Research on Hydro-pneumatic Suspension

Test Bench Based on Electro-hydraulic

Proportional Control

Xin Bai, Liqun Lu∗ , Meng Sun, Leilei Zhao and Hui Li

School of Transportation and Vehicle Engineering, Shandong University of

Technology, Zibo 255000, China
E-mail: luliqun@sdut.edu.cn
∗
Corresponding Author

Received 29 March 2022; Accepted 26 May 2022;

Publication 12 June 2023

Abstract
Compared with the traditional automotive suspension, hydro-pneumatic sus-
pension has the characteristics of large energy storage ratio, nonlinear stiff-
ness and can change the ground clearance of the vehicle body, which makes
the vehicle have good ride comfort and handling stability during driving.
In order to improve the performance of hydro-pneumatic suspension, it is
necessary to design hydro-pneumatic suspension test bench for performance
test. Aiming at the problem that the output signal of the mechanical test
bench used in China is single and has large error, which is difficult to meet
the performance test requirements of hydro-pneumatic suspension, a hydro-
pneumatic suspension test bench based on electro-hydraulic proportional
control is designed. Through AMESim/MATLAB joint system modeling and
simulation, in the tracking comparison of sinusoidal signal, compared with
the traditional PID control method, the fuzzy PID control method reduces the
error by 56.8% and the lag time by 70%; Through the experimental analysis

International Journal of Fluid Power, Vol. 24 3, 537–566.

doi: 10.13052/ijfp1439-9776.2436
© 2023 River Publishers
538 X. Bai et al.

of hydro-pneumatic suspension elastic force characteristic diagram, indicator

diagram and damping force velocity characteristic diagram, the error rate
of the test bench in sinusoidal signal tracking experiment is less than 15%,
which meets the test requirements of hydro-pneumatic suspension.

Keywords: Hydro-pneumatic suspension, electro-hydraulic proportional

control system, fuzzy PID control, AMESim/Simulink, test bench.

1 Introduction
As a special suspension, hydro-pneumatic suspension combines the elastic
element with the shock absorber, so it has good nonlinear characteristics
and damping performance. Hydro-pneumatic suspension has the functions of
balancing load, generating damping vibration and adjusting body height [1].
It can meet a variety of driving conditions and improve vehicle ride comfort
and handling stability. Therefore, it is widely used in all kinds of heavy vehi-
cles. In order to improve the performance of hydro-pneumatic suspension, it
needs to be tested. Because the internal structure of hydro-pneumatic suspen-
sion is relatively complex, and many of its design theories are established on
simplified mathematical models, its performance cannot be evaluated simply
by simulation. It is necessary to verify its actual performance by test, and test
the hydro-pneumatic suspension on the test bench.
The performance of the test bench has a great influence on the test results
of hydro-pneumatic suspension. The research on suspension test abroad is
relatively early, and its mainstream loading mode is hydraulic servo control.
Since the end of last century, various test benches have been produced.
Among them, MTS company in the United States, Schenck company in
Germany and ABD company in the United Kingdom have begun to develop
road simulation test bench and damping test bench. So far, they are still
the leaders in this industry, and their road simulation technology is at the
international leading level [2–5]. The domestic test bench has developed
rapidly in recent years, and its loading methods have mainly experienced
mechanical, electric test, electro-hydraulic servo, etc. [6]. The vertical load-
ing test bench of hard point adjustable suspension designed by Chen Xinbo
of Tongji University can realize the output of vertical excitation signals such
as step, sinusoidal and integral white noise [7]. The State Key Laboratory of
Jilin University has developed a set of K & C characteristic parameter test
platform for single axle suspension of the whole vehicle [8], The loading
mode adopted is the matching transmission of servo motor and ball screw.
 Research on Hydro-pneumatic Suspension Test Bench 539

With the increasing requirements of suspension test bench, electro-hydraulic

servo control, as an advanced control technology, gradually occupies a major
position in suspension test equipment. However, the cost of servo control is
too high for ordinary enterprises to bear, and servo control has high require-
ments for the cleanliness of oil medium, and there are many equipments
in the factory, which will inevitably affect the cleanliness of oil and the
normal operation of the system. The performance of the test bench has
great influence on the test results of hydro-pneumatic suspension. Foreign
test bench precision is high, but the price is high, small and medium-sized
enterprises can not afford; But the domestic test bench output waveform
is not accurate, large error and other shortcomings, these situations limit
the development of China’s automobile industry. Therefore, it is necessary
to design an acceptable price and fully functional test bed according to
the nonlinear characteristics of hydro-pneumatic suspension, so as to more
truly simulate the actual operating conditions of the car, and lay a better
foundation for the development of a higher level of hydro-pneumatic sus-
pension. Because the performance of electro-hydraulic proportional control
technology meets the test requirements, the operation of its control system
is relatively simple, and the cost of electro-hydraulic proportional control
system is lower than servo control, and the requirement for oil cleanliness is
low, which greatly reduces the system failure and makes the loading system
more stable and reliable [9]. Therefore, the electro-hydraulic proportional
control method is selected to complete the loading of the test system.
In this paper, the hydro-pneumatic suspension test bench is designed
based on the electro-hydraulic control proportion, the schematic diagram of
the hydraulic loading system is completed, and the electro-hydraulic propor-
tional valve components required by the system are selected. The fuzzy con-
trol algorithm is added on the basis of the conventional PID control algorithm,
and the fuzzy PID controller of the electro-hydraulic proportional system
is established. The modeling and simulation of the AMESim/MATLAB
joint system, the test rig construction and the characteristic analysis of the
hydro-pneumatic suspension test are carried out. Through the modeling and
simulation of the AMESim/MATLAB joint system, the error of the fuzzy
PID control method is reduced by 56.8% compared with the traditional
PID control method in sinusoidal signal tracking comparison. The lag time
was reduced by 70%; Based on the analysis of elastic force characteristic
diagram, indicator diagram and damping force velocity characteristic dia-
gram of hydro-pneumatic suspension, the error rate of the test bench in
sinusoidal signal tracking experiment is less than 15%, which meets the
540 X. Bai et al.

requirements of hydro-pneumatic suspension test, and verifies the correctness

of the mathematical model and the feasibility of the test bench design.

2 Design of Hydro-pneumatic Suspension Test Bench

Based on Electro-hydraulic Proportional Control
2.1 Structural Design of Test Bench
During the performance test of hydro-pneumatic suspension, when the hydro-
pneumatic suspension is placed and installed, the hydraulic lock remains
locked, and the upper and lower sliding blocks are connected and fixed.
The actuating cylinder directly provides sinusoidal signal excitation for the
hydro-pneumatic suspension, in which the force sensor completes the mea-
surement of the output force of the hydro-pneumatic suspension, and the
relative displacement between the actuating cylinder barrel and the piston
rod is measured and recorded by the displacement sensor, and the displace-
ment and output force are fitted to complete the displacement characteristic
test of the hydro-pneumatic suspension; By deriving the displacement, the
speed characteristic test of hydro-pneumatic suspension can be completed.
The layout of the test bench is shown in Figure 1.
During the 1/4 vehicle road simulation test, adjust the height of the
slider assembly 1 to place the vehicle tire and suspension guide mechanism,

1.base; 2. lower beam;3. upright column; 4. slider assembly 1; 5. slider assembly 2;

6 .upper beam; 7. force sensor; 8. hydraulic lock; 9. hydro-pneumatic suspension; 10. electro
hydraulic jacking cylinder; 11. hydraulic cylinder actuating cylinder
Figure 1 Hydro-pneumatic suspension performance test bench installation layout diagram.
 Research on Hydro-pneumatic Suspension Test Bench 541

Figure 2 Schematic diagram of installation and layout of 1/4 vehicle road simulation test
bench.

and place the counterweight above the slider assembly 2 to simulate the
vehicle mass. The hydro-pneumatic suspension is installed between the slider
1 and the slider 2. At this time, the hydraulic locking device is in a free
state. The actuating cylinder drives the tire, hydro-pneumatic suspension and
counterweight to vibrate at the same time. Through this arrangement, the
actual operating conditions of the vehicle are simulated. The installation and
layout of the test bench is shown in Figure 2.

2.2 Working Principle of Hydraulic System

Through the analysis, it is found that the hydro-pneumatic suspension has
nonlinear characteristics, and although the hydro-pneumatic suspension with
regressive stiffness has been developed [10], the stiffness displacement of
ordinary hydro-pneumatic suspension increases with the increase of dis-
placement, and the change is nonlinear. When the input displacement of the
suspension is less, the stiffness of the suspension increases relatively slowly;
With the gradual increase of stroke, the growth rate of stiffness increases
gradually. It is precisely because of this feature that vehicles equipped with
hydro-pneumatic suspension maintain good ride comfort when driving on flat
roads; When driving on poor roads, the vehicle can maintain a certain driving
speed. By referring to the design scheme of hydro-pneumatic suspension test
bench at home and abroad, the hydraulic system of the test bench is designed.
The schematic diagram of the hydraulic system is shown in Figure 3.
542 X. Bai et al.

1. tank; 2. liquid level meter; 3. air filter; 4. Level relay; 5. electric heater; 6. constant
power plunger pump; 7. pump sleeve + coupling; 8. dust explosion proof motor; 9.
electromagnetic overflow valve; 10. check valve; 11. pressure tap; 12. pressure measuring
hose; 13. pressure gauge; 14. high pressure oil filter;15. accumulator;16. proportional
directional valve;17. superimposed hydraulic control check valve; 18. pressure transmitter;
19. pressure tap; 20. hydraulic cylinder; 21. cooler; 22. low pressure ball valve; 23. oil return
filter
Figure 3 Schematic diagram of hydraulic excitation system.

2.3 Design and Selection of Key Parts

2.3.1 Selection of electro-hydraulic proportional valve
Because the electro-hydraulic proportional directional valve has the charac-
teristics of strong anti pollution ability, high work efficiency, relatively low
price, high control accuracy, and its performance is similar to that of the
 Research on Hydro-pneumatic Suspension Test Bench 543

on-off valve. The comprehensive performance of proportional valve is no less

than that of servo valve [11, 12]. Therefore, the electro-hydraulic proportional
directional valve is selected to control the liquid flow and flow direction.
According to the design and calculation results of the hydraulic cylin-
der of the test bench, the maximum flow qm of the hydraulic cylinder is
60.2 L/min. Therefore, the flow of proportional valve is [13]:
s
∆p1
qv = qm (1)
∆pv

Where, qv is the working flow of the proportional valve, L/min; qm

is the maximum flow of hydraulic cylinder, L/min; ∆p1 is the pressure
drop at the proportional valve port when the hydraulic cylinder is working,
taken as 1 MPa; ∆pv is the nominal pressure drop of proportional valve,
taken as 0.9 mpa. (According to the selected proportional valve model, the
pressure drop is evaluated. In this paper, the direct acting electro-hydraulic
proportional valve manufactured by Rexroth company is selected, and its
model is 4WREE10W-75-2X/G24K31/F1V).
According to the above formula, the working flow of the proportional
valve is 64.2 l/min.
According to the flow, pressure and other information required by the
hydraulic cylinder, the direct acting electro-hydraulic proportional direc-
tional valve produced by Rexroth company is selected, and its model
is 4WREE10W-75-2X/G24K31/F1V. The median function of the valve is
Y-shaped with a diameter of 10 mm. When the pressure drop of the valve
is 10 bar, its rated flow is 75 L/min. The technical parameters are shown in
Table 1.
Compared with the traditional electromagnetic directional valve, the
electro-hydraulic proportional directional valve can take into account the
control of oil flow direction and flow. Its working principle is: when the coils
5 and 6 are powered off, the control valve core 2 is maintained in the central
position under the action of compression springs 3 and 4. When the coil 6 is
powered on, the control valve core 2 will move to the left, while the spring 4
is in the tension state and the spring 3 is in the compression state, in which the
displacement of the control valve core is proportional to the electrical input
signal; On the contrary, when the coil 5 is powered on, the control valve core
2 will move to the right in proportion to the electrical signal. At this time, the
spring 3 is in the tension state and the spring 4 is in the compression state.
The schematic diagram of the valve is shown in Figure 4.
544 X. Bai et al.

Table 1 Electro-hydraulic proportional valve main parameters

Summary Parameter
Valve weight (kg) 6.5
Maximum working pressure (MPa) 31.5
Maximum flow (L/min) 180
Working ambient temperature (◦ C) −20∼50
Repetition accuracy (VDC) 24
Current control signal (mA) 4∼20
Drift diameter (mm) 10
Lag (%) ≤0.1
Response sensitivity (%) ≤0.05
Reverse error (%) ≤0.05

1. Valve body; 2. Control valve core; 3. Compression spring 1; 4. Compression spring 2;

5. Coil 1 with centering thread; 6. Including centering thread 2; 7. Sensor; 8. Integrated
control element; 9. Mechanical zero potential regulation; 10. Electrical zero potential
regulation
Figure 4 Electro-hydraulic proportional discharge valve.

The electro-hydraulic proportional directional valve has zero dead zone

during actual operation. At this time, the proportional valve in the dead zone
has no flow output, and the starting current of the dead zone is about one fifth
of the rated current of the proportional valve. The causes of zero dead zone
mainly include two aspects: one is that the valve core of electro-hydraulic
proportional valve will cover the valve port when it is in the middle position,
and the other is that the valve core will be affected by static friction during
the initial movement. In order to solve the problem of zero dead zone, a
compensation system is added to the control system to improve the dynamic
performance of the proportional valve.

2.3.2 Fuzzy PID control principle

Fuzzy PID control algorithm has many forms. Its principle is: constantly
detect the deviation E and deviation change rate EC of the system, according
 Research on Hydro-pneumatic Suspension Test Bench 545

Figure 5 Fuzzy PID self-tuning control system.

to the fuzzy relationship set by the system, modify the three key parameters
of PID control online in real time: Kp is proportional coefficient; Ki is the
integral time constant; Kd is the differential time constant. In order to meet
the requirements of PID control parameters in the case of different E and
EC, the system has better dynamic performance. The structure diagram of
the fuzzy PID self-tuning control system is shown in Figure 5.
The specific calculation formula of fuzzy PID parameter self-tuning
algorithm is as follows:
′

Kp = Kp + ∆Kp

Ki = Ki′ + ∆Ki (2)

 ′
Kd = Kd + ∆Kd

Where, ∆Kp , ∆Ki and ∆Kd are the adjusted values of PID parameters,
Kp′ , Ki′ and Kd′ are the set initial values, and Kp , Ki and Kd are the values
obtained after adjustment.

2.3.3 Design of fuzzy PID controller for electro-hydraulic

proportional control system
(1) Determination of the domain of input and output variables of control
system
The fuzzy universe of the input variables E and EC of the fuzzy PID control
system is defined as [−3, 3], and the fuzzy universe of output variables ∆Kp
is [−6, 6], the fuzzy universe of ∆Ki is [−0.3, 0.3], the fuzzy universe of
∆Kd is [−0.03, 0.03].
According to the operation characteristics of the hydro-pneumatic sus-
pension test bench, the system is determined as seven fuzzy language
values, and the English abbreviations of the fuzzy set can be expressed
as {NB, NM, NS, ZO, PS, PM, PB}. Therefore, the set of E and
EC fuzzy universe is {−3, −2, −1, −0, 1, 2, 3}, The fuzzy universe set
546 X. Bai et al.

Figure 6 The membership function of E.

of ∆Kp is {−6, −4, −2, 0, 2, 4, 6}, and the fuzzy universe set of ∆Ki
is {−0.3, −0.2, −0.1, 0, 0.1, 0.2, 0.3}, the fuzzy universe set of ∆Kd is
{−0.003, −0.002, −0.001, 0, 0.001, 0.002, 0.003}.

(2) Determination of membership function

Considering the actual operating conditions of the system and the complexity
of the function, the membership function of the system is determined as a
triangular membership function with more sensitive response.
Although the fuzzy universe of each input and output of the system is
different, the membership functions of each part are not different, so the
membership functions of one input variable and two output variables are
given. The membership function curve is shown in Figures 6 and 7.

(3) Fuzzy reasoning

The fuzzy reasoning process of fuzzy PID control system is the output rule
according to which ∆Kp , ∆Ki and ∆Kd are output when the system input
E and EC are different combinations. According to the control effect of
various parameters of PID algorithm on the system, combined with the actual
working conditions of the hydro-pneumatic suspension test-bed controlled
by electro-hydraulic proportion in this paper, the fuzzy rules of the control
system are obtained, as shown in Tables 2, 3 and 4 [14, 15]. Import the
49 fuzzy rules obtained in Table 4 into the fuzzy rule editor of MATLAB
software. As shown in Figure 8.
 Research on Hydro-pneumatic Suspension Test Bench 547

Figure 7 The membership function of ∆Kp .

Table 2 Fuzzy rule adjustment table of ∆Kp

EC
E NB NM NS ZO PS PM PB
NB PB PB PM PM PS ZO ZO
NM PB PB PM PS PS ZO NS
NS PM PM PM PS ZO NS NS
ZO PM PM PS ZO NS NM NM
PS PS PS ZO NS NS NM NM
PM PS ZO NS NM NM NM NB
PB ZO ZO NM NM NM NB NB

Table 3 Fuzzy rule adjustment table of ∆Ki

EC
E NB NM NS ZO PS PM PB
NB NB NB NM NM NS ZO ZO
NM NB NB NM NS NS ZO ZO
NS NB NM NS NS ZO PS PS
ZO NM NM NS ZO PS PM PM
PS NM NS ZO PS PS PM PB
PM PM ZO PS PS PM PB PB
PB ZO ZO PS PM PM PB PB
548 X. Bai et al.

Table 4 Fuzzy rule adjustment table of ∆Kd

EC
E NB NM NS ZO PS PM PB
NB PS NS NB NB NB NM PS
NM PS NS NB NM NM NS ZO
NS ZO NS NM NM NS NS ZO
ZO ZO NS NS NS NS NS ZO
PS NS NS NS ZO PS PS PS
PM ZO ZO ZO ZO ZO ZO ZO
PB PB NS PS PS PS PS PM

Figure 8 Fuzzy rule editor.

This paper selects Mamdina fuzzy reasoning method for reasoning. After
the input of fuzzy rules is completed, 3d surface diagrams of three outputs
can be obtained in the surface module, as shown in Figures 9–11.
The three-dimensional surface graph can more intuitively represent the
fuzzy control rules designed above. Taking Figure 8 as an example, the graph
shows the change relationship between the output variable ∆Kp and the
two input variables E and EC, in which the abscissa is the domain of the
input variable and the ordinate is the fuzzy domain of the output variable.
The smoothness of the surface graph reflects the performance of the control
rules to a certain extent, so the fuzzy control rules can be improved according
to its smoothness. Then the center of gravity method is selected to complete
the defuzzification of the control system.
Research on Hydro-pneumatic Suspension Test Bench 549

Figure 9 The surface diagram of ∆Kp .

Figure 10 The surface diagram of ∆Ki .

Figure 11 The surface diagram of ∆Kd .

550 X. Bai et al.

3 Simulation of Electro-hydraulic Proportional Control

System Based on AMESim/MATLAB
AMESim software has excellent performance in the field of system modeling.
The hydraulic system can be established through the hydraulic library and
other application libraries in the software [16, 17]. It can accurately complete
the construction of the hydraulic loading system. Its disadvantage is that
the control ability is poor, and the characteristics of MATLAB with strong
control ability and excellent data processing ability can make up for this
defect [18–20]. In this paper, AMESim and MATLAB are used for system
modeling and simulation. The physical model of the control system is built
by AMESim software, and the PID control and fuzzy PID control models are
built in Matlab/Simulink. AMESim and MATLAB are connected through the
interface module, so as to complete the import and output of data and realize
the joint simulation.

3.1 Modeling of Hydraulic System Based on AMESim

AMESim software has the characteristics of simple operation, accurate and
convenient modeling, which makes the operator no longer need to spend a
lot of time and energy on the establishment of mathematical model and the
editing of program code. It only needs to drag and connect the components
in the software to complete the model construction, which greatly simplifies
the model construction process of the system. Based on this mode, the actual
working principle of the system can be reflected more intuitively, and the
simulation and calculation of the system can be completed more accurately.
The simulation model is built according to the hydro-pneumatic suspen-
sion test platform, so as to compare the control effect of PID and fuzzy
PID control algorithm. The physical model of hydraulic system based on
AMESim is shown in Figure 12, which simulates the layout of loading
system and hydro-pneumatic suspension during hydro-pneumatic suspension
performance test. Input the hydraulic system parameters into AMESim and
set the sampling time of the system to 0.01 s.

3.2 Control System Modeling Based on MATLAB/Simulink

In order to verify the performance of fuzzy PID control, the fuzzy PID
control model and PID control model are built, as shown in Figures 13
and 14 respectively, to compare the control effects of the two algorithms.
The parameters of PID control system are determined according to the trial
 Research on Hydro-pneumatic Suspension Test Bench 551

Figure 12 Hydro-pneumatic suspension test model based on AMESim.

Figure 13 Fuzzy PID control model.

Figure 14 PID control model.

552 X. Bai et al.

and error method. After simulation and adjustment, Kp is 30, Ki is 1.6 and
Kd is 0.03.

3.3 Comparison and Analysis of Simulation Results

(1) The input signals in models 13 and 14 are sinusoidal signals with ampli-
tude of 0.05 m, frequency of 1 Hz and simulation time of 2 s. The output
effects of the two control methods are shown in Figures 15 and 16.
As shown in Table 5, in the tracking comparison of sinusoidal signals,
compared with the traditional PID control method, the maximum error of
fuzzy PID control method is reduced by 56.8% and the lag time is reduced by
70%. Therefore, compared with the traditional PID control, the error of fuzzy
PID control is smaller and the following performance is better.

Figure 15 PID control sine simulation curve.

Figure 16 Fuzzy PID control sinusoidal simulation curve.

 Research on Hydro-pneumatic Suspension Test Bench 553

Table 5 Two control methods for sinusoidal signal tracking pairs

Control Method Maximum Error/mm Lag Time/s
PID control 8.1 0.04
Fuzzy PID control 3.5 0.012

Figure 17 Loading simulation test.

(2) Figure 17 is the physical model diagram of the system during the loading
simulation test, and the 1/4 vehicle dynamics model is established. Among
them, the unsprung mass of the car is 280 kg and the unsprung mass is
3000 kg.
The step signal is set to simulate the road bulge encountered by the vehicle
during driving. The step signal is set to 0.05 m and the simulation time is 1 s.
The comparison diagram of the step response effect of the system is obtained
through simulation, as shown in Figure 18. The dotted line is conventional
PID control and the solid line is fuzzy PID control. As can be seen from
Figure 16, compared with the conventional PID control, the overshoot of the
fuzzy PID control system and the time required to reach the steady state are
greatly reduced. The time required for the conventional PID control method
to reach the steady state is 0.33 s, and the fuzzy PID control reaches the
steady state after 0.16 s, and the adjustment time is shortened by 51.5%.
The maximum overshoot of conventional PID control system is about 7%,
while fuzzy PID control system has almost no overshoot, and the control
effect is better.
554 X. Bai et al.

Figure 18 Step response comparison diagram.

4 Analysis of Test Characteristics of Hydro-pneumatic

Suspension
4.1 Test System Composition
4.1.1 Hardware of test system
The test hardware equipment includes test bench, tested hydro-pneumatic
suspension, hydraulic source system, signal conditioning module, data acqui-
sition card and output card.
The test bench is mainly composed of guide column, loading cylinder and
hydro-pneumatic suspension. The test bench is equipped with displacement
sensor and force sensor. The test of hydro-pneumatic suspension is com-
pleted through data acquisition. The test bench can realize the performance
test of hydro-pneumatic suspension, including displacement characteristic
test, speed characteristic test, fatigue test and so on. The three-dimensional
diagram of the test bench is shown in Figure 19.
The test object is the hydro-pneumatic suspension of the snow removal
vehicle. The total stroke of the hydro-pneumatic suspension is 200 mm, the
diameter of the cylinder barrel is 110 mm, the diameter of the piston rod
is 90 mm, the volume of the accumulator is 1.2 L, and the initial inflation
pressure is 2 MPa.

4.1.2 Test system software

LabVIEW is selected as the measurement and control system development
software of hydro-pneumatic suspension test bench, and the test parameters
are displayed and recorded in the computer. LabVIEW software can be
 Research on Hydro-pneumatic Suspension Test Bench 555

1. Guide column; 2. Loading cylinder; 3. Guide rail; 4. Pull pressure sensor; 5. Hydro-
pneumatic suspension; 6. Displacement sensor.
Figure 19 Hydro-pneumatic suspension test bench structure diagram.

developed and used by users according to their own needs and corresponding
experimental purposes through graphical symbols.

4.2 Test Data Analysis

4.2.1 Sinusoidal signal reproduction of loading system
In order to verify the effectiveness of fuzzy PID control algorithm with
compensation in the loading system, the sinusoidal signal tracking test is
carried out on the electro-hydraulic proportional position control system
of hydro-pneumatic suspension test-bed. The specific process of the test
is to input sinusoidal signal I with excitation frequency of 0.01 Hz and
amplitude of 30 mm and sinusoidal signal II with excitation frequency of
1 Hz and amplitude of 30 mm to the loading control system respectively.
The output effects of the two sinusoidal curves are shown in Figures 20 and 21
respectively. The upper half of the Figure is divided into sinusoidal input and
feedback signal test curves, the blue curve represents the given signal and
the yellow curve represents the actual output signal; The lower part is the
real-time position error of the two curves in a period of time.
In order to test the output effect of loading cylinder under different
amplitude conditions, the input amplitude is 50 mm without changing the
excitation frequency. The output effects are shown in Figures 22 and 23
respectively.
The maximum absolute error values of Figures 20 and 21 are 0.82 mm
and 3.4 mm respectively, and the error rates are 2.73% and 11.3% respec-
tively. The absolute values of the maximum errors in Figures 22 and 23 are
556 X. Bai et al.

Figure 20 Test signal 0.01 Hz/30 mm.

Figure 21 Test signal 1 Hz/30 mm.

Figure 22 Test signal 0.01 Hz/50 mm.

 Research on Hydro-pneumatic Suspension Test Bench 557

Figure 23 Test signal 1 Hz/50 mm.

Figure 24 The original curve of elastic force.

1.36 mm and 6.23 mm respectively, and the error rates are 2.72% and 12.5%
respectively. The test error rate is less than 15%, which meets the standard of
construction machinery. Therefore, the test bench meets the test requirements
of hydro-pneumatic suspension. (In Figure 23, the error increases over time
because of sensor drift caused by interference from the external environment).

4.2.2 Hydro-pneumatic suspension stiffness characteristic test

Under low-frequency excitation, because the relative movement speed of
suspension cylinder and cylinder barrel is very small, the damping hole has
little effect on the obstruction of low flow rate oil, so it can be approxi-
mately considered that the elastic force is the only output force of piston
rod [21]. Therefore, the loading curve of stiffness characteristic test is signal
I, with excitation frequency of 0.01 Hz and amplitude of 30 mm. Before
the test, adjust the hydro-pneumatic suspension to the balanced position, and
Figure 24 shows the original curve of elastic force.
558 X. Bai et al.

Figure 25 Elastic force curve after removal of friction.

It can be seen from Figure 24 that the compression and tensile stroke of
the test curve do not coincide, and the noise generated by the vibration of
the test bench during the hydro-pneumatic suspension stiffness characteristic
test makes Figure 24 with sawtooth fluctuations. In order to obtain the elastic
force curve of hydro-pneumatic suspension, in view of the small fluctuation
of velocity, it can be assumed that the friction force is a pair of fixed values
with the same size and opposite direction, and the average value of the two is
the friction force and the filtering algorithm is used for denoising. The smooth
elastic force curve after removing friction is shown in Figure 25.
As can be seen from the figure, the stiffness of the hydro-pneumatic
suspension increases with the increase of the relative displacement between
the piston and the cylinder barrel. When the relative displacement is small, the
stiffness of the suspension is small. With the gradual increase of the relative
displacement, the stiffness also becomes larger and larger.

4.2.3 Hydro-pneumatic suspension damping characteristic test

The relationship curve between the damping force of hydro-pneumatic sus-
pension and the relative displacement between cylinder barrel and piston
is the indicator diagram, and the relationship curve between the damping
force and its relative speed is the speed characteristic diagram. The indicator
diagram can characterize the advantages and disadvantages of the vibration
damping performance of hydro-pneumatic suspension. The fuller, smoother
and undistorted indicator diagram indicates that the higher the efficiency of
the vibration damping performance of hydro-pneumatic suspension.
 Research on Hydro-pneumatic Suspension Test Bench 559

Figure 26 Indicator diagram.

Figure 27 Velocity characteristic diagram of damping force.

The indicator loading curve selected in this paper is signal II, with
frequency of 1 Hz and amplitude of 30 mm. At this time, the output force of
hydro-pneumatic suspension is the sum of damping force, elastic force and
friction force. Therefore, the damping force can be obtained by removing
the elasticity and friction force from the output force curve. The indicator
diagram curve and damping force speed characteristic diagram are shown in
Figures 26 and 27. The compression and extension stroke of hydro-pneumatic
suspension are distinguished by the damping force. The part greater than zero
is the compression stroke, and vice versa.
It can be seen from Figures 26 and 27 that the damping force of the hydro-
pneumatic suspension extension stroke is greater than that of the compression
560 X. Bai et al.

stroke. This way can make the hydro-pneumatic suspension give full play to
its elastic characteristics when it is in the compression stroke, and give full
play to its damping performance when it is in the extension stroke, so as
to quickly attenuate the vibration. In addition, the damping force of hydro-
pneumatic suspension increases with the increase of piston speed. At the
same speed, the damping force of extension stroke is about 2∼4 times that of
compression stroke.

5 Conclusion
(1) According to the test requirements, the test bench is built, which can
complete the performance test of hydro-pneumatic suspension and 1/4
vehicle road simulation test.
(2) The conventional PID control model and fuzzy PID control model are
built in Matlab/Simulink platform. Compared with conventional PID
control algorithm, the maximum error of fuzzy PID control algorithm for
sinusoidal signal reproduction is reduced by 56.8%, and the lag time is
reduced by 70%; For step signal reproduction, the time required to reach
the steady state is reduced by 51.5%, and there is almost no overshoot.
The fuzzy PID control algorithm is suitable for the electro-hydraulic
proportional system of hydro-pneumatic suspension test bench.
(3) Taking LabVIEW as the software platform, the electro-hydraulic propor-
tional loading control system program of hydro-pneumatic suspension
test bench is designed and implemented. The sinusoidal system tracking
test results show that when the test signals are 0.01 hz/30 mm and
1 Hz/30 mm, the error rates are 2.73% and 11.3% respectively; When the
test signal is 0.01 hz/50 mm and 1 Hz/50 mm, the error rate is 2.72% and
12.5% respectively. The results show that the sinusoidal curve output
by the electro-hydraulic proportional loading control system meets the
actual requirements.

Authors’ Contributions
Relevant investigation, Meng Sun and Hui Li; conceptualization, Liqun Lu;
computing method, Xin Bai; model establishment, Meng Sun and Leilei Zhao
and Hui Li; reliability study, Liqun Lu and Leilei Zhao; resources, Liqun Lu;
Write manuscript, Liqun Lu and Xin Bai.
 Research on Hydro-pneumatic Suspension Test Bench 561

Acknowledgments
General project of Shandong Natural Science Foundation (ZR2020ME127).

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Biographies

Xin Bai, born in 1999, she is a master’s student in the School of Transporta-
tion and Vehicle Engineering, Shandong University of Technology, China,
mainly engaged in the research of vehicle suspension control system and parts
design theory and technology.

Liqun Lu, born in 1969, associate professor of the School of Transportation

and Vehicle Engineering of Shandong University of Technology, China.
He obtained his Ph.D. degree in vehicle engineering from the University
of Science and Technology Beijing in December 2008, mainly engaged in
the research of intelligent control of special vehicles and key components,
electro-hydraulic control system related technologies.
564 X. Bai et al.

Meng Sun, born in 1998, she is a master’s student in the School of Trans-
portation and Vehicle Engineering of Shandong University of Technology,
China, mainly engaged in fluid transmission control technology and the
design and research of key components of hydraulic systems.

Leilei Zhao, born in 1982, associate professor of the School of Transporta-

tion and Vehicle Engineering of Shandong University of Technology, China.
He received his Ph.D. degree in mechanical and electronic engineering from
Beijing University of Posts and Telecommunications in June 2019, mainly
engaged in the design theory and technology research of vehicle suspension
systems.
 Research on Hydro-pneumatic Suspension Test Bench 565

Hui Li, born in 1995, he obtained a master’s degree in transportation

engineering from Shandong University of Technology, China in June 2021,
mainly engaged in the design theory and technology research of vehicle
suspension systems.