modelling and analysis of closed loop servo hydraulic actuation system

8/7/2019 Modelling and Analysis of Closed Loop Servo Hydraulic Actuation System

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MODELLING AND ANALYSIS OF

CLOSED LOOP SERVO HYDRAULIC ACTUATION SYSTEM

Authorised By

SANTOSH BHARADWAJ REDDYEmail: [email protected]

More Papers and Presentations available on above site

Abstract:The servo hydraulic actuation system drives the control surfaces to put the under water system at its target. The dynamic performance servo actuation system contains an error.The error minimization and the system characteristics are possible only with thecharacteristic knowledge of each component of the system. The over all system contains

servo valve, piston pump, heat exchanger, check and relief valves and actuator. Themanufacturer provides the characteristics of each product. Actuator contains two vaneswith shoe, and these vanes contain rotary motion in clock wise and anti clock wisedirection due to the input pressure. The output of the actuator contains rotary motion andthe output is taken in terms of angle. The input to the actuator is flow in terms of pressurethis comes from servo valve. Comparing with all the components actuator plays importantroll for actuation. As the total system is closed loop system. Feedback is pot. Thecharacteristic response of the overall system can be studied from the responsecharacteristics knowledge of the overall system. The rotary actuator contains some internalleakage due to vane movement and they are some friction effects which intern generatestemperature in the system. In This actuator system by using MIL5606H hydraulicpetroleum based fluid the temperature increases and affects the viscosity. In this paper weare concentrating linearised model for double vane rotary actuator in terms of state spaceform, and transfer function of hydraulic servo valve and then calculating the temperatureviscosity relation for MIL 5606H and also calculating the internal leakage of the rotaryactuator.

Introduction:Opposite chambers in the actuator are connected by pressure equalizing passages

in the upper and lower heads. In this manner, the actuator produces perfectly balancedtorque as hydraulic force simultaneously pushes both of the rotor vanes away from thestationary shoes. Torque output of the rotary vane actuator remains constant throughoutthe full rotation of the valve. Constant torque output is an especially important feature inhigh flow applications. Constant torque output ensures that our specified safety factor willnot diminish at various positions during the valve stroke. which are essentially noncontinuous motors consisting of a cylindrical body to which two vanes are rigidly attached

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the output shaft carries a moving vane the torque output of the double vane is twice thanthat of single vane actuator max angle of rotation in double vane actuator is 150 degreesthese actuators are most widely useful for position control for high torque output unitsindirectly these are converted mechanical energy into hydraulic energy by prime mover of drive shaft. The spool is shifted with a rotary actuator mounted on the top of the valverather than the solenoid mounted at the end of the spool in three stage valve the pilot stageshifts the second stage which shifts the third stage. Three stage valves are used for theapplications of high pressure and high flow large forces are required to shifts the thirdstage which directs the high volume flow to the actuator. In this servo valve fluid flowsacross the fixed orifices and enters into the centre manifold orifices are formed on eachside between the flapper and opposing nozzles. As long as the flapper is centered and theorifice is same on both sides and the pressure drop to the return is same if the pressures areequal in both sides then spool is in force balance depends on the flapper movement orificearea is taken.

Scope of the project:This work deals with identifying the overall system response characteristics. This involvesthe investigation of the characteristics of rotary actuator. Internal leakage in the actuator isa concern which dictates its performance. It necessitates the study of the characteristics of the actuator to reveal the relation between input pressure, output (angle) and importantlyinternal leakage. The temperature of the oil is a major factor which affects the response of the actuator. The response-characteristics for the entire system are a transfer function for the output angular displacement (angle) and the input command voltage. Derivemathematical modeling of a double vane rotary actuator. Using torque balance and

chamber continuity and chamber volume equations. Prove mathematical relations for inputpressure and output angular displacement and internal leakage.

Methodology:.

2

ControlPID

ServoValve Actuator

POT

-

CommandVoltage

Feedback voltage

Pressure

DifferentialPressureError

voltage

Controlvoltage

Angle


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Figure1: overall system model diagram

Study of the double vane rotary actuator. And identify the governing laws. Write themathematical expressions from the laws for torque balance, chamber continuity, andchamber volume.Derive the mathematical relation for input (pressure), output (angular displacement) and internal leakage. With the numerical data, calculate internal leakage for input pressure value ranging from minimum to maximum. Graphical representation of thisfor experimental data and theoretical

Double vane rotary Actuator:

Figure2:

Double

vane

rotary

actuator

model

Parameter considerations:

Input pressure to the actuator is 140 bar (variable) Nominal flow 8 lpm (max)Supply current to the servo valve 10mA (max) Peak to peak voltage 2 voltsOutput pressure from actuator is 66.5bar (variable) Max angle of rotation 12 deg.

3

Vanes

Chamber partition

Red arrowed lines indicate oil entering andleaving the Chamber between the partition andthe vane.

This in and out of oil is through single inlet/outlet hole in each chamber

InletPressure P1 Flow Q1OutletPressure P2

Flow Q2

Inlet PressureP3Flow Q3OutletPressure P4 Flow Q4


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Supply pressure to the servo valve 210 bar (constant) Return pressure 3.5 bar Load pressure 70bar MIL PRF 5606H hydraulic oil viscosity V s temperature relation:Properties of MIL PRF 5606H hydraulic fluid:

Oil type mineral normal Europe European

Kinematic viscosity mm^2/sec

@ 100c 4.90 min 6.13 5.30

@ 40c 13.2 min 15.68 14.1

@ -40c 600 max 384 491

@ -54c 2500 max 1450 2300

Flash point 82min 104 105

Pour point -60max


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Equation of continuity in actuator:The equation of continuity for both compartments is depends on the flow, leakage,pressure, volume parameters. The equation of continuity is taken from the continuityconsiderations of actuator because the device is a mechanical and these equations aredepends on the change in pressure with respect to timeThe two differential equations for the pressure dynamics are obtained as,

1= [ 1- lv - aV r ] (4)

2= [- 2+ lv+ aV r ]............................................ (5)

Chamber volume equations :The compartment volumes are product of the actuator volume per radian (V r ) and effectivelength of each compartment is ( j j=1, 2)

In rotary actuator two opposite chambers volumes are equel at a particular position of thevane movement these volumes are represented V 1 and V 2.The volumes are depends oneffective stroke and in effective stroke in actuator and angle.

In double vane rotary actuator we assume the ineffective strokes of both compartments areequal then Change in volume with respect to time is equals to the differentiation of anglewith the multiple of volumetric displacement means the both the volumes in the bothcompartments are opposite.

The compressibility of oil:The finite stiffness of oil causes a second order dynamic behavior of a hydraulic

servo system for the compressibility measure is depends on the bulk modulus of the oilwhich relates the variation of pressure and volume of oil in a closed path

Leakage flow:

The load dynamics:Due to pressure difference across the vane the actuator generate a torque which drive thesystem with a certain mass with inertia or with stand an external torque

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T =V r (P1-P2) w a (6)

Due to a pressure difference across the vane, the actuator can generate a torque which candrive a certain mass with inertia. The seals and bearings inside the actuator are assumed tobe the main cause of the friction effects. The external torque is acting upon the load.

Friction effects:Friction effects are characterized by the opposite movements the modeled friction T fr composed of a linear viscous friction component w and dry friction T d here dry friction isneglected

T fr = T d-w a (7)

The dry friction is either a result of Coulomb friction or stiction this is the most commonlyused friction model in engineering The Coulomb friction is modeled as a constant force T c

which exists whenever a not equals to zero The stiction is only defined when the actuator

does not move It matches any torque generated by the actuator or an external torque up to

a certain limit T s such that no movement of the System will occur.Actuator contains Four equel chambers due to angle change chamber volumes are variedActuator contains internal leakage only. External leakage is minimized Actuator containseffective and Ineffective strokes. Ineffective strokes in opposite chambers are equel.

1= [ 1-LV - aV r ] from eq (4)

By applying Laplace transform on both sides

Considerations:

S=110 deg q a = 12 deg SL1 = S L2 = (S/2)-12 = 43 deg

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Scaling for linearization model in actuator :Scaling is a useful tool to obtain a model in which the numerical values of the parametersare of comparable order of magnitude. This can be an advantage with respect to thenumerical accuracy of simulations performed with the model on a computer .As a result of scaling the magnitude of the signals which will evolve during simulation will be of thesame order This implies that the visual inspection of the time signals as a result of onespecific realization of the behavior of the dynamical system gives immediately a clear impression of the (dynamic) load imposed upon the system irrespective of knowledgeconcerning e.g. the specific size of the actuator the actual supply pressure or the attachedload

From the servo valve flow equations [2], [3]

The above equation represents flow scaling factor in servo valve=

From Eq [4], [5]

(9)

Similarly,

... (10)

These are the scaling equations for pressure variations in the respective compartmentsFrom Eq [6]

T = (P s, P sc, 1-P s, P sc, 2)-w a .. (11)

The model describes for double vane rotary actuator with limited stroke and ordinarybearings and seals. The hydraulic servo valve delivers a constant supply pressure

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irrespective of the oil flow. The flows through the valve are turbulent and the leakageflows are laminar. The inefficient volumes of e.g. the transmission lines between valveand actuator can be modeled as additive inefficient strokes. Due to vane movementviscous friction acting upon the actuator. The valve is placed directly on the actuator.For the purpose of control design and identification purposes we simplifies the model in asimple way of such a linearized model related to a rigid or a flexible connection shaftbetween Actuator and load are presented Representations of the model in a state space.P sc = P sc, 1 P sc, 2 Both pressures are modeled by first order differential equations only the pressuredifference is measured at actuator and both pressures are not controllable under certainconditions. The mean pressure level in the compartments is depends on half of the supplypressure

............ (12)

........................ (13)

From [9], [10], [12], [13]

Formulation of Linearised model in state space form:The scaled version of the nonlinear model is well suited for simulation purpose. However,with respect to control design and identification there are reasons to simplify The modelslightly.

.... (14) Suppose 1= 2From [9], [10]

Sc, 1 = sc, 2 sc = sc,1 - sc,2

sc = ( sc,1- sc,lv ) - - (- sc,2+ sc,lv)-

= ( + ) - ( )

The leakage across the vane is modeled as, lv = R v (P1-P2)

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The leakage across the vane depends on pressure difference but pressure is variable herepressures are converted into scaling factors at a particular coil resistance.P1=P s Psc, 1P2=P s Psc, 2 sc lv . n=R vPs (P sc, 1 -P sc,2) sc, lv = R vPs (P sc, 1 -P sc, 2)/ nFrom the above equation sc, lv =LP v (P sc, 1-P sc, 2 ) . (15)From The above equations

Therefore,

= [i sc - LP v P sc]

The above equation represents variable pressure in terms of scaling factors this equationcan be written as constants and these constants contains relationship between one andother here K 2 represents in terms of K 1 with some angle change and K 3 represents in termsof K 2

K 3 = K 2LP vFrom

(P sc) = [i sc ] [K 3P sc] [K 1 ]

Splitting equal and un equal terms

P sc ( +K 3) = -- K 1 +K 2 isc

The above equation represents some constants in the left hand term and some change inpressure with time is summation with constant pressure from right side we assume onlypressure variation with respect to current.

= li scl

In these equations most considerations are variables first these are all variables areconsidered as a function then after construct the linerizing model to those equations

= - K 1 +K 2isc K 2 (LPv ) P sc

= - K 1 ( ) +K 2isc K 2 (1-sgn ( ) ) i sc K 2 (LP v+ P sc)

=- K 1 ( ) + 2( , , ) i sc - 3 , P sc and P sc= + P sc

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1 = S+q a+SL 1 and 2 = S-q a+SL 2

= +

=

T=J a a T e Ja a T e = T max P sc - a

a= - +

a= max p sc +

Linearization of the model equations:A linearization of a nonlinear model is often necessary before (linear) identification or control design techniques can be applied. An approximation of the square root in thepressure equation by a first order Taylor series is:

= +

Here the valve input nonlinearity is a function of p sc and sgn ( isc)Leakage and friction are introducing damping in the system suppose both are zero thenpoles on the imaginary axis. Only parameter w is available for the parameterization of friction effects because the Coulomb friction parameter Td has been excluded from themodel as a result of the linearization process Coulomb friction is independent of thevelocity consequently w partly reflects Coulomb friction. Effects in a certain point of operation this parameter will be velocity dependent.

0.1474 /rad

= 0.0064 bar

P1 = =140 bar P 2= = 66.5bar

Load flow depends on discharge coefficient C d = 0.65 [Q L = C dA1 ]

Torque = 0.5 (D 2-d2) LP = 3.381 kg-m

Fluid volume = = 0.0257 in 3

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Nominal Flow Q = Q=5.7289 lpm

Internal leakage across vane:Oil flow (L/min) = Displacement* required angular velocity * + Leaked Oil (L/min)

Actuator leakage flow = 7.99

Results:1. Rotary actuator volume Vs pressure relation for various leakage values:

0 0.5 1 1.5 2 2.5 30.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2x 10

5

The above plots represent the chamber volume variations with respect to differentpressures keeping leakage constant.

2. Modeling the Actuator to pressure, flow and angle variations: I= 10mA, =8lpm

0 20 40 60 80 100 120 1400

50

100

0 20 40 60 80 100 120 1400

50

100pressu re vs f l ow

1 2 3 4 5 6 7 80

5

10PRESSUR E Vs ANG LE

-8 -7 -6 -5 -4 -3 -2 -10

5

10PRESSUR E Vs ANG LE

Inlet pressure V s flow for various current values 2.out let pressure V s flow for variouscurrent values.3.Inlet pressure V s angle for various current readings change 4.outletpressure V s angle for various current values.

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3. Actuator flow variation with respect to the input signal:

0 1 2 3 4 5 6 7 8-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

The above response indicates the input voltage (2v) variation with respect to actuator flowby using venders pole demo model.

4. Feed back in the overall system POT characteristic graph: R = 5K Ohms V=13.5 VdcMaximum Rotation of Angle 130 Degrees.

-15 -10 -5 0 5 10 15-1.5

-1

-0.5

0

0.5

1

1.5

2

The output angle (degree) varied with respect to input supply peak-peak voltage (volt).The graph represents expontial increasing and decaying.

5. Viscosity V s temperature variation for MIL PRF 5606H:Due to vane clockwise and anti clock wise movement generate some friction. This interngenerates temperature due to temperature viscosity of the oil is decreased. This causesinternal leakage due to internal leakage system output performance is degraded.

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0 10 20 30 40 50 60 70 80 90 1001

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6x 10

-3

6. Servo valve input current Vs flow variation:

-10 -8 -6 -4 -2 0 2 4 6 8 10-8

-6

-4

-2

0

2

4

6

8

The servo valve contains 0.3 hysteresis. Output Flow 8lpm and i/p current 10mA max

7. Actuator output response:

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-8

-6

-4

-2

0

2

4

6

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The response of the double vane actuator without feedback and test at no-load conditions.Output response contains some lagging and error each time the output response containslagging gradually the overall performance is affected.

8. Bode plot:

When we wants to use or controls a real system we must know how it behaves whendifferent signals are applied to it this will give a measure of the dynamic response of thesystem one way to find the response of the system is to apply a test signal to the input andlook at the output how it responds. Many test signals are possible but the simple signal issinusoidal signal this is because the output of a system is sine wave and input is also a sinewave but with a different amplitude and phase by measuring the output amplitude andphase of a system over a range of frequencies of the input sine wave. The above boderepresents how the actuator responds for different frequencies. Find the stability propertiesof the system in a closed loop control.The above frequency response analysis are mostuseful to directly quantifying the system performance. System identification techniquesare also possible.

9. Actuator Error:The above response is closed loop response from this analysis describing the function of the system the given system contains high and fast dynamics and analysis is done onefrequency at a time the total test time is quite long. Also it is easy to miss some frequencyvalues in initial positions after the signal contains wave nature.

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10. with Feedback:

Input sinusoidal signal, only one frequency is used at a time and the amplitude of the sine

wave changes for each frequency. This means that if the system has a strong resonance at

some frequencies the input amplitude can be reduced to prevent damaging the system.

Likewise if the system has a low gain in a frequency range we can increase the test signal

amplitude. In this plot the output response totally follows with the input test signal.

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11. Square wave error:

12. Total output response with feedback in actuator:

The above response is closed loop response feedback is pot. The overall system containsfour actuators the output actuation of the four actuators are equal. We take the responseonly for single block. This block contains servo valve, actuator, feedback and controlparameters. From servo valve calculate the over all transfer function and from actuator angle is calculated by using Laplace transform and P, I, D parameters are used toimplement the model. The above model indicated the Actuator output response thisresponse is oscillatory because the system is multiple system with closed loop the aboveresponse represents the closed loop control parameters output response. and actuator response for each value of the input step change.

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Symbols:Supply pressure = P s (bar)Input pressure to the actuator = P 1 (bar)Output pressure from the actuator = P 2 (bar)Return pressure = P R (bar)Load flow = QL (lpm)Input flow to the servo valve = 1 (lpm)Nominal flow = N (lpm)Load pressure = P L (bar)Oil bulk modulus = E (sq/sq.in)Volumetric displacement = V r (cu.in/rad)Vane diameter = D (sq.in)Shaft diameter = d (sq.in)Output angle = , q a (deg, rad)

Internal leakage = LV (cu.cm/min)Effective stroke = S (deg, rad)Ineffective stroke = SL 1 (deg, rad)Discharge coefficient = C d (con)Chamber volume = V (cu.in)No of vanes = N (con)Vane length = L (in)Input supply current = I (mA)Peak-Peak voltage = V (volt)Inertia of actuator = J a ()

External torque = T e ()Viscous friction = w ()Dry friction = T d ()Vane Inertia = J ()Speed of rotation = (rad/sec)Valve pressure drop = P V (bar)Constants = K j (con)Torque = ()Viscosity = (lb-sec/in^2)Frequency = f (Hz)Orifice area = A 1 (sq.in)Torque = T max ()Resistance variation = R V (ohms)Pressure difference = P (bar)Oil density = ()Constant which depends on the fluid = (-F)T is a Temperature = T (F)

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References:1. MOOG servo valve data sheets2. Defense documentation centre for science and technology centre Cameron centre

Alexandria Virginia3. Aero sheel hydraulic fluids4. Modeling and control of a industrial hydraulic rotary vane actuator by j.heintze5. Feed back linearization control for electro hydraulic system of a robot excavator by6. Proportional and hydraulic servo valve technology by hydraulic trainer volume7. Hydraulic control systems by Herbert E.meritt (Wiley 1991).8. Mechanical engineering hand books9. Pioneering series for rotary actuation system10. Neural adaptive control of a non linear MIMO electro hydraulic servo system a thesis

submitted to the college of graduate and research studies.11. Development of a hydraulically manipulated servo actuator model:

12. Automated grasp planning and execution for real world objects using computer visionand tactile probing P.A.Bender and G.M.Bone.13. Phillips 66 aviation hydraulic fluid for MIL PRF 5606 H.14. Product technical information for 120 series rotary actuator.15. Model 552 E servo valve star hydraulic company ltd.16. The stability of hydraulic system to determine methods based on MATLAB17. Modeling identification and experimental validation of a hydraulic manipulator joint

for control18. Hydraulic double balanced rotary actuator perpendicular rotation data sheet19. Interactive analysis of closed loop electro hydraulic rotary actuation system by medkat

K bahr kalil PhD20. System modeling and simulation by koji koyamada21. Robust stability analysis of servo hydraulic system in parameter space by university of

Cincinnati22. Hydraulic servo control valves analog simulation pressure control and high

temperature test facility design WADC technical report part 5.23. Effective maintenance of hydraulic systems work shop data sheets.24. Mechanical engineering system and control group by Delft University of technology.

Authorised BySANTOSH BHARADWAJ REDDYEmail: [email protected]

More Papers and Presentations available on above site

18
mailto:[email protected]:[email protected]:[email protected]

modelling and analysis of closed loop servo hydraulic actuation system

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