HIGH FREQUENCY MODELING OF A HYDRAULIC ACTUATION FLIGHT CONTROL
SYSTEM
Carlos Augusto Constantino 1
Prof. Dr. Luiz Carlos Sandoval Góes 2
Dr. Fernando José de Oliveira Moreira
3
1
ITA, São José dos Campos, Brazil, [email protected]
2
ITA, São José dos Campos, Brazil, [email protected]
3
ITA, São José dos Campos, Brazil, [email protected]
Abstract: The objective of this work was to develop a high
fidelity model representative on high frequencies of a FCS
with an active-active hydraulic actuation. The performance
for step input and frequency response were analyzed,
showing to be a model close to a real system and
representative even in high frequencies.
1. Subject of Work
Early Aircraft used mechanical systems, in which the
amount of force that can be applied into the surface is
directly related to the forces that a pilot can make.
To solve the mechanical control issues it was developed
the hydraulic powered system, which consists in a linkage
between the pilot command and a servovalve that controls a
hydraulic powered actuator.
Due to safety requirements, usually it is needed more
than one actuator per surface, each one connected to a
different hydraulic supply. Each actuator has a specific
normal operation mode, such as active, bypass, damped or
blocked. On an active-active design both actuators work in
parallel to move the surface, in case of an actuator failure,
the system will go to an active-bypass mode.
Another breakthrough in FCS technology was the advent
of the Fly-by-Wire system, which consists on the same
actuators connected to the surface, but instead of cables
transmitting the pilot command to the servovalve, it is used
an electronic signal processed by a Flight Control Computer
for a given pilot input. This system allowed reduction of
weight for bigger aircrafts and also the implementation of a
closed loop control law of the aircraft, allowing the
development of higher performance aircraft.
The work here presented will study a Fly-by-Wire
hydraulic powered FCS with an active-active configuration
and will be analyzed one of its critical drawbacks, the ForceFight that is generated between the actuators.
There are methods on the industry used to eliminate the
Force-Flight by developing an active control of each
actuator individually, but these controls do not eliminate
completely the Force-Fight especially at dynamic
conditions.
Nevertheless the aircraft structure can be designed to
tolerate a predicted level of Force-Fight throughout the
aircraft life, unless a failure that generates a higher ForceFight occurs.
The studies developed up to date were made considering
a model of low frequencies dynamics of the hydraulic
actuation. The subject of this work intent to study this
response considering that it is possible to have structural
fatigue damage even for high frequencies – up to 100Hz –
for that was developed a high fidelity model considering
relevant dynamics up to high frequencies.
2. System Description
2.1. FCS Description
The architecture of a hydraulic powered Fly-by-Wire
system can be basically divided by these 3 parts: the Pilot
Input, the Electronic System and the Hydraulic Actuation
System
The Pilot Input made by a column wheel or a sidestick,
is sent to the Electronic System, which will process the
signal and send a command to the servovalve of the
hydraulic actuator, such that the resultant surface
displacement meets the pilot input.
2.2. Electronic System Description
The Electronic System is composed by a Flight Control
Computer which receives the pilot command and processes
it into a command current for the actuator servovalve.
To make this conversion it is implemented a position
loop, where the error signal between the actuator command
and the real position is processed and converted in a current
command to the servovalve.
This position loop controller is critical in order to meet
performance requirements of the actuation system and will
be modeled herein.
2.3. Hydraulic Actuation System Description
The hydraulic actuation system is composed by series of
control valves, such as the servovalve, mode select valve,
1
Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications
Serra Negra, SP - ISSN 2178-3667
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HYDRAULIC ACTUATION SYSTEM MODELING: AN ANALYSIS OF HIGH FREQUENCY MODELING
Carlos Augusto Constantino
check valve, pressure relief valve and solenoid operated
valves, all of them are joined together in order to allow a
safe and proper function of the actuator.
A schematic diagram of a hydraulic actuator can be seen
on the Fig. 2-1, where the number means:
1. Servovalve
2. Mode Select Valve
3. Anti-Cavitation Valves
4. Solenoid Operated Valve
5. Check Valves
6. Reservoir
7. Actuator
8. Surface of control
hydraulic loss considering all the external leakages of the
actuator. The pressure must be guaranteed since the
damping characteristics of the actuator changes drastically
with a reduction of the pressures inside the chambers.
3. FCS Model
The overview of the whole modeled system can be seen
on the Fig. 3-1.
Fig. 3-1 – Overview of the Hydraulic Actuation System
Fig. 2-1 – Hydraulic Diagram
The servovalve is a solenoid commanded valve which
connects the pressure and return lines from the hydraulic
system to each chamber of the actuator depending on the
amount of current that is inserted on the solenoid.
The mode select valve herein presented is a two-mode
valve, active and damped mode, in the industry there is also
tri-mode valves, where one of the mode is the active and the
others are a combination of damped, bypass and blocked
mode.
The mode select valve is piloted by a solenoid operated
valve, which is a valve that connects the hydraulic or the
return pressure to the pilot line by an input command from
the Electronic System, therefore in case of a loss of the
Electronic System the actuator will be automatic set at a
damped state, also the same will happen in case of a
hydraulic loss. Therefore the system is protected in the event
of a hydraulic or electrical failure.
The Anti-Cavitation Valve are used to prevent the
pressure inside each chamber to be less than the return
pressure, possibly causing a cavitation on the actuator, this
valve is very similar to the Check Valves where its function
is to allow the flow to move only to one side.
All the check valves have a spring in order to keep the
flow blocked in one direction, although the difference
between the inlet check valve, connected to the pressure
line, and the return check valve is that the inlet has a very
low cracking pressure to not degrade the actuator
performance, where the return check valve has a high
cracking pressure in order to guarantee a minimum pressure
inside the actuator in case of a rupture of the hydraulic line.
The Reservoir is used to guarantee a minimum fluid
volume and pressure inside the actuator in case of a
It can be seen on the Fig. 3-1only the Hydraulic System
and the Actuation System, this is due to the decision to
group all the Flight Control Systems (FCS) on one block.
Theta_Cmd_(deg): The Theta Command in degrees is an
input from the Pilot to the actuations system.
Load_(Nm): Is the Hinge Moment of the aerodynamic
load.
Hydraulic System 1 & 2: It is a simplified model of the
Hydraulic System, emulating the pressure loss due to the
flow demand.
FF_Loads_(N): Resultant load applied on the Surface
Structure due to the actuator movement.
ThetaS_(deg): Resultant surface position in degrees.
Q_Suppy1 & 2_(gpm): Hydraulic flow demand of the
actuators.
3.1. Hydraulic System
The Hydraulic System modeled is based on a fixed
pressure pump usually found on airplanes, this pump does
not regulate the flow however it controls the stagnation
pressure of the pump line.
Through the Bernoulli equation one can find [1]:
1
(1)
p0= p + ρV 2
2
p0 : Stagnation Pressure
p : Static Pressure
1
ρV 2 : Dynamic Pressure
2
Once that we have a constant stagnation pressure, as we
increase the hydraulic flow through the line, the available
static pressure decreases.
Since the actuation system force is generated by the
static pressure, the effects of a pressure loss due to the
actuator displacement must be designed in order to have a
minimum degree of fidelity.
Proceedings of the 9th Brazilian Conference on Dynamics Control
2 and their Applications
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Nonetheless there is also the pressure loss of the
hydraulic system, due to the line flow and the tubing losses,
which must be considered.
As described in Fox [1];
(2)
p1 − p2 =ρ ⋅ hl
hl = f
L V2
D 2
(3)
64
Re
(4)
hl : The pressure loss
f : The friction factor, which is a function of Reynolds
and the tubing properties.
For laminar flow the value for the friction factor f is:
f =
model is designed here, which is the interaction between the
two displacements of both actuator, once that is not possible
to have a perfect aligned displacement between both
actuators, there will be always some force being generated
by the difference of the movements.
3.3. Electronic System
Once that the flight control computer receives a analog
input and the position loop is processed digitally, it was
designed a Hardware_in block and a Hardware_out block
where the analogical signal is converted to digital and vice
versa.
Also it was added an LVDT block which represents the
dynamics of the signal of the LVDT sensor and the
tolerances of it.
Therefore the resultant pressure loss, considering a
laminar flow through the hydraulic system, is proportional
to the velocity.
On the Hydraulic System block was also implemented a
Fluid Inertia that can be understood as a Low Pass Filter,
where the high frequency variations of flow does not impact
the pressure due to the inertia of the hydraulic line.
3.2. Actuation System
The actuation system was divided in 3 parts: electronic
system, actuator and surface, as can be seen on the Fig. 3-2
below.
Fig. 3-3 – Electronic System Block
3.3.1. Position Loop
Fig. 3-4 – Position Loop Block
Fig. 3-2 - Actuation System Block
The electronic part represents the signal processing and
the position loop, where the command in degrees is
processed with the actual piston position to generate the
equivalent command as a current to the EHSV in the
actuator.
The actuator block represents the EHSV and the piston
dynamic, the input of this block is the Hydraulic pressure
given by the Hydraulic System 1 & 2 and the current
command. The results of the actuator block are the actuator
dynamics, the feedback position of the piston and the flow
demand to the Hydraulic system.
The surface block represents the interface with the
surface, where for a given increment of piston position, the
surface reacts due to its inertia, also an important part of the
The Position Loop Block converts theta command into
current command for the servovalve. To do so it has a PID
Controller of the error in linear actuator position, feedback
from the ram lvdt of the actuator.
The theta commanded signal is treated in order to be
transformed in a linear command. First the command input
rate is limited in order to not demand too much velocity of
the actuator, depleting the hydraulic system due to a high
flow demand.
After limiting the command rate, the command is limited
to the surface design stops. Afterward, the signal in theta
command is converted in linear command by the kinematics
block, which is subtracted by the feedback position from the
ram lvdt, resulting in the position error.
The Position error is then processed by a discrete PID
controller as shown on Fig. 3-5.
3
Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications
Serra Negra, SP - ISSN 2178-3667
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HYDRAULIC ACTUATION SYSTEM MODELING: AN ANALYSIS OF HIGH FREQUENCY MODELING
Carlos Augusto Constantino
Fig. 3-5 – PID Controller Block
3.4. Actuator Block
Fig. 3-6 – Actuator Block
The actuator Block is composed by the Valve and the
Cylinder Dynamics.
The Valve Dynamics Block evaluates the dynamics of
the EHSV and the inlet and return check valves, defining the
hydraulic pressures inside the inlet and return lines.
Afterward the flow through each chamber will be
evaluated taking into account the lines and the chambers
pressures.
The Cylinder Dynamics evaluates, for a given hydraulic
flow in and out the cylinder, the amount of hydraulic
pressure that results inside each chamber, which will be
integrated in a 2nd order piston dynamics, resulting in the
piston position, Xp.
3.4.1. Valves Dynamics
represented by two blocks, the EHSV 1st Stage Block and
the EHSV 2nd Stage Block.
The hydraulic pressure provided by the hydraulic system
is inserted on the Inlet and Return Check Valves, which, in
possession of the other flows going inside and outside the
volume, will evaluate the remaining pressure downstream
the check valve, and also the resultant flow through the
hydraulic system.
The pressures downstream the check valves will be used
as input to the EHSV, which, with the current command,
will result in a spool position – 1st Stage – and with the
spool position will allow a hydraulic flow through each path
inside the EHSV – 2nd Stage.
The equation of the flow through an orifice can be
applied to evaluate the flow of the inlet check valve,
although the value of the discharge coefficient is variable
with the differential pressure on the valve.
The discharge coefficient will be zero when the pressure
Ps_CV is higher than the Ps, and will be maximum when Ps
minus Ps_CV is equal to the cracking pressure of the spring
inside the check valve.
Usually for the inlet check valve is used a low cracking
pressure in order to not corrupt the hydraulic flow coming
inside the actuator.
The flow though the valve can be evaluated by the
Bernoulli Equation for incompressible fluids as can be
found on Fox [1] and is given by:
2∆P
(5)
QCV = Cd ACV
ρ
Where:
QCV : Flow though the valve
Cd : Coefficient of Discharge
ACV : Check Valve Orifice Area
∆P : Delta Pressure on the valve sides
ρ : Fluid density
To evaluate the pressure Ps_CV it can be used the
continuity equation given by:
Q=
net
dV V dP
+
dt β e dt
(6)
Where:
Qnet : Net Flow through the volume
dV : Volume variation during time
dt
β e : Bulk Modulus
V dP : Fluid compressibility
β e dt
Fig. 3-7 – Valves Dynamics
The volume of analysis is the line between the check
valve and the EHSV, therefore the net flow is the flow
through the inlet valve minus the flow going inside the
servovalve.
The Fig. 3-8 shows the Inlet Check Valve as designed on
the model based on equations (5) and (6).
The Valve Dynamics Block, as mentioned before,
evaluates the EHSV and the check valves dynamics.
Therefore it is divided in 3 parts, the Inlet Check Valve
Block, the Return Check Valve Block and the EHSV herein
Proceedings of the 9th Brazilian Conference on Dynamics Control
4 and their Applications
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The flapper then directs the hydraulic flow to one side of
the spool, increasing the pressure of this side, thus making it
moves to the opposite direction of the flapper displacement,
until the feedback spring force balances the flapper torque.
The Fig. 3-10 shows the operation of the EHSV as
described above.
Fig. 3-8 – Inlet Check Valve Block
The Return Check Valve is essentially the same valve as
the Inlet Check Valve, but in this case its intent is to prevent
pressure lost inside the actuator in case of a failure in the
hydraulic system.
The minimum pressure required inside the actuator in a
failure scenario usually is around 100psi. Therefore the
cracking pressure of the return check valve must be sized for
this particular case.
Although the Anti-Cavitation Valves will be
implemented furthermore, the flow through these valves will
have to be considered for the evaluation of the net flow
inside the volume of the return line.
3.4.2. EHSV Modeling
In order to model an actuation system with a high
fidelity up to high frequencies, a high detailed servovalve
must be modeled. Therefore some clarifications of how the
ESVH works will be described.
The Fig. 3-9 shows a schematic two stage EHSV
Fig. 3-10 – EHSV Operation
Source: http://www.moog.com/literature/ICD/jet_pipe_servovalves_overview.pdf
accessed at 07 Mar 2010
The armature torque equation can be evaluated as by
Merrit [2]:
(7)
K=
J a s 2θ + K anθ + rPLp AN + ( r + b ) K f ( r + b ) θ + xv 
t ∆i

Where:
K t : Torque constant of the torque motor
∆i : Delta current as input to the servovalve
J a : Inertia of armature and any attached load

θ : Rotation angle of the flapper
K an : Net spring rate
r : Distance between center of armature and flapper
PLp : Flapper valve load pressure
AN : Nozzle area
b : Distance between flapper and spool
K f : Spring constant feedback spring at the free end
xv : Spool position
The value of the coefficient rPLp AN was considered very
Fig. 3-9 – 2 Stage Electro-Hydraulic Servovalve (EHSV) Schematic
Source: Merrit, Herbert E. – “Hydraulic Control Systems” [2]
A given delta current is inserted on the EHSV and is
generated an electromagnetic field though the solenoid. This
field, in the presence of the permanent magnet, generates a
torque on the flapper.
small and should not interfere on the spool dynamics. Also it
is a standard practice on the servovalves design that the
value of K an is equal to zero in order to maximize the spool
velocity constant [2], therefore the transfer function between
the current and the flapper angle is:
∆θ
1
(8)
=
K t ∆i − ( r + b ) K f ∆xv
Ja s2 + K f ( r + b)
2
5
Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications
Serra Negra, SP - ISSN 2178-3667
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HYDRAULIC ACTUATION SYSTEM MODELING: AN ANALYSIS OF HIGH FREQUENCY MODELING
Carlos Augusto Constantino
The transfer function of the flapper to the spool position
is given by Merrit [2]:
K qp
(9)
Av
∆xv
=
2
∆x f
 s

2δ
+ hp + 1
s
 ωhp 2 ωhp



Also there is a 5th path between Ps and T that will always
have some amount of flow. This is due to the concept of the
valve, using the supply pressure to direct the flow to the
sides of the spool.
The Fig. 3-13 shows the modeled flows through each
path by using the Eq. (5) with an variable orifice area,
function of the spool position.
Where the variables not yet defined are:
∆x f = r∆θ : Linear displacement of the flapper
ωhp =
δ hp =
2 β e Av 2
V0 p M v
: Hydraulic natural frequency of pilot stage
ωhp K cp M v : Damping ratio of pilot stage
2 Av
2
K qp : Flow gain of flapper valve
Av : Area of spool
β e : Bulk Modulus
V0 p : Contained volume at each end spool
K cp : Flow pressure coefficient of pilot valve
In possession of these equations it is possible to create
the block diagram of the servovalve as can be seen on Fig.
3-11.
Fig. 3-11 – EHSV 1st Stage Block
Afterward it has to be evaluated the flow through each
path on the EHSV for a given spool position.
As can be seen on the Fig. 3-12, when the spool moves
to the left, the flow through the land between Ps and A is
released, the same occurs between B and T, where A and B
means the pressure on each chamber of the actuator and Ps
and T, means the supply and return pressure respectively.
Fig. 3-13 – EHSV 2nd Stage Block
After evaluating the flow through each path, the flows
are joined accordingly to the sign convention in order to
evaluate the resultant flow through each chamber and on the
hydraulic lines.
3.4.3. Cylinder Dynamics Modeling
After evaluating the amount of flow that is going in or
out of each chamber, it can be evaluated the build up
pressure inside the chamber and with this value, calculate
the piston dynamics resulting on the piston head position.
Fig. 3-14 – Valve-piston Combination
Source: Merrit, Herbert E. – “Hydraulic Control Systems”
Fig. 3-12 – EHSV Flow Paths
Although the main flow is the one described above, it
has to be considered a leakage value through each land, once
that some amount of leakage is inherent of the construction
of the valve.
Taking as reference the Fig. 3-14 extracted from Merrit
[2] and considering that it should be added the anticavitation valves on the lines that connects the EHSV to the
piston, the continuity equation of the system can be
evaluated and given by:
dV1 V1 dP1
(10)
+
Q1 − Qip − Qep1 + QAC1 =
dt β e dt
Proceedings of the 9th Brazilian Conference on Dynamics Control
6 and their Applications
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Qip − Qep 2 − Q2 + QAC 2 =
Where:
Qip = Cd Aip
dV2 V2 dP2
+
dt β e dt
Ap : Piston Area
(11)
M p : Piston mass
B p : Viscous damping coefficient
2(P1 − P2 ) : Internal leakage between chambers
Qep1 = Cd Aip
Qep 2 = Cd Aip
QAC1 = Cd ACV
QAC 2 = Cd ACV
ρ
2P1
: External leakage on chamber 1
2P2
: External leakage on chamber 2
ρ
ρ
2 ( Pt − P1 )
K p : Piston stiffness
FL : External load
Considering the Eq. (14) it was modeled the Piston
Dynamics Block as shown on the Fig. 3-15.
: Anti-cavitation flow on line 1
ρ
2 ( Pt − P2 ) :
ρ
Anti-cavitation flow on line 2
V2 dP2 : Fluid compressibility
β e dt
Therefore the pressure on each chamber can be found by
the following equations:
1 βe
(12)
( Q1 − Ap x p − Qep − Qip )
s V1
1 βe
(13)
P2
=
( Ap x p − Qep + Qip − Q2 )
s V2
Considering the Eq. (12) and (13) it was modeled the
Fluid Dynamics Block as shown on the Fig. 3-15.
=
P1
Fig. 3-16 – Piston Dynamics Block
It was also implemented another two components on the
equation, these components were added in order to evaluate
the forces reacting on the piston in case of the actuator
hitting the hard stop.
The output of the block is the piston head position, and
in possession of this value, the forces to move the surface
will be evaluated by the Surface Block that will be described
on the next chapter.
3.5. Surface
Fig. 3-15 – Fluid Dynamics Block
Applying Newton’s second law to the forces on the
piston, the force equation can be evaluated as shown by
Merrit [2].
Ap ( P1 − P=
M p s 2 x p + B p sx p + K p x p + FL
2)
Where:
(14)
Fig. 3-17 – Surface Block
The Surface was divided in two parts: the lug that
connects the actuator rod end to the control surface.
In possession of each actuator rod end position Xp1 and
Xp2, and with the linear position of the surface, it can be
found the compression or extension loads within the lug.
7
Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications
Serra Negra, SP - ISSN 2178-3667
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HYDRAULIC ACTUATION SYSTEM MODELING: AN ANALYSIS OF HIGH FREQUENCY MODELING
Carlos Augusto Constantino
Thus the Surface Dynamics Block evaluates the
Newton’s second law in terms of a rotational displacements
and evaluates the new position of the surface, which with
the kinematics, it can be evaluated the horn arm, used to
calculate the torque force on the surface, and the linear
displacement of the surface.
T=
Iθs + Bstrθs + K strθ s + HM
(15)
Where:
θ s = Surface angular displacement
I = Surface Inertia
Bstr = Structural Damping
K str = Structural Stiffness
HM = External Hinge Moment (Air load)
Therefore the Surface Dynamics Block was modeled as
shown on Fig. 3-21.
Fig. 3-18 – Surface Control
Consider that the system is at a static state without
forces, at this scenario the piston head position – Xp – must
be the same of the linear surface position – Xs.
Fig. 3-21 – Surface Dynamics Block
Fig. 3-19 – Xp and Xs at static state without forces
When piston imposes a displacement of Xp compressing
the lug against the surface, the amount of force required is
simply evaluated by Hooke’s Law considering the lug as a
spring.
It was also implemented the reaction between the
differences of displacements from each actuator. It is
expected that each actuator will have its tolerances and
proper dynamics, therefore the position of Xp1 and Xp2 will
not be perfect aligned and a force will be generated torquing
the surface, this is called the Force-Fight forces.
Taking into account all these factors, it was designed the
Lug Forces Block as can be seen on the Figure 3-34.
Fig. 3-20 – Lug Forces Block
After the forces within the Lug were evaluated, the
resultant force that will move the surface is given by the
sum of each actuator force.
Therefore the dynamic of the surface can be evaluated
by the following equation:
With the value of Theta calculated, the only remaining
value to be evaluated is the equivalent linear displacement
of the surface position – Xs.
Therefore it was modeled the Kinematics block which
evaluates the effective horn radius and the linear
displacement of the surface for a given value of Theta.
4. Simulation of the Active-Active System
4.1. Model Results
The first analysis that must be done with the model
intents to show that the dynamic of a hydraulic actuation
system is proper represented. Therefore the model will be
submitted to two types of analysis, the step input and the
frequency response.
4.1.1. Step Input Analysis
The Step Input analysis is used to measure some
indicators of the system performance [3], such as:
• Delay Time (Td): time required to reach for the first time
50% of the final value;
• Rate Time (Tr): time required to go from 10% to 90% of
the final value;
• Peak Time (Tp): time required to reach the first peak
value;
• Settle Time (Ts): time required to reach under 2%
around the final value;
• Overshoot (Mp): maximum percentage of the peak
compared to the final value.
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The peak time compared to the settle time shows that the
system has a good and fast response, and also the overshoot
was very low, something desirable on a real actuation
system.
Both of these cases was run without aerodynamic load,
which can alter the response significantly, therefore it was
run two more cases with 90% of the maximum load that the
actuation was designed to withstand, one case applied as an
opposing load and the other as an aiding load.
The results of these analyses are shown on the Figure 4-5
and Figure 4-6.
Step Input Response Analy sis
18
Ts 0.434
16
14
Fig. 4-1 – Performance Criteria for a Step Input
Mp -0.2%
Tp 0.532
Ess 0.106
Tr2 0.382
Command
System Response
12
Theta (deg)
The results are shown on the Fig. 4-2 and Fig. 4-3, where
the first represents the response to a positive step input of
+15º; and the second a negative step input of -25º.
10
8
Td 0.230
6
4
Step Input Response Analy sis
18
2
Mp 2.1%
Tp 0.434
16
14
Ts 0.437
Command
System Response
Tr2 0.358
0.5
0
1.5
1
Time (s)
Fig. 4-4 – Step Input Response with an opposing load of 90% of
maximum load
12
Theta (deg)
Tr1 0.075
0
10
8
Td 0.208
Step Input Response Analy sis
18
6
Mp 3.9%
Tp 0.430
16
Ess 0.109
Ts 0.525
4
14
2
0
Tr2 0.344
Command
System Response
12
0.5
1
Time (s)
Theta (deg)
0
Tr1 0.061
1.5
Fig. 4-2 – Step Input Response 0º to 15º
10
8
Td 0.195
6
4
Step Input Response Analy sis
0
2
Tr1 0.055
Tr1 0.084
0
-5
0.5
Command
System Response
Time (s)
1
1.5
Fig. 4-5 – Step Input Response with an aiding load of 90% of maximum
load
-10
Theta (deg)
0
Td 0.334
-15
Taking into consideration all the cases for the step input
herein presented, it can be concluded that, for the step input
response perspective, the hydraulic actuation system was
modeled properly.
-20
Tr2 0.583
Ts 0.633
-25
Mp 1.3%
Tp 0.684
0
0.5
Time (s)
1
1.5
Fig. 4-3 – Step Input Response 0º to -25º
The rate of the actuator was limited on the Position
Loop of 40º/s, this can be observed using the values of Tr,
where the average rate measured was 40.4º/s and 40.1º/s.
Once that the average rate of the response was
determined, it can be possible to evaluate the delay time
using the Td information, therefore the response delay
measured was 0.022s for both directions.
4.1.2. Frequency Response Analysis
The frequency response analysis is used to verify the
response of the actuator system under a sine wave input of
command going from 0.1Hz up to 100Hz.
There are two criteria that will be used here to analyze
the frequency response of the actuation system modeled, the
first is the gain and phase margins, and the second is the
frequency at which the system gain is at -3dB, which means
that the response amplitude is 70% of the input command.
9
Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications
Serra Negra, SP - ISSN 2178-3667
1088
HYDRAULIC ACTUATION SYSTEM MODELING: AN ANALYSIS OF HIGH FREQUENCY MODELING
Carlos Augusto Constantino
A positive gain margin means that the system is stable
and a negative, instable, also the value of the gain margin
means how much the gain of the system can be increased
without changing the system stability.
The phase margin is the amount of phase necessary to
change the system stability. A positive phase margin means
a stable system and a negative, instable.
The frequency at -3dB is considered to be the highest
frequency in which the actuator will respond with a
representative level, values higher than 5Hz are expected in
a good actuation system.
The results of the model frequency response are shown
on the Fig. 4-6 and Fig. 4-7.
ωhp =
(16)
Substituting by the values used on the model the
resultant hydraulic frequency of the valve is:
ωhp = 501.3 rad s
Or:
f hp = 79.8 Hz
Therefore if the EHSV is excited at the frequency f hp
the valve shall resonate, just as shown on the Figure 4-1 .
Frequency Response Analy sis
-48
Frequency Response Analysis
5
2 β e Av 2
V0 p M v
-50
Gain (dB)
-52
Gain (dB)
0
-5
-54
-56
-58
-10
-14.37dB
-60
-15
-62
-1
10
-20
-1
10
1
0
10
10
Frequency (Hz)
0
10
2
10
1
Frequency (Hz)
10
2
10
0
0
Phase (deg)
-50
Phase (deg)
-50
-74.43º
-100
-100
-150
-200
-150
-200
-1
10
-250
-1
10
1
0
10
Frequency (Hz)
10
Fig. 4-6 – Gain and Phase Margins
Gain (dB)
0
1
Frequency (Hz)
10
2
10
Fig. 4-8 – Frequency Response of the EHSV
The result of this analysis has shown that the model of
the EHSV is representative at high frequency, which is a
major improvement of this model compared to a simplified
one.
Frequency Response Analysis
5
0
10
2
10
8.28Hz
-5
-10
-15
-20
-1
10
0
10
1
Frequency (Hz)
10
2
10
0
Phase (deg)
-50
-100
-150
-200
-1
10
0
10
1
Frequency (Hz)
10
2
10
Fig. 4-7 – Frequency at -3dB
As shown on Fig. 4-6, the Gain margin is 14.37dB and
the Phase margin is 105.57º, therefore the system is stable
and also Gain margin is higher than 10dB, which is
considered a good gain margin for real actuation systems.
The Fig. 4-7 shows that the frequency at -3dB is at
8.28Hz. Therefore the system will have a good response for
frequencies higher than Hz, which is also considered good
enough.
Considering the conclusions made by the Step Input
analyses and with the results of the Frequency Response
analyses, it is possible to conclude that the system herein
developed is stable, fast and representative of a real
hydraulic actuation system.
4.2. High Frequencies Analysis
One of the most important improvements made on this
model was the high detailed model of the EHSV, which has
relevant dynamics close to the hydraulic natural frequency
of the servovalve, which can be evaluated as shown on
Merrit [2]:
5. Conclusion
The objective of developing a model that represents a
hydraulic actuation system up to high frequencies is a very
complex and challenging effort. Therefore the model
develop herein must be considered as one step further on
this direction.
Although some of the most relevant high frequencies
dynamics were implemented, like the EHSV dynamics, only
a complete model with all dynamics implemented can be
considered good enough to represent all the coupling that
will be observed on a real system.
Until this detailed model is created, it is a good practice
to use the state of art models and work with a secure margin
of safety. Nevertheless even with the best model developed
there still will be a level of uncertainties that will require
some amount of margin of safety as well as a model
validation through a real test bench.
Nevertheless this work has shown that a high frequency
modeling detects relevant behaviors that a simplified model
cannot catch. These behaviors will affect the load either
positively or negatively depending on each case of study or
frequency range of analysis.
Therefore it is highly recommended the usage of this
model in the design phase of an aircraft in order to produce a
more mature product and reduce costs of design errors. Also
it is a suggested further work to develop an analysis of
failure cases that are relevant at high frequencies, as well as
the development of monitors which are able to detect the
studied failure in case it is necessary.
Proceedings of the 9th Brazilian Conference on Dynamics Control
10and their Applications
Serra Negra, SP - ISSN 2178-3667
1089
REFERENCES
[1] R. W. Fox, and A. T. McDonald, “Introduction to Fluid
Dynamics”, New York: Wiley, 1998.
[2] H. E. Merritt, “Hydraulic Control Systems”, New York:
Wiley, 1967.
[3] K Ogata, “Modern Control Engineering”, New Jersey:
Pearson, 2002.
[4] AIR4094
“Aircraft
Flight
Control
System
Descriptions”, SAE International, 1990.
[5] AIR4253 “Description of Actuation Systems for
Aircraft With Fly-By-Wire Flight Control Systems”,
rev. A, SAE International, 2001.
11
Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications
Serra Negra, SP - ISSN 2178-3667
1090