This document presents SEA, an experimental testing environment for electrohydraulic actuators. SEA allows for precise measurement of important actuator variables to enable comprehensive static and dynamic characterization. It includes a hydraulic pump and pipelines, configurable loads, an instrumented manifold for measurements, and a DAQ system. Experimental results from characterizing an aerospace actuator using SEA are provided, including static calibration, transient response testing showing high pressure and flow demands, and system identification to develop an input-output mathematical model. SEA provides an effective environment for full experimental characterization of electrohydraulic actuators.

1. SEA - an identification and testing environment for
electrohydraulic actuators
Alexandro Garro Brito
Institute of Aeronautics and Space – Brazil
alegbrito2@gmail.com
Abstract
The electrohydraulic actuators are commonly used in applications where a high
power×weight ratio is necessary, such as attitude control system of aerospace vehicles.
During the system design, the full actuator characterization is an important task and it
should be performed in a safe, versatile and precise testing bench. This paper presents
a complete experimental environment for electrohydraulic actuators. In addition to
an easy and fast charge selection, the proposed system provides precise measurement
of the most important variables for a comprehensive static and dynamical character-
ization. Some results from a real aerospace actuator are presented to illustrate the
testing bench efficacy.
1 Introduction
The EHA consists of a powerful component in control systems that blends the versatility
of electrical components with hydraulic actuators performance at high power levels. In this
way, several dynamic effects are present and one should pay attention to some details in the
modeling procedure.
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2. 2 Electrohydraulic actuators – EHA
The EHA consists of a powerful component in control systems that blends the versatility
of electrical components with hydraulic actuators performance at high power levels. In this
way, several dynamic effects are present and one should pay attention to some details in
the modeling procedure. Fig. 1 presents a simplified block diagram for this system. The
servovalve stage converts the input voltage (Vi), the supply pressure (PS) and the load
pressure (PL) in a load flow (QL) to be applied to the hydraulic cylinder. This cylinder is
in charge of producing the load force (fL) necessary to provide the load stroke displacement
(xp).
A thorough modeling discussion for the electrohydraulic actuator is present in (Merritt
1967). In this paper, only the most important equations are presented.
Figure 1: Electrohydraulic actuator block diagram
2.1 The servovalve dynamics
The turbulent flow through an orifice occurs at high Reynolds number and is modeled by
applying the Bernoulli’s equation. This analysis yields the well-known volumetric flow rate
Q = CdA0
2
ρ
(P1 − P2) (1)
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3. where Cd is the discharge coefficient, A0 the orifice area, ρ the mass density of fluid and
(P1 − P2) the pressure drop. Considering a typical four-way spool valve where the orifice
areas depend on the valve geometry, their four areas are functions of valve displacement
xv which is related to the input voltage. The mechanical actuator mounting can introduce
nonlinearities in this displacement, mainly dead-zones.
The load flow as a function of valve position and load pressure is given by the nonlinear
relation
QL = Cdwxv
1
ρ
(PS −
xv
|xv|
PL) (2)
where PS is the supply pressure and w ≡ ∂A/∂xv ([w] = m2
/m) is the area gradient of the
valve.
The fluid flowing through uncompensated valve orifices causes forces with a direction
such that it tends to close the valve port. The magnitude of this force is given by
F1 = 2CdCvA0(P1 − P2)cos(θ) (3)
where, typically θ ≈ 69◦
is the jet angle of vena contracta, Cd ≈ 0.61 is the discharge
coefficient, Cv ≈ 0.98 is the empirical factor called velocity coefficient and ∆P = P1 − P2
the pressure drop. By using Eq. 3 and the numerical values above, one can yield the usual
form of the steady-state flow force equation
F1 = 0.43w∆Pxv = Kf xv. (4)
Merritt (Merritt 1967) comments that on larger single stage EHA this force can exceed 20lb
(9kgf). The reduction of this steady-force flow force can be obtained by using two-stage
configuration or geometric compensating techniques. These compensations can lead to a
nonlinear function between the flow force and the stroke displacement.
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4. 2.2 The cylinder dynamics
The continuity equation combined with the equation of state (ρ = ρ(P, T)) leads to the
expression for the load flow in the cylinder chamber
QL = Ap
dxp
dt
+
Vp
4β
dPL
dt
(5)
where β is the Bulk modulus (for mineral oils and for common values for pressure and
temperature, β is typically 1400 to 1600 MPa) and Ap and Vp are, respectively, the section
area and the chamber volume of the cylinder. The term Vp/(4β) is equivalent to a linear
hydraulic capacitance, known as CH. Since the servovalve is generally attached to the
cylinder, the high pressure lines are sufficiently short and additional hydraulic capacitances
due to this lines can be neglected. Finally, the load force (fL) is given by
fL = ApPL. (6)
3 SEA testing environment
A complete environment is necessary to perform the experimental characterization of electro-
hydraulic actuators. By providing reliable measurements in a proper operational condition,
this testing bench is important to deliver the necessary data to be used in further studies.
This section presents SEA, a portuguese acronymous for Experimental System for Actu-
ators. A general SEA schematic diagram is presented in Figure 2(a), while a picture of its
final configuration is shown in Figure 2(b). The main idea behind SEA is to drive proper
levels of pressure and flow rate to the actuator for different load levels and excitation inputs.
Meanwhile, several measurements are performed and the final data is used for a complete
actuator characterization. It follows a comprehensive description of SEA components.
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5. (a)
(b)
Figure 2: SEA servovalve testing bench – functional diagram (a) and system picture (b).
3.1 Hydraulic pump and pipelines
The hydraulic pump is the main power source and its design is obviously based on the
pressure demanded by the actuator. In this experimental environment, a Hydraulic Unity is
used. The nominal operational pressure is set to 120 Bar with a flow rate of 12 lpm. These
are common values for a wide range of actuators commercially available.
The pipelines which carry the hydraulic fluid to the actuator should be designed to
support extremely high pressure values. Moreover, they should be leakage and corrosion
free. A pipeline with such characteristics is generally constructed through stainless steel
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6. tubes with proper connections. SEA uses a pipeline circuit made from stain-steel tubes with
diameters 16 and 24 mm for the pressure and return hydraulic lines, respectively. Special
connection process is used to avoid leakage. Each hydraulic line is about 12 meters long
from the pump to the testing bench.
3.2 Load
For a proper EHA characterization and identification, several load conditions should be
available. Additionally, it is important an easy and fast load replacement during the tests,
what improves the productivity.
In SEA, the actuator load is formed by a mass-spring set attached to the testing bench.
There are four available mass weights and five different springs. The values were carefully
measured, what provides proper control over the applied forces during the experiments. In
addition, the values were chosen so that the actuator is tested in all of its operational range.
The load can be selected by mounting the available masses and springs in the SEA load
chart, as it can be seen in Figure 3. If necessary, the load condition can be easily modified
by replacing the mass-spring combination.
(a) (b)
Figure 3: SEA load scheme – mass (a) and spring (b) mounting options.
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7. 3.3 Measurement unity
In many electrohydraulic actuators, both servovalve and cylinder are directly mounted as
a unique element. This is very common in aerospace applications where the dimension
restriction is a strong issue. Then, direct measurements from cylinder pressure and flow
rate are difficult to obtain, and most of the actuator characterization should be performed
through the actuator input pressure and flow rate.
In SEA, there is a instrumented manifold which measures the main hydraulic input
variables (Figure 4). This is connected to the actuator and the pipelines through proper
high-pressure hoses. Three hydraulic measurements are available: pressure supply, input
flow rate, and fluid temperature. In addition, a precise measurement of the actuator stroke
displacement is provided. These four variables can be used to obtain the most important
actuator phenomenological behavior.
Figure 4: SEA instrumented manifold.
The pressure is measured by an extensimetric thick film transmitter with range 0 to
250 Bar. The flow rate measurement is provided by a turbine flow meter picked up with a
pulse counter. In this case, the pulse frequency is proportional to the actual flow rate, in a
range between 0 to 25 lpm. The pressure and flow sensors are attached to the manifold and
cover a wide range of values with fast response, thereby enabling proper static and transient
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8. operational characterization.
The fluid temperature is provided by a termoresistence sensor also attached to the man-
ifold. Values up to 120 ◦
C can be precisely measured. Finally, the stroke displacement is
measured through a high-precision potentiometer transducer.
3.4 DAQ and Command generator
All the measurements are digitally acquired by a software implemented in LabView c . A
computer running a specific acquisition routine is connected to a National Instruments NI
USB-6259 system. This is a very flexible equipment that enables fast and reliable input
and output analog signal acquisition. The four measured signals are connected to analog
inputs and the acquired data is properly saved into files for further analysis. The routine
also generates the actuator command profile, which is available at an analog output of
DAQ system and it is applied to the servovalve input. In addition to the classical input
signals used for characterization and identification (sine, square, step and swept-sine signals),
the software can also read points from an external data file. This increases the testbench
versatility, by enabling arbitrary signals whose sampling frequency is up to 1kHz. Figure 5
shows the routine screen in a typical experiment.
Figure 5: FOTO TELA
4 Aerospace actuator characterization
This section presents some experiments aiming at a whole actuator characterization through
SEA testing bench. For this paper, an aerospace electrohydraulic servovalve is studied. This
class of equipment has the servovalve and cylinder parts directly mounted. Although this is
very important for weight and dimension saving, many important internal variables cannot
be measured, and all the characterization should be obtained through the hydraulic supply
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9. variables (pressure, flow rate and temperature), the input command voltage and the stroke
displacement.
4.1 Static and transient characteristics
Although a simple test, the static characterization is the main experiment for the general
actuator knowledge. It consists in obtaining the relation between the commanded input
voltage and the actuator stroke displacement. In SEA context, this experiment can be
performed with different loads and several hydraulic supply conditions (pressure, flow rate,
etc). This testing bench also enables the hysteresis evaluation by applying a proper input
profile. An example of such experiment for the actual actuator under test is presented in
Figure BLA. Notice that...
In real applications, aerospace actuators are commonly supplied by pressurized vassels
instead pumps. These vassels and the whole hydraulic circuit should be properly designed
for normal operational conditions. However, the servovalve can demand extremely high
pressure and flow rate during the transient condition where a fast stroke displacement is
required, and the hydraulic circuit has to resist such condition as well. Hence, the transient
characterization, which consists in measuring the pressure and flow rate values during an
impulsive command, is extremely important during the hydraulic design. Figure 6 shows
a transient test performed for the aerospace actuator. Square input profiles with different
amplitudes are used, and the pressure supply, line flow rate and stroke displacement are
acquired. In this case, full load is considered.
Some conclusions can be drawn from Figure 6. While maintaining nominal values for
pressure and flow rate during a static condition, very high values are demanded in transients.
In fact, the pressure supply can achieve values almost 20% higher than nominal and the flow
rate can be increased up to 20 times from the nominal value. Such transient experiment
is useful to improve the actuator knowledge and, in addition, it provides information that
should be considered during the hydraulic circuit design.
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10. (a) (b)
Figure 6: Aerospace actuator dynamic characterization. Pressure (a) and flow rate (b)
responses.
4.2 Model identification
A mathematical model of the actuator is necessary for many control and simulation purposes.
In spite of being possible to obtain the internal physical parameters of Section 2 so that those
equations can be used, such procedure is a hard task due to the several unmeasured internal
variables. Hence, an input-to-output model is commonly used, and SEA enables an easy
data acquisition to obtain it.
The input signal used for model identification in this paper is the random pulse train. It is
basically a square signal where both amplitude and pulse width is continuously changed along
the experiment. The limitations for such amplitude and pulse width are based on general
dynamic system characteristics such as time constant. This signal has a rich excitation
profile which is able to provide reasonable conditions for linear and nonlinear identification.
For the studied aerospace actuator the maximum stroke displacement was less than 6 mm
and the pulse width was in the interval between 0.01 and 0.06 seconds. The actuator stroke
response for such signal is presented in Figure BLA.
For this paper a discrete autorregressive input-output ARX model was used (Ljung 1987).
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11. This model relates the output at a defined instant of time to values from input and output
for previous instants. The adopted model for the aerospace actuator is represented by
Equation 7.
y(k) = α1y(k − 1) + α2y(k − 2) + β1u(k − 1) + β2u(k − 2). (7)
The objective is to obtain the parameter values such that the model is adequate to represent
the actuator dynamic behavior. An extended least squares procedure (Ljung 1987) was used
for parameter estimation and it resulted in the parameter values presented in Table ??. The
model response was then verified by using a different data set with similar characteristics.
The result is presented in Fig. ??. Notice that the model was able to represent the actuator
behavior for such operational condition.
5 Conclusions
The main objective of this paper is to provide some information about electrohydraulic
actuators. It discusses the most important experiments that should be performed during
their characterization and, in addition, it presents SEA – a proposed environment for the
actuator testing. As demonstrated, such testing bench is useful for performing many exper-
iments, what includes static and dynamic tests and actuator modeling. Then, it provides
the necessary experimental resources for a complete actuator study.
Some experiments were performed for a specific aerospace actuator. Initially, a calibra-
tion test was presented and some remarks concerning its utility were drawn. The dynamic
characterization showed that extremely high values of pressure and flow rate should be ex-
pected during transients, and the designer should be aware of such behavior. Finally, it was
peresented the identification step of an autorregressive ARX model.
By using the provided information, the reader can have some insights of how perform-
ing similar experiments. Moreover, the presented ideas can be used as inspiration during a
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12. similar testing bench development, which fits its necessities. Finally, one finds relevant infor-
mation about electrohydraulic actuators, their physical characteristics, and some remarkable
experimental issues.
References
Ljung, L. (1987). System identification - theory for the user, Prentice Hall.
Merritt, H. E. (1967). Hydraulic control systems, John Willey & Sons.
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