high frequency modeling of a hydraulic actuation flight control system

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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] 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 FCSwith 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 Force-Fight 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 Force-Fight 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,

Proceedings of the 9th Brazilian Conference on Dynamics Control and their Applications Serra Negra, SP - ISSN 2178-3667 1080

HYDRAULIC ACTUATION SYSTEM MODELING: AN ANALYSIS OF HIGH FREQUENCY MODELINGCarlos Augusto Constantino

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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. Servovalve2. Mode Select Valve3. Anti-Cavitation Valves4. Solenoid Operated Valve5. Check Valves6. Reservoir7. Actuator8. Surface of control

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

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

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]:2

012

p p Vρ= + (1)

0p : Stagnation Pressurep : Static Pressure

2

21 Vρ : Dynamic Pressure

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.


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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];1 2 lp p hρ− = ⋅ (2)

2

2lL Vh fD

= (3)

lh : The pressure lossf : The friction factor, which is a function of Reynolds

and the tubing properties.For laminar flow the value for the friction factor f is:

64fRe

= (4)

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. 3-2below.

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

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.

Fig. 3-3 – Electronic System Block

3.3.1. Position Loop

Fig. 3-4 – Position Loop Block

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.



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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

Fig. 3-7 – Valves Dynamics

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

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 springinside 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:

2CV d CV

PQ C Aρ∆

= (5)

Where:

CVQ : Flow though the valve dC : Coefficient of Discharge

CVA : Check Valve Orifice Area

P∆ : Delta Pressure on the valve sides ρ : Fluid densityTo evaluate the pressure Ps_CV it can be used the

continuity equation given by:

nete

dV V dPQdt dtβ

= + (6)

Where: netQ : Net Flow through the volume

dVdt

: Volume variation during time

eβ : Bulk Modulus

e

V dPdtβ

: Fluid compressibility

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).


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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 forthis 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 flowinside the volume of the return line.

3.4.2. EHSV ModelingIn 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. 3-9 – 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.

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. 3-10 – EHSV Operation

Source: http://www.moog.com/literature/ICD/jet_pipe_servovalves_overview.pdfaccessed at 07 Mar 2010

The armature torque equation can be evaluated as by Merrit [2]:

( ) ( )2t a an Lp N f vK i J s K rP A r b K r b xθ θ θ ∆ = + + + + + +

(7)

Where:tK : Torque constant of the torque motori∆ : Delta current as input to the servovalveaJ : Inertia of armature and any attached load

θ : Rotation angle of the flapper

anK : Net spring rate r : Distance between center of armature and flapper

LpP : Flapper valve load pressure

NA : Nozzle area b : Distance between flapper and spool

fK : Spring constant feedback spring at the free end

vx : Spool positionThe value of the coefficient

NLp ArP was considered very small and should not interfere on the spool dynamics. Also it is a standard practice on the servovalves design that the value of anK 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:

( ) ( )22

1

t f v a fK i r b K x J s K r b

θ∆=

∆ − + ∆ + + (8)



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The transfer function of the flapper to the spool position is given by Merrit [2]:

2

2

21

qp

v v

f hp

hp hp

Kx Ax ss

δω ω

∆=

∆ + +

(9)

Where the variables not yet defined are:θ∆=∆ rx f : Linear displacement of the flapper

2

0

2 e vhp

p v

AV Mβω =

: Hydraulic natural frequency of pilot stage

22 v

vcphphp A

MKωδ = : Damping ratio of pilot stage

qpK : Flow gain of flapper valve

vA : Area of spool

eβ : Bulk Modulus

pV0: Contained volume at each end spool

cpK : Flow pressure coefficient of pilot valveIn 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. 3-12 – 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.

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.

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 ModelingAfter 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”

Taking as reference the Fig. 3-14 extracted from Merrit [2] and considering that it should be added the anti-cavitation valves on the lines that connects the EHSV to the piston, the continuity equation of the system can be evaluated and given by:

1 1 11 1 1ip ep AC

e

dV V dPQ Q Q Qdt dtβ

− − + = + (10)


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2 2 22 2 2ip ep AC

e

dV V dPQ Q Q Qdt dtβ

− − + = + (11)

Where:( )ρ

212 PPACQ ipdip−

= : Internal leakage between chambers

ρ1

12PACQ ipdep = : External leakage on chamber 1

ρ2

22PACQ ipdep = : External leakage on chamber 2

( )11

2 tAC d CV

P PQ C A

ρ−

=: Anti-cavitation flow on line 1

( )22

2 tAC d CV

P PQ C A

ρ−

=: Anti-cavitation flow on line 2

dtdPV

e

22

β: Fluid compressibility

Therefore the pressure on each chamber can be found by the following equations:

( )1 11

1 ep p ep ipP Q A x Q Q

s Vβ

= − − −

(12)

( )2 22

1 ep p ep ipP A x Q Q Q

s Vβ

= − + −

(13)

Considering the Eq. (12) and (13) it was modeled the Fluid Dynamics Block as shown on the Fig. 3-15.

Fig. 3-15 – Fluid Dynamics Block

Applying Newton’s second law to the forces on thepiston, the force equation can be evaluated as shown by Merrit [2].

( ) 21 2p p p p p p p LA P P M s x B sx K x F− = + + + (14)

Where:

pA : Piston Area

pM : Piston mass

pB : Viscous damping coefficient

pK : Piston stiffness

LF : External loadConsidering the Eq. (14) it was modeled the Piston

Dynamics Block as shown on the Fig. 3-15.

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. 3-17 – 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.



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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.

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. 3-19 – Xp and Xs at static state without forces

When piston imposes a displacement of Xp compressingthe lug against the surface, the amount of force required is simply evaluated by Hooke’s Law considering the lug as aspring.

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:

s str s str sT I B K HMθ θ θ= + + + (15)

Where:sθ = Surface angular displacement

I = Surface InertiastrB = Structural Damping

strK = Structural StiffnessHM = External Hinge Moment (Air load)Therefore the Surface Dynamics Block was modeled as

shown on Fig. 3-21.

Fig. 3-21 – Surface Dynamics Block

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 AnalysisThe 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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Fig. 4-1 – Performance Criteria for a Step Input

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.

0 0.5 1 1.50

2

4

6

8

10

12

14

16

18

Td 0.208

Tr1 0.061

Tr2 0.358

Ts 0.437Mp 2.1%Tp 0.434

Time (s)

Thet

a (d

eg)

Step Input Response Analysis

CommandSystem Response

Fig. 4-2 – Step Input Response 0º to 15º

0 0.5 1 1.5

-25

-20

-15

-10

-5

0

Td 0.334

Tr1 0.084

Tr2 0.583

Ts 0.633

Mp 1.3%Tp 0.684

Time (s)

Thet

a (d

eg)



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.

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 4-5and Figure 4-6.

0 0.5 1 1.5

0

2

4

6

8

10

12

14

16

18

Td 0.230

Tr1 0.075

Tr2 0.382

Ts 0.434Mp -0.2%Tp 0.532

Time (s)

Thet

a (d

eg)



Ess 0.106

Fig. 4-4 – Step Input Response with an opposing load of 90% of maximum load

0 0.5 1 1.50

2

4

6

8

10

12

14

16

18

Td 0.195

Tr1 0.055

Tr2 0.344

Ts 0.525

Mp 3.9%Tp 0.430

Time (s)

Thet

a (d

eg)



Ess 0.109

Fig. 4-5 – Step Input Response with an aiding load of 90% of maximum load

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.

4.1.2. Frequency Response AnalysisThe 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.



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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.

10-1

100

101

102

-200

-150

-100

-50

0

Frequency (Hz)

Pha

se (d

eg)

10-1

100

101

102

-20

-15

-10

-5

0

5

Frequency (Hz)

Gai

n (d

B)

Frequency Response Analysis

-14.37dB

-74.43º

Fig. 4-6 – Gain and Phase Margins

10-1

100

101

102

-200

-150

-100

-50

0

Frequency (Hz)

Pha

se (d

eg)

10-1

100

101

102

-20

-15

-10

-5

0

5

Frequency (Hz)

Gai

n (d

B)


8.28Hz

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 goodenough.

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]:

2

0

2 e vhp

p v

AV Mβω = (16)

Substituting by the values used on the model the resultant hydraulic frequency of the valve is:

501.3hp rad sω =Or:

79.8hpf Hz=Therefore if the EHSV is excited at the frequency hpf

the valve shall resonate, just as shown on the Figure 4-1 .

10-1

100

101

102

-62

-60

-58

-56

-54

-52

-50

-48

Frequency (Hz)

Gai

n (d

B)


10-1

100

101

102

-250

-200

-150

-100

-50

0

Frequency (Hz)

Pha

se (d

eg)

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.

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.


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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.


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high frequency modeling of a hydraulic actuation flight control system

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