Electro-Hydraulic Servo Valve Construction, Models and Use

From Merritt, H. E., Hydraulic Control Systems, J. Wiley, 1967. The input to an electro-hydraulic (EH) servovalve is typically a current or a differential current that powers an electromagnetic torque motor. The differential current Δi is typically supplied by an amplifier to avoid excess loading of the interface to the computer or controller. In the simplest (but not typical) form, the torque motor moves a spool valve as shown below. The spool valve allows the hydraulic fluid to pass from the supply to the return across two variable metering orifices with a controlled flow rate QL. If the spool is shifted in the other direction the direction of flow will reverse. Since the clearances between the spool and the valve body is small, the forces required to move a large spool are large. Hence the single stage or direct acting EH valve is limited to low rates of flow (small valves). Figure 7-11 from Merritt shows the pictorial representation of the motion system in this case.

In order to achieve higher flow rates, a two or three stage servovalve may be necessary. In this case the torque motor controls the first stage valve that actuates the spool on the second stage. The first stage valve is typically not a spool valve but either a flapper-nozzle valve or a jet pipe valve. The flapper-nozzle is more common. For these valves

flow passes from the nozzle through a cylindrical area between the nozzle and the flat flapper that is near to it. As shown in Fig 7-14 and 7-17 from Merritt, the EH valve uses one flapper between two nozzles to produce a differential pressure that is applied to each side of the spool. The displacement of the flapper from a neutral position is powered by the torque motor and resisted by a torsional spring. The “fixed upstream orifice” in both types of valve is important to allow the pressure on either end of the spool to be below the supply pressure. A small flapper motion creates an imbalanced pressure in one direction or the other on the ends of the spool of the second stage. Obviously the spool will tend to move in response to this imbalance and allow flow QL to the actuator. Since continued imbalance in pressure would quickly move the spool to its limits of travel, a form of feedback connects the motion of the spool to the effective displacement of the flapper. A very small spool displacement will result in a large flow at high pressures typically used. Two common forms of feedback are illustrated in the figures from Merritt. Direct position feedback moves the nozzle with the spool as shown in Fig 7-14. Thus the equilibrium position of the spool is 1:1 with the position of the flapper. Fig 1-17 shows the force feedback arrangement in which a feedback leaf spring applies a force to the flapper to restore equilibrium. The ratio between the spring constant of this spring and the torsional spring on the torque motor determine the ratio between motion of the flapper and the spool. Valve Models Mathematical models of the EH valve can be constructed at various levels of detail depending on the purpose of the model. The models may represent the nonlinear square root relation between pressure and flow, or may be linearized about an operating position. When designing the valve itself, a more detailed model is typically required than when modeling the system controlled by a well designed valve. The model of the dynamics of the electromagnetic behavior is typically ignored or aggregated into the overall valve behavior, for example. Block diagram 7-18 shows a very detailed model of the force feedback valve that is simplified in the block diagram of Fig 8-5 constructed for analysis of the valve in a position control system. The transfer function of Equation (8-17) excerpted from Merritt is further simplified. This is the form you should hope to apply to a system design. Some of the parameters of this model are readily calculated, provided by the manufacturer or obtained from manufacturer’s specifications. Other terms in (8-17) are better identified from aggregate measurements of the system’s overall behavior. Even in this case it is generally desirable to compare the identified parameters to estimates based on first principles. The effective bulk modulus βe is an example. It depends not only on the compressibility of the pure fluid, but the effect of entrained air and vapor and the expansion of the walls containing a fluid. These effects are very hard to compute directly but they result in an increased compressibility (decrease bulk modulus), so the limiting case can be estimated from knowledge of the ideal properties.

The most common model of the load used for system design assumes the load is essentially an inertia and that

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Possible simplifications, refinements and extensions of this model are numerous:

o The simplest valve model would give the steady state flow for a given electrical input. As one can see from the final value theorem and the blocks representing the valve in Merritt’s Figure 8-5, for a step input (i.e. sse /1)( =θ ) to the error signal,

amplitude)(input x gain)constant (a 1)(lim)(lim0

=⋅==→

→∞ sdevs

tv KKKtxsxs

Thus if the valve dynamics are fast compared to those of the load, one can essentially ignore the dynamics of the electrical drive and the electromagnetics of the valve, leaving the effect of the valve as a constant.

o A more accurate model of the servo valve spool motion is given by a first or second order transfer function. The Merritt model shows a fourth order model for the electrical drive and spool dynamics but today’s electrical drives are so fast that their dynamics may be ignored. See the Moog Company’s venerable publication, “Transfer Function for Moog Servovalves” by Thayer for example models and parameters for a high performance servo valve.

o For an example extension, consider TL which is shown in the block diagram as an external input, when it is likely to be dependent on the flow through the valve. This would be represented with a feedback loop representing the effects of inertia, compliance, damping, etc. of the load.

o There are other connections that are of interest. The pressure in the actuator will reduce the pressure drop across the valve orifice. This effect is not explicit in the block diagram and would require further considerations of the back pressure if it is a substantial fraction of the supply pressure.

Identification of Hydraulic System Parameters The model requires coefficients to be known within reasonable accuracy to be of any value. Some of the values can be measured directly, such as lengths and volumes. Other

parameters may be determined in groups by certain experiments. This is particularly true of the valve model. To “identify” the parameters of any dynamic experiments, a number of experiments can be performed. They include steady state measurements, time-domain measurements such as step responses, and frequency response measurements either from sinusoidal or other inputs. Often these experiments identify a coefficient of the transfer function that is a grouping of physical constants. In most cases it may be desirable to check the identified coefficients with the feasible range of values of the physical constants. One difficulty is the measurement in an open loop fashion due to the presence of a pure integrator in the system. Small amounts of flow through the valve in the null position cause the position to drift to the limits of travel. One alternative is to provide a position feedback which eliminates the drift although it alters the response. The true response has to be back calculated in these circumstances.

MOOG INC. CONTROLS DIVISION, EAST AURORA, NY 14052

TRANSFER

INTRODUCTION

FUNCTIONS FOR MOOG SERVOVALVES

It is often convenient in servoanalysis

or in system synthesis work to represent

an electrohydraulic servovalve by a sim-

plified, equivalent transfer function. Such

a representation is, at best, only an ap-

proximation of actual servovalve perform-

ance. However, the usefulness of linear

transfer functions for approximating serv-

ovalve response in analytical work is well

established.

The difficulty in assuming an explicit

transfer function for electrohydraulic ser-

vovalves is that many design factors and

many operational and environmental var-

iables produce significant differences in

the actual dynamic response. Consider

the variables of the valve design. It is

well known that internal valve paramaters

(e.g., nozzle and orifice sizes, spring

rates, spool diameter, spool displace-

ment, etc.) may be adjusted to produce

wide variations in dynamic response. An

analytic approach for relating servovalve

dynamic response to internal valve para-

meters is given in Appendix I of this tech-

nical bulletin.

Once a servovalve is built, the actual

dynamic response will vary somewhat

W. J. THAYER, DECEMBER 1958Rev. JANUARY 1965

with operating conditions such as supply

pressure, input signal level, hydraulic

fluid temperature, ambient temperature,

valve loading, and so forth. These effects

a re i ns ign i f i can t f o r sma l l va r i a t i ons

about design values, but should be con-

sidered where wide excursions are antici-

pated. It is important to appreciate and

control these and other operational vari-

ables when performing measurements of

servovalve dynamics. If such precautions

are not taken, misleading and inaccurate

results may be obtained. Appendix II to

this Bulletin describes the production

equipment presently used by Moog to

measure servovalve dynamic response.

Another difficulty in assigning simplified,

linear transfer functions to represent

servovalve response is that these valves are

highly complex devices that exhibit

high-order, nonlinear responses. If a first,

second, or even third-order transfer function

is selected to represent servovalve

dynamics, still only an approximation to

actual response is possible. Fortunately, for

most physical systems, the servovalve is not

the primary dynamic element, so it is only

necessary to represent valve response

throughout a relatively low frequency

spectrum. For instance, if a

servovalve-actuator is coupled to a load

which exhibits a 50 cps resonant frequency,

it is meaningful only to represent valve

dynamic response in the frequency range to50 cps. Similarly, for lower response

physical systems, the contribution of valve

dynamics throughout a correspondingly

smaller frequency range need be

considered. This simplification of actual

servo response should be applied whenever

practicable, for the reduced analytical task

associated with the system analysis is

obvious.

These approximations to servovalve

response have resulted in such expressions

as "the equivalent time constant of the

servovalve is - seconds" or "the apparent

natural frequency of the servovalve is -

radians /second." If a representation of

servovalve response throughout the

frequency range to about 50 cps is sufficient,

then a first-order expression is usually

adequate. Figure I shows a typical valve

dynamic response, together with the

response of a first-order transfer function.

The first-order approximation is seen to be

quite good throughout the lower frequency

region. The time constant for the first-order

transfer function (i.e., the equivalent

servovalve time constant) is best established

by curve fitting techniques. If a quick

approximation is desired, the equivalent time

constant should correspond to the 45°

phase point rather than the 0.7

amplitude point (-3 db). In general, thesepoints will not coincide as the higher-order dynamic effects contribute low fre-quency phase lag in the servovalve re-sponse, while not detracting appreciably

from the amplitude ratio.

If servovalve response to frequenciesnear the 90 ° phase lag point is of in-terest , then a second-order responseshould be used. In a positional servo-mechanism, a second-order representa-tion of the servovalve response is usually

sufficient, as the actuator contributes anadditional 90 ° phase lag from the in-herent integration. Figure 2 shows a sec-ond-order approximation to the servo-valve dynamics of Figure 1. Here, thenatural frequency is best associated withthe 90 ° phase point, and the dampingratio with the amplitude characteristic.

Other factors will often weigh more heav-ily in the choice of an approximate nat-ural frequency and damping ratio. Forexample, it may be desirable to approxi-mate the low frequency phase character-

istic accurately and, to do so, a second-order transfer function which does notcorrelate with the 90 ° phase point maybe used. A good deal of judgment must,therefore, be exercised to select the mostappropriate transfer function approxima-

tion.

SERVOVALVET R A N S F E R F U N C T I O N S

Appropr ia te t rans fe r func t ions fo r

standard Moog servovalves are given be-low. These expressions are linear, em-pirical relationships which approximatethe response of actual servovalves when

operating without saturation. The timeconstants, na tu ra l f requenc ies , anddamping ratios cited are representative;however, the response of individual serv-ovalve designs may vary quite widelyfrom those listed. Nevertheless, theserepresentations are very useful for ana-lytical studies and can reasonably form

the basis for detailed system design.

FLOW CONTROLSERVOVALVES

This basic servovalve is one in whichthe control flow at constant load is pro-portional to the electrical input current.Flow from these servovalves will be in-fluenced in varying degrees by changingload pressures, as indicated in Figure 4.For null stability considerations, only theregion of this plot about the origin needbe considered. Here, the influence of theload on flow gain of the servovalve canbe considered negligible. In general, theassumption of zero load influence is con-servative with respect to system stability

analyses.

TORQUE MOTOR

VALVE

SPOOL

TO ACTUATOR

FIGURE 3

FIGURE 4

Another linearity assumption which isoften made is that servovalve flow gainis constant through null. This is theoret-ically true for an ideal “zero lap” nullcut of the valve spool; however, the ac-tual lap condition will vary with produc-tion tolerances. If the spool becomesoverlapped, the servovalve flow gain isreduced at null. Likewise, an underlapproduces higher-than-normal servovalvegain. Normal production tolerances main-tained at Moog hold the spool lap within±O.OOOl inch for all four null edges. Thisclose control gives a very small range ofpossible nonlinear flow control throughnull (about ±3% for an “axis” null cut);

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SYMBOLSF R E Q U E N T L Y U S E D

differential current m ainput to servovalve

servovalve flow in’/sec (cis)to the load

servovalve differential Ibs/in’ (psi)pressure output

servovalve sensitivity,as defined

time constants sec.

natural frequencies rad/sec.

damping ratios nondimensional

Laplace operator

but within this range, flow gain may befrom 50% to 200% of nominal.

The change in servovalve flow gain atnull may sometimes cause system insta-bility; or, in other cases, poor positioningaccuracy, or poor dynamic response ofthe actuator at low-amplitude input sig-nals. This situation can be varied oneway or the other by holding a nominaloverlap or underlap, as appropriate.

The dynamic response of Moog flowcontrol servovalves can be approximatedin the frequency range to about 50 cpsby the following first-order expression:

3

+W=K (l ;,,>where

K -= servovalve static flow gain

at zero load pressure drop

7 = apparent servovalve time

constant

cis

m a

set

Standard flow control servovalves areavailable in several sizes and with manyinternal design configurations. The valueof servovalve sensitivity K depends uponthe rated flow and input current. Typi-cally, for a 5 gpm valve at a rated 8 mainput current, K = 2.4 cis/ma.

The appropriate time constant for rep-resenting servovalve dynamics will de-pend largely upon the flow capacity ofthe valve. Typical time constant approxi-mations for Moog Type 30 servovalvesare given in the table below.

If it is necessary to represent servo-va lve dynamics th rough a w ider f re -quency range, a second-order responsecan be used, as:

K

where

(J, = 27r f, apparent

natural frequency rad/sec

5 = apparent damping ratio

30

31

32

34

35

.0013

.0015

.0020

.0023

.0029

nd Order

fncpr

t;

240 .5

200 .5

160 .55

140 6

110 .65

The first and second-order transferfunction approximations for servovalvedynamic response listed in the abovetable give reasonably good correlationwith actual measured response. It ispossible to relate servovalve response tointernal valve parameters, as discussedin Appendix I. However, the analyticalapproach to servovalve dynamics is mostuseful during preliminary servovalve de-sign, or when attempting to change theresponse of a given design. It is better,and more accurate, for system design touse emp i r i ca l app rox ima t ions o f t hemeasured servovalve response.

P R E S S U R E C O N T R O LSERVOVALVES

TORQUE MOTOR

PVALVE SPOOL

PRESSUREA C K

FIGURE 5TO ACTUATOR

These servovalves provide a differ-ential pressure output in response to theelectrical input current. The static flow-pressure curves for a typical pressurecontrol servovalve are shown ill Figure 6.A small droop, or decrease in the con-trolled pressure with flow, does occur,even throughout the null region. Thisdroop is usually small in pressure-controlservovalves; however, in some applica-tions even a small droop can significantlyalter the system response. In pressure-flow servovalves, droop is purposely in-troduced. Transfer functions for thesevalves are discussed in the next section.

It is convenient to measure the dy- When a pressure control servovalve isnamic response of a pressure control required to supply flow to the load, theservovalve by capping the load lines and blocked-load transfer function no longer

sensing the relationship of load pressureto input current. A second-order transferfunction closely approximates the meas-ured response in the frequency range toabout 200 cps.

+ (s) = K,[1+(%ls+(%)j

where

K, = pressure control servo-

valve static gain psi/ma

Wn = 2 n f, apparent natural

frequency rad/sec

< = apparent damping rationondimensional

FIGURE 6

The controlled differential pressuremay be any rated maximum up to thesystem pressure. For a 1000 psi ratedcontrol pressure at 8 ma electrical input,K, = 125 psi/ma.

With a blocked load, the apparent na-tura l f requency for pressure cont ro lservovalves is approximately 250 cps,and the damping ratio is about 0.3 to0.5. The actual blocked-load responsefor a pressure-control servovalve dependssomewhat on the entrapped oil volumeof the load, so the load volume should benoted with response data.

4

APPENDIX IANALYTICANALYSIS OFSERVOVALVEDYNAMICS

It is possible to derive meaningfultransfer functions for electrohydraulicservovalves, and several papers havereported such work (ref). Unfortunately,servovalves are complex devices andhave many nonlinear characteristicswhich are significant in their operation.These nonlinearities include: electricalhysteresis of the torque motor, changein torque-motor output withdisplacement, change in orifice fluid-impedance with flow and with fluidcharacteristics, change in orificedischarge coefficient with pressureratio, sliding friction of the spool, andothers.

Many servovalve parts are small sohave a shape which is analytically non-ideal. For example, fixed inlet orificesare often 0.006 to 0.008 inch indiameter. Ideally, the length of theorifice would be small with respect toits diameter to avoid both laminar andsharp-edge orifice effects; however,this becomes physically impracticalwith small orifices due to lack ofstrength for differential pressureloading, and lack of material foradequate life with fluid erosion.Therefore, the practical design from theperformance standpoint is notnecessarily the ideal design from theanalytical standpoint.

Experience has shown that these non-linear and non-ideal characteristicslimit the usefulness of theoreticalanalysis of servovalve dynamics insystems design. Instead, the moremeaningful approach is to approximatemeasured servovalve response withsuitable transfer functions, asdiscussed in the body of this technicalbulletin.

The analytic representation of servo-valve dynamics is useful during prelim-

inary design of a new valveconfiguration, or when attempting toalter response of a given design byparameter variation. Analysis alsocontributes to a clearer understandingof servovalve operation.

Rather elaborate analyses ofservovalve dynamic response havebeen performed at Moog, includingcomputer studies which involve severalnonlinear effects, and up to eightdynamic orders (excluding any loaddynamics). Unfortunately, thesecomplex analyses have not contributedsignificantly to servovalve design due touncertainties and inaccuraciesassociated with the higher-order effects.

These analyses have been extremelyuseful when reduced to their simplerform. A very adequate transfer functionrepresentation for the basic Type 30mechanical feedback servovalve isgiven in Figure 12. This simplifiedrepresentation results from the followingassumptions:

1. An ideal current source (infiniteimpedance) is used.

2. Negligible load pressure exists.3. All nonlinearities can either be

approximated by linear dynamiceffects, or can be neglected.

4. The armature/flapper can be rep-resented as a simple lumped-parameter system.

5. Perturbation conditions can beapplied to the hydraulic amplifierorifice characteristics.

6. Fluid compressibility and viscosityeffects are negligible.

7. Motions of the flapper are smallwith respect to spool motion.

8. The forces necessary to move thespool are small with respect to thedriving force available.

The last assumption implies that thedifferential pressure across the spool is

FIGURE 12

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TORQUESUMMATION

SIMPLIFIED SERVOVALVE BLOCK DIAGRAM

negligible during dynamic conditions. If so,then spool mass, friction, flow forces, andother spool force effects can be neglected. Atfirst this assumption may seem unreasonable;but it can be shown to be quite valid, and thesimplification which results more than justifiesits use.

The simplified block diagram is a third ordersystem consisting of the armature/ flappermass, damping and stiffness, together withthe flow-integration effect of the spool. Thespool, in this case, is analogous to the pistonof a simple position servoloop.

The rotational mass of the armature/ flapper isquite easy to calculate. The effective stiffnessof the armature/flapper is a composite ofseveral effects, the most important of whichare the centering effect of the flexure tube,and the decentering effect of the permanentmagnet flux. The latter is set by charge level

of the torque motor, and is individuallyadjusted in each servovalve to meetprescribed dynamic response limits. Thedamping force on the armature/flapper islikewise a composite effect. Here, it is knownfrom experience that the equivalent ζ is about0.4.

The hydraulic-amplifier orifice bridge reducesto a simple gain term with the assumptionslisted earlier. This gain is the differential flowunbalance between opposite arms of thebridge, per increment of flapper motion.

Internal loop gain of the servovalve isdetermined by the following parameters.

The hydraulic amplifier flow gain, K2, can berelated to nozzle parameters by the following:

Any of the loop gain parameters can bealtered to change servovalve response. Forexample, the following changes wouldincrease internal servovalve loop gain: (1)smaller spool diameter, (2) larger nozzlediameter, (3) higher nozzle pressure drop, (4)higher torque motor charge level. The highertorque motor charge gives a lower kf whichincreases loop gain, but this also lowers thenatural frequency of the first stage.Unfortunately, the directions of these twoeffects are not compatible in that higher loopgain cannot be used with a lower naturalfrequency first stage. Therefore, an optimumcharge level exists which produces maximumloop gain for the stability margin desired.