_{t}$ is the pressure signal of hydraulic cylinder at the time of t; $P_{t - 1}$ the pressure signal of hydraulic cylinder at the time of t–1; and $t$ is the time of detecting.

Set the load pressure $F_{L}$ as constant, after the load is loaded, we get the equilibrium equation between servo cylinder and load between t and t–1 according to the formula (14) as follows

A_{1} p_{t - 1} = m_{t} a_{t - 1} + B_{p} v_{t - 1} + K x_{t - 1} + F_{L}

(19)

A_{1} p_{t} = m_{t} a_{t} + B_{p} v_{t} + K x_{t} + F_{L}

(20)

Set equation (20) minus equation (8), we can get

\frac{X_{t} - X_{t - 1}}{P_{t} - P_{t - 1}} = \frac{A_{1}}{K} - \frac{m_{t} (a_{t} - a_{t - 1})}{P_{t} - P_{t - 1}} - \frac{B_{p} (v_{t} - v_{t - 1})}{P_{t} - P_{t - 1}}

(21)

In the process of practical work, the change of acceleration and speed is very small during the time of $Δ t$ , $m_{t} (a_{t} - a_{t - 1})$ and $B_{p} (v_{t} - v_{t - 1})$ can be regarded as zero. Hence, in order to simplify the control process $m_{t} (a_{t} - a_{t - 1})$ and $B_{p} (v_{t} - v_{t - 1})$ can be ignored, hence we can get

K_{f} = \frac{X_{t} - X_{t - 1}}{P_{t} - P_{t - 1}} = \frac{A_{1}}{K}

(22)

According to the position-pressure master-slave control requirements of valve control cylinder electro-hydraulic servo control system, we get the main calculation basis in the transformation control model, as is shown in the following formula

X_{z} = {\begin{matrix} (P_{g} - P_{t}) \times K_{f} (P_{t} \geq P_{0}) \\ 0 (P_{t} < P_{0}) \end{matrix}

(23)

where $X_{z}$ is displacement which is converted by pressure; $P_{0}$ is set point when conversion is beginning; $P_{g}$ is the pressure signal that has been given; $P_{t}$ is the pressure signal at the time of t.

From equation (22) and (23), we get

X_{z} = {\begin{matrix} (P_{g} - P_{t}) \times K_{f} = (P_{g} - P_{t}) \times \frac{A}{K} = \frac{F_{g} - F_{t}}{K} & (P_{t} \geq P_{0}) \\ 0 & (P_{t} < P_{0}) \end{matrix}

(24)

Building the mathematical model of other control elements

The mathematical model of displacement sensor

Displacement sensor response frequency is far greater than the response frequency of the whole system, hence its transfer function is approximated with the proportional element

K_{r} = \frac{U_{r}}{X_{r}}

(25)

where $K_{r}$ is the displacement sensor gain; $U_{r}$ is the output voltage signal of the displacement sensor; and $X_{r}$ is the stroke of displacement sensor.

The mathematical model of pressure sensor

Pressure sensor has advantages of small volume and high sensitivity and good stability, the role of sensor is pressure signal acquisition by computing and transforming it into a feedback current signal, which is proportional to the pressure

K_{i} = \frac{U_{i}}{P}

(26)

where $K_{i}$ is the pressure sensor gain; $U_{i}$ is the output voltage signal of the pressure sensor.

The mathematical model of position-pressure master-slave control

According to the system components and the master-slave control principles, combined with the conversion formula of pressure, the position-pressure master-slave control system block diagram as shown in Figure 3.

Figure 3.

The position and pressure master-slave control system block diagram.

Where $U_{g}$ is input; $X_{p}$ is output; $U_{0}$ is the set voltage signal.

Simulation of the system

In this article, relevant parameters of the electro-hydraulic servo system, as is shown in Tables 1 and 2.

Table 1.

The parameter in hydraulic system.

Number	Name	Symbol	Value	Unit
1	Working pressure	$P_{s}$	250	$bar$
2	Density	$ρ$	0.9	$g / c m^{3}$
3	Load stiffness	$K$	$1.0 \times 10^{7}$	$N / mm$
3	Bulk modulus	$β_{e}$	$1.0 \times 10^{9}$	$N / m$
4	Conversion formula	$k_{f}$	0.0322	$m m^{3} / KN$
5	Servo amplifier gain	$K_{A}$	0.003	$A / V$
6	Displacement sensor gain	$K_{r}$	200	$V / m$
7	Pressure sensor gain	$K_{i}$	$0.5 \times 10^{- 4}$	$A / bar$

Table 2.

The parameter of main working element.

Number	Name	Symbol	Value	Unit
1	Flow coefficient	$C_{d}$	0.6
2	Area of gradient	$ω$	$16 π$	$g / c m^{3}$
3	Quality of the piston rod	$m_{i}$	950	$kg$
4	Area of rear cavity	$A_{i 1}$	321,536	$m m^{2}$
5	Area of rod cavity	$A_{i 2}$	162,574	$m m^{2}$
6	Working stroke	$L$	300	$mm$

Aiming at the proposed position-pressure master-slave control method, in this article, using MATLAB/Simulink software simulate the straightening Q345B steel plates process of straightening machine under the condition of the output power is 5.5 × 10³ kN in a single servo cylinder. As is shown in Figure 4, simulation model of position-pressure master-slave control of electro-hydraulic servo system can be represented.

Figure 4.

Electro-hydraulic servo position-pressure master-slave control system simulation model.

As is shown in Figures 5 and 6, system simulation time is 5.5 s, and the load pressure signal is loaded when the simulation time is 0.4 s, we obtain the simulation position curve of the cylinder and pressure curve.

Figure 5.

The position simulation curve of straightening 25 mm Q345B steel.

Figure 6.

The pressure simulation curve of straightening 25 mm Q345B steel.

From the data (Figure 5) in the field, it is known that the displacement is fluctuated when the master-slave control system of single servo cylinder is loaded instantly, maximum fluctuation to 25.074 mm and the minimum fluctuation to 24.917 mm. The impact of load has not been dramatic after the adjustment of the master-slave control method which has replied to load change quickly and make position steadily in a very short time that location control accuracy within 0.066 mm.

From the data (Figure 6) in the field, it is known that the pressure response is lagged and then increased rapidly when the master-slave control system of single servo cylinder is loaded instantly. This is because the load leads to fluctuating position, and then the results in pressure change needs certain time response. After establishment of pressure, the pressure response increases rapidly and appears a fluctuation phenomenon that maximum fluctuates to 17.056 MPa. The transformation that pressure turns into position during the process that makes the deviation of the average pressure of cylinder is controlled in less than 0.1 MPa after the system is stable.

From the simulation results above, it is known that position-pressure master-slave control system can quickly reply to pressure fluctuation by load changes caused, thereby adjusting the position control of the system, guarantee high precision of position control, meanwhile also can control pressure of the system. This control method is not only correct and feasible but could be achieved better using online unified control of different variables for position and pressure.

Experimental studies

All experiments were performed on eleven-roll-plate leveler equipment of Wuyang Iron & Steel Co., Ltd. and installed HYDAC pressure sensor, MTS displacement sensor, and REXTROH high-response servo valve on the hydraulic cylinder in order to obtain accurate data. Research the straightening Q345B steel plate process of straightening machine under the condition of the output in double servo cylinder. Block control schematic of the experiment, as is shown in Figure 7.

Figure 7.

Block control schematic of the experiment.

Set the roll gap value as 25 mm, when system tends to be stable after contacting load, respectively, collecting the roll gap value and the pressure signal of servo cylinder. The comparison of roll gap experimental fluctuations is shown in Figure 8. The comparison of experimental pressure fluctuations is shown in Figure 9.

Figure 8.

The comparison of roll gap experimental fluctuations.

Figure 9.

The comparison of experimental pressure fluctuations.

From the table data and Figure 8, under position closed-loop control, the maximum deviation between the experimental value and the target value of the roll gap position of the servo cylinder is 0.31 mm, the average deviation is controlled within 0.131 mm; under the position and pressure master-slave control process. The maximum deviation between the experimental value and the target value of the roll gap position of the servo cylinder is about 0.12 mm, and the average deviation is controlled within 0.078 mm. It can be seen that the latter has higher position control accuracy. According to the table data and Figure 9, under position closed-loop control, the pressure deviation of the servo cylinder is 0.55 MPa at the maximum, the average deviation is controlled within 0.402 MPa; under the position and pressure master-slave control, the pressure deviation of the servo cylinder is 0.42 MPa and the average deviation is controlled within 0.3 MPa. It can be seen that both the closed-loop position control and the position-pressure master-slave control can satisfy the working requirements of a single hydraulic cylinder system, while the latter has a better pressure control effect.

Therefore, the Simulink simulation result of position-pressure master-slave control is ideal because Simulink simulation system is based on electro-hydraulic servo system mathematical model of position-pressure master-slave control which ignores the impact of nonlinear instability and other factors. Thus, no matter the control accuracy or the deviation of simulation results is better than the experimental results, while in the field experiment, when the hydraulic oil has different temperature and gas content, it causes different hydraulic spring stiffness. Hence, the experiment error and the simulation error have a certain gap.

Discussion

The proposed method in this article has improved the control accuracy of position of the system: the simulation position maximum deviation is about 0.083 mm, the average deviation is controlled in less than 0.066 mm; the position maximum deviation by experiment between experimental value and target value is about 0.12 mm, the average deviation is controlled in less than 0.078 mm. The simulation pressure maximum deviation is about 0.207 MPa, the average deviation is controlled in less than 0.1 MPa; the pressure maximum deviation by experiment between experimental value and target value is about 0.42 MPa, the average deviation is controlled in less than 0.3 MPa. This control method can satisfy the needs of actual production.

The proposed method in this article mainly carried out on a single servo cylinder system by modeling, simulation, and experimental research. Later work requires a combination of multi-DOF feedback decoupling control theory knowledge and the online calculating partial load of hydraulic cylinder theory to research dynamic change and put the single cylinder position-pressure master-slave control model into the multiple control channels in order to achieve the precision master-slave control of multi cylinder electro-hydraulic system.

Conclusion

In conclusion, through simulation and experimental research, it was found that the proposed idea of control method is simple, which can achieve online converting between position and pressure which are different variables and improve the response speed and control precision of the system. The position control accuracy of the entire leveler control system can be improved, and the position and pressure of the system can be controlled more reasonably at the same time, which also has certain guiding significance to other electro-hydraulic servo system design and research.

Footnotes

Acknowledgements

H.H. and Z.L. were responsible for building a model and performed the experiment and wrote the paper. Y.L. and L.M. were responsible for the acquisition and analysis of experimental data. L.Q. supervised the research.

Handling Editor: Farzad Ebrahimi

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the National Natural Science Foundation of China (grant no.: 51505315, “Youth SanJin scholars” plan in Shanxi Province, Focus on research and development plan in Shanxi Province (201603D111004, 201603D121010),and the Taiyuan Heavy Machinery and Equipment Collaborative Innovation Center funded at the provincial level, sponsored by the Fund for Shanxi “1331 Project” Key Subjects Construction.

ORCID iD

Heyong Han

Zhiqi Liu

References

Quan

. Simulation and test of electro-hydraulic servo position and pressure hybrid control principle. Chin J Mech Eng2008; 44: 100–105.

Han

Wang

Huang

. Analysis of unsymmertrical valve controlling unsymmetrical cylinder stability in hydraulic leveler. Nonlinear Dynam2012; 70: 1199–1203.

Zhang

Huang

. Modeling and experimental analysis of valve-control-cylinder system for full-hydraulic leveler. Chin Mech Eng2014; 25: 1299–1302.

Guo

Han

. Analysis of asymmetric valve control asymmetric cylinder system of hydraulic leveler. Rolling Equip Technol2011; 145: 477–481.

Han

Huang

Zhang

. Analysis and comparison of dynamic characteristics of hydraulic leveler servo system. J Jilin Univ2012; 42: 372–376.

Guan

Pan

. Adaptive sliding mode control of electro-hydraulic with nonlinear unknown parameters. Control Eng Pract2008; 16: 1275–1284.

Wonohadidjojo

Ganesh

Hassan

. Position control of electro-hydraulic actuator system using fuzzy logic controller optimized by particle swarm optimization. Int J Auto Comput2013; 10: 181–193.

Bessa

Dutra

Kreuzer

. Sliding mode control with adaptive fuzzy dead-zone compensation of an electro-hydraulic servo-system. J Intell Robot Syst2010; 58: 3–16.

Zulfatman

. Application of self-tuning fuzzy PID controller on industrial hydraulic actuator using system identification approach. Int J Smart Sensors Intell Syst2009; 2: 246.

10.

Lei

Wang

. Sliding mode control in position control for asymmetrical hydraulic cylinder with chambers connected. J Shanghai Jiaotong Univ2013; 18: 454–459.

11.

Han

Huang

Wang

et al . The analysis of new hydraulic rolling shear servo system dynamic characteristics. Proc IMechE, Part B: J Eng Manufacture2013; 227: 453–459.

12.

Han

Wang

et al . Research on a new hydraulic rolling shear shearing mechanism and its control system. Proc IMechE, Part B: J Eng Manufacture2014; 229: 1827–1833.

13.

Bai

Quan

. New method to improve dynamic stiffness of electro-hydraulic servo systems. Chin J Mech Eng2013; 26: 997–1005.

14.

Shen

Zhu

et al . Real-time electro-hydraulic hybrid system for structural testing subjected to vibration and force loading. Mechatronics2015; 33: 49–70.

15.

Shen

Zhu

Zhang

et al . Adaptive feed-forward compensation for hybrid control with acceleration time waveform replication on electro-hydraulic shaking table. Control Eng Pract2013; 21: 1128–1142.