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There are many different measures ofperformance to consider whenchoosing a particular positioningstage. Understanding the definitionsof the various parameters and howthey affect performance will simplifythe selection process.
Minimum Incremental MotionThe smallest motion a device is capa-ble of delivering reliably. Not to beconfused with resolution claims, whichare typically based on the smallestcontroller display increment and whichcan be more than an order of magni-tude more impressive than the actualmotion output. This is a key distinc-tion but is rarely disclosed.
ResolutionThe smallest position increment thata motion system can detect, which isnot the same as the minimum incre-mental motion. Also referred to as dis-play or encoder resolution, it is usuallydetermined by the encoder output,but due to inefficiencies in the drive-train—like hysteresis, backlash andwindup—most systems cannot makea minimum incremental move equalto the resolution unless the encoderis directly measuring the deliveredmotion. See the discussion ondirect output metrology in the sec-tion on Feedback Devices, page 7-15.
SensitivityThe minimum input capable of pro-ducing output motion (most oftenused to describe motion in manualstages). It is also defined as the ratioof the output motion to input drive.This term is often used incorrectly inplace of resolution.
AccuracyThe maximum expected differencebetween the actual and the ideal(desired) position for a given input(Figure 3). Accuracy of a motiondevice is highly dependent on howthe actual position is measured.Therefore accuracy is not a meaning-ful specification for open-loopdevices.
Absolute AccuracyThe output of a system versus thecommanded or ideal input; it ismore intuitively called inaccuracy.When a motion system that is com-manded to move 10 mm actuallymoves 9.99 mm as measured by aperfect ruler, the inaccuracy is 0.01mm. Misalignment of the stage axisversus the ruler’s axis will result in amonotonically increasing inaccuracyproportional to the cosine of themisalignment. This is commonlyreferred to as cosine error.
Important Specifications
Motion Control Coordinate SystemAny positioning stage is consideredto have six degrees of freedom: threelinear, along the x, y, and z axes; andthree rotational about those sameaxes (Figure 1).
All motions described here arewith respect to a right-handedcoordinate system. All movements
can be considered to be composed oftranslations along and/or rotationsabout the coordinate axes.
One key differentiating feature ofNewport products is how wellmotion is constrained in all but thedesired directions. In other words, ifvery “straight” motion in the x direc-tion is required, then the stage mustbe well constrained from moving inthe five off-axis directions (Figure 9).
Introduction
7-2
Figure 1 — Right-handed coordinatesystem showing six degrees of freedom.
ZY
X
θz
θy
θx
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Figure 3 — The difference betweenaccuracy and precision.
MICROMETER READING (mm)
Accuracy = .05 mm
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Precision = ± .08 mm
On-Axis AccuracyThe uncertainty of position after allsources of linear error are eliminated.Linear (or monotonically increasing)errors include cosine error, inaccuracyof the leadscrew pitch, the angulardeviation effect at the measuringpoint (Abbe error) and thermal expan-sion effects. Graphically these errorsare represented by the slope of abest fit line on a plot of position versus error (Figure 2). Knowing theslope of this line (error/travel), wecan approximate absolute accuracy as:
Absolute Accuracy = On-AxisAccuracy + Slope x Travel.
For stages with direct-output metrology such as a linear glassscale, the slope approaches zero andthe absolute accuracy becomes thesame as the on-axis accuracy.
PrecisionThe range of deviations in outputposition that will occur for 95% ofthe motion excursions from the sameerror-free input. Precision is alsoknown as repeatability. Although oftenconfused in common parlance, accu-racy and precision are not the same.Figure 3 shows graphically the differ-ence between these two parameters.
RepeatabilityThe ability of a motion system toreliably achieve a commanded posi-tion over many attempts. Manufac-turers often specify uni-directionalrepeatability which is the ability torepeat a motion increment in onedirection only. This specificationside-steps issues of backlash andhysteresis, and therefore is lessmeaningful for many real-worldapplications where reversal ofmotion direction is common.
A more significant specification is bi-directional repeatability, or the ability toachieve a commanded position overmany attempts regardless of thedirection from which the position isapproached. Few other manufacturerspublicize this much tougher measureof motion performance.
BacklashThe maximum magnitude of an inputthat produces no measurable outputupon reversing direction. It can be aresult of insufficient axial preloadsor poor meshing between drivetraincomponents, i.e., gear teeth in agear-coupled drivetrain. Backlash isrelatively repeatable and can becompensated for by capable controllers.
Figure 2 — Error vs. position for a stage translated four times in each direction. This figureshows graphically the difference between backlash and hysteresis.
Pos
ition
Err
or (
µm)
Travel (mm)
On-AxisAccuracy
Repeatability(Uni-directional)
Reverse
Forward
Hysteresis
Backlash
AbsoluteAccuracy
Combined Hysteresisand Backlash
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HysteresisThe difference in the absolute position of an object for a givencommanded input when approachedfrom opposite directions (Figure 2).It is due to elastic forces accumulatedin various drivetrain components(leadscrew wind-up, for instance).This is often confused with backlashwhich can be characterized and com-pensated for by capable controllers.
ErrorThe difference between an obtainedperformance parameter and theideal or desired result. Errors fall intotwo primary categories. On-axis errors(Figure 4), like accuracy, relate toparameters along the direction oftravel. Off-axis errors, like pitch error,relate to parameters along the con-strained degrees of freedom.
Eccentricity and WobbleSometimes called concentricity,eccentricity in a rotary stage is thedeviation of the center of rotationfrom its mean position as a stageturns (Figure 5). If a stage were per-fectly centered, there would be no
eccentricity as it rotated. For a rotary stage, wobble isthe angular deviation of theaxis of rotation over onerevolution.
RunoutThe linear (versus angular) portion ofoff-axis error. It is the deviation between ideal straight linemotion and actual measured motionin a translation stage. Runout has twoorthogonal components, straightness,a measure of in-plane deviation, and
flatness, the out-of-plane deviation (Figure 6).
Tilt and WobbleThe angular portion of off-axis error.It is the deviation between idealstraight line motion and actual mea-sured motion in a translation stage.Tilt and wobble have three orthogonalcomponents commonly referred toas roll, pitch, and yaw (Figure 7). Theseterms usually dominate the overallerror due to the geometry of themotion system.
Abbe ErrorAdditional linear off-axis error intro-duced through amplification of tiltand wobble with a long moment arm(Figure 8). This type of error occurswhen the point under measurementis a relatively long distance from theaxis of motion. For example, XYZstages incorporating an angle bracketbetween the moving elements willexhibit measurable Abbe error sincethe Z stage is significantly displacedabove the X and Y axes. It appears asrunout, but unlike true runout, Abbeerror can be minimized by reducingthe lever arm.
PlayUncontrolled movement due tolooseness of mechanical parts. It isvery small in a well-built componentand can increase as a componentgrows older, especially if it is roughlyhandled or overloaded. Play is a con-tributor to backlash.
7-4
Figure 6 — Off-axis errors in a linear stage.
Flatness
Typical PitchDeviation
Typical Yaw Deviation
Straightness
Z
Y
X
Figure 7 — Roll, pitch, and yaw aredefined with respect to the direction of travel.
α Z
Pitch Axis
Z
Y
Yaw Axis
Roll Axisα Yα X
X
Figure 8 — Abbe error can be reduced by mini-mizing the height, h, from the stage surface.
δx
θ
h
Figure 5 — Off-axis errors in a rotarystage.
Ball RaceDiameter
Eccentricity
Wobble
Figure 4 — Position error in a translation stage.
Desired Movement
Actual Movement
Error
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FrictionFriction is defined as the resistance tomotion between surfaces in contact.Friction can be constant or it can varywith speed. Elements contributingto overall friction may be in the formof drag, sliding friction, system wearor lubricant viscosity.
StictionThe static friction that must be over-come to impart motion to a body atrest. Since static friction is higherthan sliding friction, the force whichmust be applied to impart motion isgreater than the force required tokeep the body in motion. As a result,when a force is initially applied, thebody will begin to move with a“jump” at some unpredictable andunrepeatable force threshold, givinga non-linear, non-repeatable motionthat controllers cannot compensate.
Position StabilityThe ability to maintain a constantposition over time. Variation from astable position is called drift.Contributors to drift include wornparts, migration of lubricant, andthermal variation.
Load CapacityThe allowable resultant force due toload applied at the center of the stagecarriage with a direction perpendicularto the axis of motion and carriage
surface for linear stages (Figure 10).For rotary stages, the direction of theresultant force is along the axis ofrotation. For loads with a resultantforce which is not centered, thespecified load capacity must be derated appropriately.
One of the primary determinants ofa stage’s load capacity is the bearingsystem. See the Bearings section forfurther discussion.
Normal Load CapacityThe maximum centered load thatcan be placed directly on the movingcarriage. It is typically limited by theload capacity of the bearings in amotion stage.
Transverse Load CapacityAlso called side load capacity, it is themaximum load that can be appliedperpendicular to the axis of motionand along the carriage surface. Thisis usually limited by the loadcapacity of the bearings and is typ-ically smaller than the normal loadcapacity since fewer of the bearingscarry the load.
Axial Load CapacityThe maximum load along the direc-tion of the drivetrain. For linearstages mounted vertically, the speci-fied vertical load capacity is usuallylimited by the axial load capacity.Most often, axial load capacity isdetermined by the load capacity ofthe motor and leadscrew.
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PolarizationShear
Stabilized,dual-polarizationHeNe Laser (633 nm)
BeatDetector
MotorizedStage
V-Reflector
StraightnessPrism
PolarizationBeamsplitter
X Runouts (microns) : Flatness (Z) : Straightness (Y)
Figure 9 — Simplified schematic of Newport’s interferometric testsetup for measuring off-axis errors and sample test results. Highquality translation stages have sub-micron runout errors withangular deviations on the order of 100–150 µradians.
Figure 10 — Load capacity specificationsrefer to loads which are centered and perpendicular.
Load
AxialLoad
TransverseLoad
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Derating Normal Load Capacityfor Off-Axis LoadsSelecting a stage requires under-standing system load requirementsand how the load is applied to thestage.
If the load is cantilevered, the allow-able load capacity must be deratedusing the cantilever equation shownbelow.
The cantilevered load derating equation is:
C = Q (1 + D/a)
where:
C is the equivalent centered load
Q is actual applied load
D is the distance from the center ofthe carriage in centimeters
a is a stage specific constant relatedto the bearing geometry
+Cx in Figure 11 is definedas away from the motor.When a stage is positionedvertically, the motor mustbe on top to meet statedvertical load capacity.
The angular deflectionsresulting from the off-
center load are:
αx = kx Qdx
αy = ky Qdy
αz = kz Qdz
where :
Qdx, Qdy and Qdz are the projectionsof the torque applied by Q onto thex, y and z axes.
Dynamic LoadThe sum of all static loads anddynamic resistance to motion. Somedynamic characteristics of the loadthat need to be considered includefriction and inertia. Dynamic loadmust be considered when evaluatingoverall performance of a motion sys-tem since it limits the system’sachievable acceleration.
Velocity (Speed)The change in distance per unittime. Specifications for maximumspeed are stated at the normal loadcapacity of the stage. Higher speedsmay be possible with lower loads.Minimum stated speeds are highlydependent on a motion device’sspeed stability. As stated in this cat-alog, velocity (a vector) and speed (ascalar) are used interchangeably.
Speed StabilityThe ability to maintain a constantspeed motion. Also specified asvelocity regulation, this parameterdepends upon the stage’s mechanicaldesign, its feedback mechanisms, the control algorithm used and themagnitude of the speed. See the discussion on tachometers in theFeedback Devices section, page 7-15.
AccelerationThe change in velocity per unit time.
InertiaThe measure of a load’s resistance tochange in velocity. The larger theinertia, the greater the torquerequired to accelerate or deceleratethe load. Inertia is a function of aload’s mass and shape. If there is aconstraint on the amount of torqueavailable, then the allowable acceler-ation and deceleration times must beincreased.
MTBFMTBF, or Mean Time Between Failure,is a measure of stage reliability. It isdefined at a rated load and dutycycle. Quoting an accurate value forthis important specification is diffi-cult due to the extensive testinginvolved.
7-6
Figure 11 — Selecting the proper stagerequires an understanding of how loadsare applied.
X
+ Cx
- Cx
C
ZQ
D Y
α x
αya
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Mechanical Stage Design
Materials
Each material used for mechanicalcomponents in motion control has itsown unique set of advantages anddisadvantages. Following is a sum-mary of the properties for the mostcommon materials used in motionmechanics.
StiffnessA measure of the amount of forcerequired to cause a given amount ofdeflection. Force and deflection areproportional and related by theequation:
F = kx
where F and x are force and deflectionrespectively and k is a materialdependent constant of proportionalitycalled the modulus of elasticity. A mate-rial is stiffer for larger values of k.
Thermal ExpansionTemperature changes cause size andshape changes in a stage. The amountof change is dependent on the sizeof the component, the amount oftemperature change, and the materialused. The equation relating dimen-sional change to temperaturechange is:
∆L = αL∆T
where α is the material dependentcoefficient of thermal expansion.
Thermal ConductivitySome materials, such as aluminum,are good choices when temperaturechange across the component isnon-uniform. This occurs whenmounting a heat source such as alaser diode. Because the diode ishotter than the surrounding environ-ment, it dissipates heat through themount setting up a temperature gra-dient along the stage. If the materialdoes not readily dissipate the heat,then distortions caused by thermalgradients can become significant.
The distortion caused by non-uniformtemperature changes is proportionalto the coefficient of thermal expan-sion, α, divided by the coefficient ofthermal conductivity, c.
Relative thermal distortion = α/c
If the ambient operating temperatureof the component is much differentfrom room temperature, then closeattention should be paid to compo-nents made with more than onematerial. In a translation stage, forexample, if the stage is aluminumwhile the bearings are stainless steel,the aluminum and steel will expandat different rates if the temperaturechanges and the stage’s bearingsmay lose preload or the stage maywarp due to stresses which build upat the aluminum-steel interface.
Material InstabilityThe change of physical dimensionwith time; so called cold flow orcreep. For aluminum, brass andstainless steel, the period of timerequired to see this creep may be onthe order of months or years.
AluminumFeaturesAluminum is a lightweight material,resistant to cold flow or creep, withgood stiffness-to-weight ratio. It hasa relatively high coefficient of thermalexpansion, but it also has a highthermal conductivity, making it agood choice in applications wherethere will be thermal gradients orwhere rapid adjustment to tempera-ture changes is required. Aluminumis fast machining, cost effective, andwidely used in stage structures.Aluminum doesn’t rust and corrosionis generally not a problem in a typicaluser’s environment, even when thesurface is unprotected. It has anexcellent finish when anodized.
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LimitationsAnodized surfaces are highly porous,making them unsuitable for use inhigh vacuum.
CoatingsAnodized aluminum provides excel-lent corrosion resistance and a goodfinish. Black is the color most oftenused. Anodizing hardens the surface,improving scratch and wear resistance.Aluminum may also be painted withexcellent results.
SteelFeaturesSteel has a high modulus of elasticity,giving it very good stiffness (nearlythree times that of aluminum), andgood material stability. It also hasabout half the thermal expansion ofaluminum (Figure 12), making it anexcellent choice for stability in typicaluser environments where there areuniform changes in temperature.Stainless steel is well-suited to highvacuum applications.
LimitationsMachining of steel is much slowerthan aluminum, making steel com-ponents considerably more expen-sive. Corrosion of steel is a seriousproblem but stainless steel alloysminimize the corrosion problems ofother steels.
CoatingsSteel parts are generally plated orpainted. Platings are often chrome,nickel, rhodium, or cadmium. Ablack oxide finish is often used onscrews and mounting hardware toprevent rust. Stainless steel alloysavoid the rust problems of othersteels. They are very clean materialswhich do not require special surfaceprotection. A glass-bead blasted surface will have a dull finish whichdoes not specularly reflect.
BrassFeaturesBrass is a heavy material, denserthan steel, and fast machining. Themain use of brass is for wear reduc-tion; it is often used as a dissimilarmetal to avoid self-welding effects
with steel or stainless steel lead-screws or shafts. Brass is used insome high precision applicationsrequiring extremely high resistanceto creep and can be diamond turnedfor extremely smooth surfaces.
LimitationsCompared to aluminum and steel,brass has a less desirable stiffness-to-weight ratio. Also, despite that thethermal expansion of brass is similarto that of aluminum, its thermalconductivity is nearly a factor of twoworse.
CoatingsFor optical use, brass is usually dyedblack. In other cases, it may be platedwith chrome or nickel for surfacedurability.
GraniteFeaturesGranite’s unique physical character-istics, combined with new advancesin machining methods, make granitestructures one of the best choices forair-bearing support structures. Theflatness of the surface is often a majorfactor in the positioning accuracyand repeatability of the total system.
The polished granite surfaces of thesestructures are among the flattestcommercially available—typically±15 microns per square meter. Skilledhand-lapping produces geometricallyperfect surfaces that exceed the flat-ness of surfaces produced by auto-mated equipment of any kind.
An important characteristic of graniteis its extreme hardness, which enablesit to be lapped to very tight flatnessspecifications. Tests confirm thatgranite is more wear-resistant andshock-resistant than steel. Granite’shigh strength makes it particularlysuitable to large-scale systems withheavy static loads. Granite is alsonon-magnetic, making it excellentfor electron beam applications, andis not affected by most chemicals.
The outstanding dimensional stabilityof granite also contributes to its use-fulness in precision support struc-tures. Granite is completely free of
7-8
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internal stresses which results inuniform, predictable response tothermal changes. Granite’s high massalso gives it high thermal inertia,which protects experiments andprocesses from being affected byshort-term ambient temperature fluctuations.
LimitationsFor large structures and table surfacesthe mass of a granite structure canbecome large. For applications whereextreme flatness is not important,steel honeycomb structures offer
better weight to stiffness propertiesand can be damped for specific frequencies to optimize system performance.
Figure 12 — Properties for common stage materials.
Parameter Steel AluminumStiffness, k (Mpsi) 28 10.5Density, ρ (lb/in3) 0.277 0.097Specific Stiffness, k/ρ 101 108Thermal Expansion, α (µin/in/°F) 5.6 12.4Thermal Conduction, c (BTU/hr-ft-°F) 15.6 104Relative Thermal Distortion, α /c 0.36 0.12
Bearings
Bearings permit smooth low-frictionrotary or linear movement betweentwo surfaces. Bearings employ eithera sliding or rolling action. In bothcases, the bearing surfaces must beseparated by a film of oil or otherlubricant for proper performance.
The load and trajectory performanceof a translation or rotation stage isprimarily determined by the type ofbearings which are used.
Ball BearingsBall bearing slides reduce friction byreplacing sliding motion with rollingmotion. Balls are captured in guideways by means of vee-ways or hard-ened steel rods as shown in Figure13. The guide ways are externallyloaded against the balls to eliminateunwanted runout in the bearings.Even with this preload, the friction isvery low resulting in extremelysmooth travel. Ball bearing slidesare relatively insensitive to contami-nation because each ball contactsthe guide ways at only a singlepoint, allowing debris to be pushedout of the way.
With a vee-groove bearing way, ballbearings have a lower load capacitythan crossed-roller bearings, sincethe contact area available to transmitloads is smaller; so in order to carrythe same size load, the balls would
need to have a larger diameter or behigher in quantity.
If the mating ways are ground witheither an arch or circular groove(Figure 14), the closer conformity tothe balls’ radii allows the use ofsmaller balls than with flat ways. Thearch approximates a Vee shapedway with the load effectivelysplit at angles of about 45degrees with the vertical into two loads on the way.
A circular shaped way has a higher load capacity, but the ballsbear the load on the bottom of thegroove which can result in side playfor loads that are perpendicular tothe direction of motion.
Crossed-Roller BearingsCrossed-roller bearings (Figure 15)offer all of the advantages of ballbearings with higher load capacityand higher stiffness. This is a conse-quence of replacing the point contactof a ball with the line contact of aroller.
Bearings of this type require more careduring manufacture and assemblywhich results in higher costs. Reservecrossed-roller slides for applicationswhich require the greatest stability,stiffness and robustness.
Figure 13 — Ball bearing slides haveextremely low friction with moderateload capacity.
Single RowV Profile
Contact Points
Ball Rotation Axis
Gothic Profile Gothic ProfileDouble Row
Figure 15 — Crossed-roller bearingshave all the advantages of ball bearingswith greater stiffness and load capacity.
Figure 14 — The type of bearing way,ball diameter and number of balls affectthe load capacity of a stage.
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Drive Systems
Common drive systems for linearand rotary precision positioningmechanics include the leadscrew,ball screw and worm drive. Shaftcouplings and gearboxes, whicheffect system dynamics such asspeed, load capacity, backlash, anddrive stiffness are located betweenthe drive system and the motor driving it. Gearboxes are most oftenintegrated with the motor.
LeadscrewA very popular technique for movingloads is to use the axial translationof a nut riding along a rotating screw(Figure 16). Leadscrews use slidingcontact, so their wear rate is directlyproportional to usage. The advantagesof leadscrews include self-lockingcapability, low initial costs, ease ofmanufacture and a wide choice ofmaterials.
Recirculating Ball ScrewRecirculating ball screws are essen-tially leadscrews with a train of ballbearings riding between the screwand nut in a recirculating track (Figure17). The large number of mating partsmakes tolerances critical and thusmanufacturing costs higher. Thescrew profile has a rounded shape toconform to the recirculating balls.The primary advantage of ball screwsover leadscrews is higher efficiency,or the amount of energy output forenergy input. However, because itcannot self-lock, a ball screwrequires an auxiliary brake to pre-vent back driving. Additional advan-tages of ball screws are predictableservice life and lower wear rate.
Worm DriveThe worm gear system is a method oftransforming rotary motion in onedirection into rotary motion in anotherdirection by meshing a screw (worm)with a gear. As the screw is turned,the worm threads meshing with thegear cause it to rotate (Figure 18).Advantages of worm drives over
direct drives include higher velocityratios and higher load capacities.
GearboxesGearboxes are used to transmit rota-tional motion and power. They arefrequently used in reduction to pro-duce increased resolution that maybe difficult or impossible to producewith standard motors. A 10:1 gear-box, for example produces one turnof its output shaft for every 10 turnsof its input shaft. A 200-step motorwith this gear combination would beviewed as a device which has aneffective resolution of 2000 pointsper revolution of the output shaft.
In addition to changing resolution,gearboxes with non-unity gear ratiosalso change the available outputtorque and speed. In the exampleabove, the torque is increased andthe speed is decreased.
Flexible Shaft CouplingsCouplings are used in a drivetrain totransmit power and motion betweentwo independent shafts which maynot be perfectly aligned (Figure 19).
Flexible couplings generally allow forsome parallel and angular misalign-ment. Depending on their design,they may accommodate more mis-alignment, have higher torsionalstiffness and load capacity, or becapable of higher speeds (Figure 20).
Figure 16 — As the leadscrew rotates,the load is translated in the axial direc-tion of the screw.
Load
NutMotor
Screw
Figure 17 — Ball screws use recircu-lating balls to reduce friction and gainhigher efficiency than conventional leadscrews.
Nut ScrewBalls
Ball Return
Figure 18 — Worm drive systems canprovide high speed and high torque.
Screw (worm)
Gear(wheel)
Figure 19 — Shaft couplings adjustfor and accommodate angular andparallel misalignment between rotat-ing shafts.
Figure 20 — Flexible couplings are made frommany designs.a) Helical. No backlash and constant velocity
under misalignment. Adaptable to high speedapplications.
b) Bellows. Generally for light-duty applications.Misalignments to 9° angular, 1⁄4" parallel.Good to 10,000 rpm.
a)
b)
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Drive Options
Manual DrivesA manual drive can be described asa high sensitivity leadscrew attachedto a knurled knob. The sensitivitydepends mainly on a comfortablehand position for the operator. Withthe manual drives that Newport pro-vides, we specify a sensitivity of onemicron. This assumes that the knobhas a diameter of 30 millimeters anddrives a leadscrew pitch of one mil-limeter. If reduction gears are incor-porated, sensitivity of 0.1 microns ispossible.
Stepper MotorsA stepper motor operates using thebasic principle of magnetic attractionand repulsion. Steppers convert digitalpulses into mechanical shaft rotation.The amount of rotation is directlyproportional to the number of inputpulses generated and speed is relativeto pulse frequency. A typical steppermotor has a permanent magnet and/oran iron rotor with a stator. Thetorque required to turn the steppermotor is generated by commutatingthe motor as illustrated in Figure 21.
CommutationThe first difference to understandbetween a DC and a stepper motor isthat when a voltage is applied to a DCservo motor, it will develop bothtorque and rotation. When a voltageis applied to a stepper motor it willdevelop only torque. For the motor torotate, the current applied must becommutated or switched.
Commutation is the principle by whichthe amplitude and direction of the cur-rent flowing in the electro-magneticcoils within the motor changes. A
brushed DC motor is designed to self-commutate while a stepper motorlacks internal commutation.
By applying current to the electro-magnetic windings, stepping motorsare able to move in a continuouspoint-to-point positioning manner.When at rest, a full-step motor’s stopposition does not drift because thereis an inherent holding or detent torquewithout power applied. For this reason,steppers at rest generate little heatmaking them suitable for position-and-hold vacuum applications whereheat dissipation is more difficult.
The three primary types of steppermotors are permanent magnet, variablereluctance and hybrid synchronous.
Permanent MagnetPermanent magnet motors have apermanent magnet armature magne-tized perpendicular to the rotationaxis. By energizing four phases insequence, the rotor will rotate as itfollows the changing magnetic field.For the motor depicted in Figure 21,the step angle is 90°. Typical stepangles for permanent magnet motorsare 45° and 90°. They step at relativelylow rates but have high torques andgood damping characteristics.
Variable ReluctanceVariable reluctance motors differfrom permanent magnet motors byhaving a multi-tooth armature, eachtooth being an individual magnet asshown in Figure 22. At rest, thesemagnets align themselves in a naturaldetent position providing largerholding torque. In the exampleshown, by alternately de-energizingpole 1 and energizing pole 2, thearmature rotates 15°.
Figure 21 — Rotation in a steppermotor is generated by alternately energizing and de-energizing the polesin the motor’s stator creating torquewhich turns the rotor.
N
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N
N S
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BD
A
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BD
A
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Step 4
S N
S
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Figure 22 — In a variable reluctancemotor, the multi-tooth armature provideshigher holding torque at each 15°rotary step. Motion is accomplishedthrough coordinated energizing of thestator poles from step 1 through 4.
Step 3
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1 23
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Hybrid SynchronousThe hybrid synchronous steppermotor combines the advantages ofvariable reluctance and permanentmagnet stepper motors. The hybridhas multi-toothed stator poles and amulti-toothed armature (Figure 23).These types of motors exhibit highdetent torque, excellent dynamicand static torque, and can achievehigh stepping rates.
Hybrids usually have two windings oneach stator pole so that the pole canbe either a magnetic north or southdepending on the direction of currentflow. Hybrid motors are manufacturedin a large torque range by varying bothlength and diameter.
DC Brush MotorsA brushed DC motor consists of acylinder shaped armature with wind-ings running parallel to the cylinder’saxis. These windings interact with themagnetic field of the stator causingthe armature to rotate when voltageis applied. To generate continuoussmooth motion with constant torque,the magnetic fields of the armatureand stator must be kept at a constantmagnitude and relative orientation.This is accomplished by constructingthe armature as a series of windingswhich can be electrically commutatedusing two brushes to electricallyconnect the armature.
DC motors are best characterized bytheir smooth motion at high speeds.A DC motor rotates continuouslywhen its windings are energized, andstops only when its windings are de-energized. For accurate and reliablepositioning, an encoder is requiredto provide position feedback.
ActuatorsActuators, as discussed here, move apayload by extending and retractinga shaft by some electromechanicalmeans. To minimize backlash andhysteresis, the payload is often pre-loaded against the actuator shaftusing a spring.
Rotating SpindleMany actuators use the torque fromthe motor to turn and extend a screw.Using this technique means that theactuator tip will be rotating againstthe payload surface. This introducesproblems with eccentricity andunevenness at the tip which can beminimized by rounding the actua-tor’s tip to reduce contact to a verysmall area. An advantage of a rotatingspindle design is small package size.
Non-Rotating SpindleA better approach is to use actuatorswith non-rotating spindles such aspiezoelectric or electrostrictive actu-ators or motorized actuators withspecially designed spindles.
Although piezoelectric devices areexcellent for sub-micron positioningthey lack repeatability because oftheir inherently high hysteresis andcreep.
Electrostrictive actuators have beendeveloped that provide open-looppositioning repeatability improve-ments over piezo devices of an orderof magnitude or more. These actua-tors offer minimum incrementalmotion as fine as 0.04 µm.
Electrostrictive materials are similarto piezoelectric materials in thatboth are ferroelectric crystals whichexpand and contract in proportion toan applied voltage. However, theelectrostrictive actuators use a lead-magnesium-niobate (PMN) crystal
7-12
Figure 23 — Hybrid synchronous steppingmotors gain superior performance by combiningthe best of permanent magnet and variable reluctance stepping motors.
13
2
4
24
1
3
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stack while piezoelectric actuatorsuse lead-zirconate-titanate (PZT)based ceramics. The PMN stack is amulti-layer configuration with verythin layers (125 to 250 microns) thatare diffusion bonded during the man-ufacturing process. The net positivedisplacement is a superposition ofthe strain from the individual layers.
For PMN materials, their change inlength is proportional to the squareof the applied voltage and on thesame order as PZTs. Unlike piezoelec-tric devices, PMN ceramics are notpoled. Positive or negative voltage
excursions result in an elongation inthe direction of the applied field,regardless of its polarity. Becausethe PMN is unpoled, it is an inher-ently more stable device without thelong term creep associated with PZT.The creep, which can range up to15% for PZT devices is reduced tojust 3% as shown in Figure 25.
PMN materials also have better hysteresis characteristics than con-ventional PZT elements. While piezo-electric devices exhibit hysteresis of12 to 15%, PMN hysteresis is only6% (Figure 26).
Figure 24 — Advantages and disadvantages of stepper and brushed DC motors.
More complex—feedback frommotor encoder/tachometerrequires analog to digitalconversion
Easier—windings are selfcommutating
Brushes can wear requiringperiodic maintenance after alarge number of cycles
Lower motor heating with nomotor current at target position(with integral gain, Ki, equalto zero)
Flatter torque curve over thespeed range provides highertorque at higher speeds
Higher for velocity andacceleration
Smooth quiet operation acrossspeed range
PID tuning can be tricky if thesystem dynamics are notunderstood
Reaches final position withclosed-loop error correction.Corrects for trajectory errorsalso. Possible overshoot,hunting, or steady-state error ifPID tuning is inadequate
ControllerElectronics &Software
Driver Electronics
Maintenance
Motor Heating
Torque vs. Speed
Dynamic Range
Resonance
Servo Tuning
Reaching FinalPosition
Easier—can do open-loopcontrol with straight-forwardmicroprocessor implementation
More complex—requirecommutation circuitry
No brushes to worry about
Higher due to continuouscurrent in windings
Full torque at very low speedsdropping off quickly as speedincreases
Lower for velocity andacceleration
Inherent vibration at certainlower frequencies can be aproblem when accelerating to ahigher speed. Ministeppingreduces this problem
None required
Reaches final position withoutovershoot. Very stable holdinga position due to natural detentforces. Open-loop may notreach final position if load orspeed capacities are exceeded
Stepper Motor DC Motor
Figure 25 — Comparing actuatorcreep-electrostrictive actuators are supe-rior to conventional PZTs when tryingto maintain position over time. The figure shows the results after one hourwith a voltage step applied at time-zero.
Figure 26 — Electrostrictive actuatorshave very little hysteresis.
1.0
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7-14
Vacuum Compatibility
Stages used in a vacuum of 10–6 torror better must be specially preparedfor that environment. Many of thematerials used in standard translationstages will outgas in high vacuum,resulting in a “virtual” leak whichlimits the ability to maintain ade-quate vacuum.
Procedures used at Newport to spe-cially prepare products for use invacuum environments ensure thatour products will function asdesigned at pressure levels down to10–6 torr and at the same time notrelease unacceptable quantities ofcontaminants into the vacuum envi-ronment. More information than justthe operating pressure is required forproper preparation. Acceptable levelsof outgassing, mass loss and volatilecondensable materials can vary withthe application, pumping capacity,temperature, etc.
Material issues that must beaddressed include the selection ofacceptable metals, ceramics, coat-ings, lubricants, adhesives, rubbers,plastics and electrical components,etc. For example, highly porousanodized aluminum surfaces traplarge amounts of air molecules,resulting in significant outgassing.For this reason, aluminum used in
high-vacuum applications is unan-odized. Motors must also be speciallyprepared for vacuum operation.
Machining practices must avoid cre-ating surfaces conducive to trappinggases and other foreign materialsthat could be released in vacuumconditions. Care must also be takento ensure that gasses are not trappedin assembly cavities.
In addition to material selection andmanufacturing practices, specialcleaning, handling, assembly andpackaging practices must be followed.These functions are carried out in aclean environment to minimize thepossibility of airborne contaminantsbecoming attached to the compo-nents. Newport does not performbakeout at an elevated temperature.
Performance specifications for prod-ucts used in a vacuum environmentmay vary from non-vacuum use. Forexample, because heat cannot be asreadily dissipated, motor duty cyclemust be reduced which in turn maylimit the maximum achievablespeed. If your application requiresvacuum preparation, please contactour Applications EngineeringDepartment to discuss your specificapplication needs.
Cleanroom Compatibility
Newport has facilities to properlyprepare products for cleanroomapplications. While many of thetechniques, practices, proceduresand material requirements for clean-room applications are similar to
those for vacuum preparation, eachapplication has its own uniquerequirements. Please contact ourApplications Engineering Departmentto discuss your specific applicationneeds.
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A feedback device’s basic function isto transform a physical parameterinto an electrical signal for use by amotion controller. Common feed-
back devices are encoders for posi-tion feedback, tachometers for veloc-ity feedback, and accelerometers foracceleration feedback.
Feedback Devices
The location in the motion systemfrom which the feedback device per-forms its measurements directlyaffects the quality of the data fedback to the controller. The closer thefeedback device is to the parameterbeing controlled, the more effective itwill be in helping the controllerachieve the desired result. Whencontrolling position, for example,measuring the linear position of thestage carriage directly provides high-er quality feedback than measuringthe angular position of the leadscrewand inferring carriage positionthrough knowledge of the drivetrainarchitecture between the encoderand the carriage (Figure 31). The for-mer is known as direct output metrologyand avoids the drivetrain inducederrors like backlash, hysteresis andwindup that can affect the latter,indirect measurement.
Rotary EncoderA rotary encoder can differentiate anumber of discrete positions per
revolution. This number is called itspoints per revolution and is analogous tothe steps per revolution of a steppermotor. A DC motor with a 2000points per revolution encoder is likea stepping motor with 200 steps perrevolution when driven by a ministepdriver. The speed of an encoder is inunits of counts-per-second. Linearand rotary stages and actuatorsincorporating indirect metrology userotary encoders measuring the motorshaft or leadscrew angle to reportposition. Conversely, rotary encoderscan also be used on rotation stagesfor direct output metrology.
Linear EncoderA linear encoder is used when directverification of the output accuracy,resolution and repeatability of thepositioning system is desired. Theseencoders can be used as direct out-put metrology devices to overcomemany of the inaccuracies present inmechanical stages due to backlash,hysteresis and leadscrew error.
Indirect vs. Direct Metrology
Figure 28 — Optical linear encodersdirect light through a glass scale withan accurately etched grating to photo-cells on the opposite side.
Light Source
Lens
ScanningReticle
Scale
GratingPitch
Photocells
ReferenceMark
Figure 27 — Optical rotary encoderscommonly use a stationary maskbetween the code wheel and the detector.
LightSource
CodeDisk
Mask
PhotodetectorAssembly
ElectronicsBoard
HousingAssembly
Although there are various kinds ofdigital encoders, the most common isthe optical encoder. Rotary and linearoptical encoders are used frequentlyfor motion and position sensing.
A disc or a plate containing opaqueand transparent segments passesbetween a light source (such anLED) and detector to interrupt alight beam (Figures 27 & 28). Theelectronic signals that are generatedare then fed into the controllerwhere position and velocity informa-tion is calculated based upon thesignals received.
Optical encoders can be further sub-divided into absolute and incrementalencoders.
Absolute EncodersAbsolute encoders contain multipledetectors and up to 20 tracks of seg-ment patterns. For each encoderposition, there is a different binaryoutput so that shaft position isabsolutely determined. Withabsolute encoders, the positioninformation is available even if theencoder is turned off and on again.
Optical Encoders
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Figure 30 — Quadrature encoder out-put provides direction as well as positionfeedback.
Ch A
Ch B
t
t
If Ch A leads Ch B, direction is forward
f ( t )
Figure 29 — To get submicronrepeatability using an index pulse froman encoder, homing should always beapproached from the same direction.
ExternalLogic
Origin Switch
0V
Disc attachedto motor shaft
Incremental EncodersWhen lower cost is important, orwhen only relative information isneeded, incremental encoders arepreferred. Their output consists ofelectronic signals corresponding toan increment of linear or rotationalmovement.
Many incremental encoders also havea feature called the index pulse. Anindex pulse occurs once per encoderrevolution in rotary encoders (Figure29). It is used to establish an absolutemechanical reference position withinone encoder count of the 360°encoder rotation. The index signalcan be used to do several tasks inthe system. It can be used to reset or preset the position counter and/orgenerate an interrupt signal to thesystem controller.
Quadrature EncodersQuadrature encoders are a particularkind of incremental encoder with of atleast two output signals, commonlycalled channel A and channel B. Asseen in Figure 30, channel B is offset90 degrees from channel A. Theaddition of a second channel pro-vides direction information in thefeedback signal. The ability to detectdirection is critical if encoder rotationstops on a pulse edge. Without theability to decode direction, thecounter may count each transition
through the rising edge of the signaland lose position.
Another benefit of the quadraturesignal scheme is the ability to elec-tronically multiply the counts duringone encoder cycle. In the times-1mode, all counts are generated onthe rising edges of channel A. In thetimes-2 mode, both the rising andfalling edges of channel A are usedto generate counts. In the times-4mode, the rising and falling edges ofchannel A and channel B are used to generate counts. This increases theresolution by a factor of four. Forencoders with sine wave output, thechannels may be interpolated forvery high resolution.
or
E M
Stage
DriverController
User
(a)
Stage
DriverController
User
(b)
Encoder
E
Stage
DriverController
User
(c)
T
or
M
M
Encoder
E M
Figure 31 — Closed-loop systems. a) Using indirect metrology rotary encoder b) Using direct metrology linear encoder c) Using encoder for position feedback and tachometer for velocity control.
For applications requiring velocityregulation, speed can be either measured directly or derived fromencoder supplied position informa-tion. For higher quality speed control,a tachometer is used which producesa voltage or current level proportionalto the speed of the motor (Figure 31).Tachometer feedback can changeinstantaneously with speed changeallowing faster correction and tighterregulation from a controller.
Tachometers
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Figure 33 — Functional block diagramof controller operations.
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A controller is a device in a motionsystem that generates electronic signals instructing the motionmechanics to move or stop. If afeedback system exists, then signalsmeasuring the actual motion outputare returned to the controller. Thecontroller compares the actual todesired output and generates anerror signal upon which correctiveaction is taken (Figure 32).
The controller sends signals to themotor driver to control motion withinthe system. A controller can havevarious features such as data commu-nications, input/output lines, memoryfor storing motion programs, andencoder feedback processing forclosed-loop positioning (Figure 33).
Although a displacement can takeseveral seconds, the controller has towork at higher speeds to make calcu-lations and output updated motioncommands. The time needed forthese actions to take place is calledthe sampling time.
Centralized versus DistributedMotion ProcessingControllers may be designed suchthat a single microprocessor controlsmotion on all axes. Alternatively, the controller may use a distributedconfiguration where a central micro-processor coordinates dedicatedspecial-purpose motion controlchips on each axis (Figures 34 & 35).
Digital Signal ProcessorDigital Signal Processors (DSPs) are special chips manufactured toaddress the increased speed require-ments in calculating advanced controlalgorithms. When these operations areperformed on an ordinary processor,they can consume too much time toprovide high-speed control.
DSPs are often built using an archi-tecture that allows instructions anddata to move in parallel instead ofsequentially. They often carry highspeed hardware multipliers and faston-chip memories that eliminatemany delays associated with informa-tion transfer to and from the chip.
An origin switch is a device whichdefines a repeatable reference point.The switch may be mechanical, suchas an on/off switch or it may be anoptical device such as the indexpulse (top zero) of optical encoders(Figure 29).
Limit switches are used to preventmotion from proceeding beyond adefined point. They are usuallylocated at the ends of stage travelimmediately before the stage’s hardtravel stops. They can be mechanicalor optical and are designed to cut
motor power when a limit is encoun-tered. Limit switches are most oftenassociated with linear stages butrotary stages can also have limits toavoid problems like cable wind-up.
Mechanically actuated micro-switchesare often used to cut motor powerand prevent over-travel. Therepeatability of mechanical switchesis limited by their hysteresis andsusceptibility to wear.
Origin and Limit Switches
Figure 32 — Basic feedback controlsystem.
DesiredOutput
Response
ActualMotionController/
Motor DriverMotion
Mechanics
Measurements
CommandInterpreter
TrajectoryGenerator
ServoController MotorDriver
Motion Controller
Encoder
Or
10V
Encoder
DC
Stepper
µP Bus
Encoder
DAC
Counter
F. Generator
Counter
MainµP orDSP
Figure 35 — Distributed motion processing provides dedicated motioncontroller chips for each axis coordinatedby a central CPU.
DedicatedChip
10V
EncoderDC
StepperEncoder
DedicatedChip
µP Bus
MainµP
Controllers
Motion Electronics Design
Figure 34 — With centralized motionprocessing, all axes are controlled by asingle microprocessor.
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Figure 37 — A high voltage chopperhelps a stepper motor reach full currentfaster enabling higher speeds.
Nominal Current
Phase ON
A motor driver receives input signalsfrom a controller and converts themto power to drive a motor. Withstepper drivers, the user has theoption of selecting from among full,half, or microstep resolutions and thedesired output power of the device.
Stepper Motor DriverFull StepA full step driver operates a steppermotor in a detent-to-detent steppingmode. When power is removed, thestepper motor will not move from itscurrent position due to its inherentholding or detent torque.
Half StepA half step driver operates a steppermotor by positioning the armaturehalfway between actual detent posi-tions. This provides higher resolutionand somewhat smoother motion overthe motor’s operating speed range.However, if power is removed, thestepper motor will move from itscurrent half step position to a physical detent position.
Microstep/MinistepA microstep driver will position astepper motor armature a definedfraction of a full step between theactual detent positions. In this cata-log, microstep is used to describe1⁄100 of a full step and ministep is 1⁄10
of a full step. Mini- and microstep-ping are used for greater resolutionand to avoid resonance problemsand skipping steps in the motor overthe speed range of the stage. Onceagain, if power is removed, themotor will move from its currentposition to a true detent position.
High-Voltage Chopper TechnologyA simple four-phase driver is fine forbasic, low performance applications.But, if high speeds are required,quickly switching the current withinductive loads becomes a problem.When voltage is applied to a winding,the current (and therefore, thetorque) approaches its nominalvalue exponentially (Figure 36). Whenthe pulse rate is fast, the currentdoes not have time to reach thedesired value before it is againturned off so the total torque gener-ated is only a fraction of nominal.
The time required for the current toreach its nominal value depends onthree factors: the motor winding’sinductance, its resistance and thevoltage applied.
The inductance cannot be reduced,but the voltage can be temporarilyincreased to bring the current to itsdesired level faster. The most widelyused technique is a high voltagechopper.
If, for instance, a stepper motorrequiring only 3 V to reach the nomi-nal current is connected momentarilyto 30 V, it will reach the same currentin only 1⁄10 the time.
Once the desired current value isreached, a chopper circuit activates tokeep the current close to the nominalvalue (Figure 37).
DC Motor DriversDrivers for DC motors convert asmall voltage signal from the con-troller (usually ± 10 V) into a usablecurrent to drive the motor.
Motor Drivers
7-18
Figure 36 — Exponential currentbuild-up in the motor is too slow forhigh speed applications.
Phase ON
Current
Nominal Current
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Common motion systems use threetypes of control methods. They areposition control, velocity control andtorque control.
The majority of Newport’s motionsystems use position control. Thistype of control moves the load fromone known fixed position to anotherknown fixed position. Feedback, orclosed-loop positioning, is impor-tant for precise positioning.
Velocity control moves the load con-tinuously for a certain time intervalor moves the load from one place toanother at a prescribed velocity.Newport’s systems use both encoderand tachometer feedback to regulatevelocity.
Torque control measures the currentapplied to a motor with a knowntorque coefficient in order to developa known constant torque. Newport’smotion systems do not employ thismethod of control.
Following ErrorThe instantaneous differencebetween actual position as reportedby the position feedback device andthe ideal position, as commandedby the controller.
Settling TimeThe amount of time elapsed betweenwhen a stage first reaches a com-manded position and when it main-tains the commanded position towithin an acceptable pre-definederror value (Figure 38).
OvershootThe amount of over-correction in an under-damped control system(Figure 39).
Steady-State ErrorThe difference between actual andcommanded position after the con-troller has finished applying correc-tions (Figure 39).
VibrationWhen the operating speed approachesa natural frequency of the mechanicalsystem, structural vibrations, or ringing, can be induced. Ringing canalso occur in a system following asudden change in velocity or posi-tion. This oscillation will lessen theeffective torque and may result inloss of synchronization between themotor and controller.
Settling times and vibrations canbest be dealt with by damping motoroscillations through mechanicalmeans such as friction or a viscousdamper. When operating a steppersystem, some additional methodsthat can change resonance vibration frequencies are:
• half stepping or microsteppingthe motor
• changing the system inertia
• accelerating through the reso-nance speed ranges
• modifying drivetrain torsionalstiffness
Control Theory Terminology
Velocity Profiles
In order to achieve smooth high-speed motion without over-taxingthe motor, the controller must directthe motor driver to change velocityjudiciously to achieve optimumresults. This is accomplished usingshaped velocity profiles to limit theaccelerations and decelerationsrequired.
Trapezoidal ProfileThe trapezoidal profile changesvelocity in a linear fashion until thetarget velocity is reached. Whendecelerating, the velocity againchanges in a linear manner until itreaches zero velocity. Graphing velocityversus time results in a trapezoidal
Figure 39 — Response for a systemusing only proportional control leads toovershoot and non-zero steady-stateerrors.
1.0O
utpu
tIn
put
Overshoot
Time0
1.0+δ
TsSettling
Time
TpPeakTime
TrRiseTime
e steady state
1.0–δ
Position
Settling Time
Acceptable error
Time
Commandedposition
Figure 38 – How settling time isdefined.
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plot (Figure 40). Advanced con-trollers allow user modification ofthe acceleration/deceleration withmore advanced controllers allowingindividual settings for accelerationand deceleration.
S Curve ProfileA trapezoidal velocity profile is adequate for most applications. Itsonly disadvantage is that it may
cause some system disturbances atthe “corners” that translate in smallvibrations which extend the settlingtime. For demanding applicationssensitive to this phenomenon, thevelocity profile can be modified tohave an S shape during the accelera-tion and deceleration periods. Thisminimizes the vibrations caused in amechanical system by a moving mass.
7-20
Open-Loop ControlOpen-loop refers to a control tech-nique which does not measure andact upon the output of the system.Most piezoelectric systems and inexpensive micrometer-replacementactuators are open-loop devices.
Open-loop positioners are usefulwhen remote control is desired forimproved accessibility or to avoiddisturbing critical components bytouching them.
Stepper and ministepper motors are also often used open-loop. Thecount of pulses is a good indicatorof position, but can be unpredictableunless loads, accelerations andvelocities are well known. Skipped orextra steps are frequent problems ifthe system is not properly designed.
Open-loop motion control hasbecome very popular. Advances inministepping technology and incor-poration of viscous motor-dampingmechanisms have greatly improvedthe positioning dependability andreduced vibration levels of today’shighest quality stepper devices.
Open-loop is by no means a synonymfor crude. Very fine incrementalmotions can be achieved even byinexpensive open-loop devices.Nanometer-scale incremental motionsare achievable by open-loop piezo-and electrostrictive-type devices.
Open-loop systems infer the approx-imate position of a motion devicewithout using an encoder. In the caseof a piezo device, the applied voltageis an indicator of position. However,the relationship is imprecise due tohysteresis and non-linearities inherentin commonplace piezo materials.More recently-developed electro-strictive materials operate in a similar manner with greatly reduced hysteresis.
Closed-Loop ControlClosed-loop refers to a control tech-nique which measures the output ofthe system compared to the desiredinput and takes corrective action toachieve the desired result. Electronicfeedback mechanisms in closed-loopsystems enhance the ability to cor-rectly place and move loads.
Control Loops
Closed-Loop Control Techniques
Depending upon how the feedbacksignals are processed by the controller,different levels of performance canbe achieved. The simplest type offeedback is called proportional control.
Other types are called derivative andintegral control. Combining all threetechniques into what’s called PIDcontrol provides the best results.
Figure 40 — Trapezoidal motion profiles are required to obtain higherspeeds without skipping steps or stalling.
Ramp Slope
Start Stop
AccelerateConstantVelocity Decelerate
TopSpeed
Start/StopRate
STEPRATE
TIME
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Proportional ControlA control technique which multipliesthe error signal (the differencebetween actual and desired position)by a user-specified gain factor Kp
and uses it as a corrective signal tothe motion system. The effectiveresult is to exaggerate the error andreact immediately to correct it.
Changes in position generally occurduring commanded acceleration,deceleration, and in moves wherevelocity changes occur in the systemdynamics during motion. As Kp isincreased the error is more quicklycorrected. However, if Kp becomestoo large, the mechanical systemwill begin to overshoot, and at somepoint, it may begin to oscillate,becoming unstable if it has insuffi-cient damping.
Kp cannot completely eliminate errors since as the following error, e,approaches zero, the proportionalcorrection element, Kp e, disappears.This results in some amount ofsteady-state error.
Integral ControlA control technique which accumu-lates the error signal over time, multi-plies the sum by a user specified gainfactor K i and uses the result as acorrective signal to the motion system.Since this technique also acts uponpast errors, the correction factordoes not go to zero as the followingerror, e, approaches zero allowingsteady-state errors to be eliminated.
The integral gain has an importantnegative side effect. It is a destabi-lizing factor for the stability of thecontrol loop. Large values or usedwithout proper damping could causesevere system oscillations.
Derivative ControlA control technique which multiplesthe rate of change of the followingerror signal by a user specified gainKd and uses the result as a correctivesignal to the motion system. Since
this type of control acts to stabilizethe transient response of a system,it may be thought of as electronicdamping.
Increasing the value of Kd, increasesthe stability of the system. Thesteady-state error, however, is unaf-fected since the derivative of thesteady-state error is zero.
PID ControlThe combination of proportional plusintegral plus derivative control. Formotion systems, the PID loop hasbecome a very popular controlalgorithm (Figure 41). The feedbackelements are interactive and knowinghow they interact is essential for tuning a motion system. Optimumsystem performance requires that thecoefficients, Kp, Ki, and Kd, be tunedfor a given combination of motionmechanics and payload inertias.
Feed Forward LoopsWhen using a PID control algorithm,an error between the desired andactual positions must exist in orderto generate a corrective input. Theimplication of this is that there willalways be some non-zero following error.The goal when using a feed forwardloop is to minimize following error.
TrajectoryGenerator
PreviousFollowing Error
CurrentFollowing Error
x Kp
x Kd
x Kii l
(n–1)
(n)
Amp M
E
Kp = proportional gain
Kd = derivative gain
Ki = integral gain
il = integral limit
M = motor
E = encoder
Current Position
DesiredPosition
Error Integral
Figure 41 — PID control implementedusing position feedback.
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Motion Without InterpolationThere are three types of non-interpo-lated motion: single-axis, simultaneous,and synchronized motion.
Simultaneous and synchronizedmotion are both multi-axis (Figure43). The difference between them isthat simultaneous motion is unsyn-chronized (Figure 44).
Motion with InterpolationWhen the controlled load must fol-low a particular path to get from itsstarting point to its stopping point,the coordination of axis movementsis said to be interpolated. There aretwo types of interpolation, linear andcircular.
Linear InterpolationLinear interpolation is required formulti-axis motion from one point toanother in a straight line. The con-troller determines the speeds oneach axis so that the movements arecoordinated. True linear interpola-tion requires the ability to modifyacceleration. Some controllersapproximate linear interpolationusing pre-calculated accelerationprofiles (Figure 45).
Circular InterpolationCircular interpolation is the ability tomove the payload around a circulartrajectory. It requires the controllerto modify acceleration on the fly(Figures 46 & 47).
Positioning Trajectory Options
Figure 44 — With non-interpolatedmotion several axes can move simulta-neously, but are not coordinated.
Axis 1Speed
Axis 2Speed
Trajectory
: Stop or start point (axis 1)
• : Stop or start point (axis 2)
Axis 2
Axis1
Time
Time
The concept in using a feed forwardloop is to predict how the systemwill function in future updates andto make corrections now based onthose estimates (Figure 42).
The corrections are generally imple-mented by multiplying the desiredvelocity with the velocity feed-forwardgain factor Kvff. The same techniquecan be used to apply an acceleration
feed-forward correction signal. Thiscorrection is being used to reducethe average following error during theacceleration and deceleration periods.Combining feed forward techniqueswith PID allows the PID loop to correctonly for the residual error left by thefeed forward loop, thereby improvingoverall system response.
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Current Position
DesiredPosition
TrajectoryGenerator
LastFollowing Error
CurrentFollowing Error
ErrorCommand
f.f.cmd.
Error Integral
x Kp
x Kd
x Kii l
x Kvf f
(n–1)
(n)
Amp M
E
Kp = proportional gain
Kd = derivative gain
Ki = integral gain
il = integral limit
Kvff = velocity feedforward gain
M = motor
E = encoder
Figure 42 — Adding a feed forward loop to the PID controller reduces following error and improves overallsystem performance.
Figure 43 — With synchronizedmotion, multiple axes may or may notmove together.
Axis 1Speed
Axis 2Speed
Axis 2
Axis1
Time
Time
Trajectory
: Stop point
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Figure 48 — Applications such as laserwriting require unusual trajectories executed at constant speed.
Axis 1Speed
Axis 2Speed
Axis 2
Axis1
Time
Time
Trajectory
1 2 3 4 5 6 7 8
12
10
5
0
Position(Inc.)
Time 00
Position
(T1)X
Y
3
1
(Inc. /s)
2
1
0
-1
-2
(Inc. /s2)
Speed
Acceleration
Time
Time
-2 -1 -0 -1 -20 -1 -2 -3 -4 -5 -6 (Inc. /s2)
Acceleration
(Inc. /s)(Inc.)
SpeedPosition
TimeTimeTime
0 -1
Axis X
Axis Y
(T1)
RealLinearInterpolation
“Pseudo”LinearInterpolation
XY Stage
Note: Inc = IncrementInc/s = Increment per second
Inc/s2 = Increment per second2
= Controller without linear interpolation
Figure 45 — “Pseudo” linearinterpolation is obtained withcontrollers using precalculatedacceleration ramps.
Figure 46 — Simple circular interpolation.
Axis 1Speed
Axis 2Speed
Axis 2
Axis1
Time
Time
Trajectory
210
-1-2-3
10
6
0
Position(Inc.)
Time0
(T1)
Y
3
(Inc./s)
210
-1-2
(Inc. /s2)
Speed
Acceleration
Time
Time
-3 0 3(Inc. /s2)
Acceleration
(Inc.)
SpeedPosition
TimeTime
Axis X
Axis Y XY Stage
2
6
2
1 3 5 7 9
(T9)
(T3)
(TC)
(T7)
10
2 6 100
1
3
5
7
-2 -1 -0 -1 -2
Time
Note: Inc = IncrementInc/s = Increment per second
Inc/s2 = Increment per second2
2 6 100(Inc. /s2)
= Controller without circular interpolation
Figure 47 — To be able tocontrol stages in “real” circu-lar interpolation, a controllermust be able to modify theacceleration on the fly.
ContouringWith contouring, the controllerchanges the speeds on the differentaxes so that the trajectories passsmoothly through a set of prede-
fined points. The speed is definedalong the trajectory and can be con-stant, except during starting andstopping (Figure 48).
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As a rule of thumb for tuning systems:
• Always start tuning with propor-tional gain Kp to get adequateresponse speed
• Next, increase the value for Kd todecrease the overshoot and stabi-lize the system
• Finally, increase the value for Ki toeliminate steady-state error
• To avoid stability problems, neveruse Kp and Ki without Kd
Servo tuning is usually performed toachieve better motion performance(such as reducing the following error
statically and/or dynamically) orbecause the system is malfunction-ing (oscillating and /or shutting offdue to excessive following error).
Acceleration plays a significant rolein the magnitudes of the followingerror and the overshoot, especiallyat start and stop. Asking the con-troller to change the velocity instan-taneously amounts to an infiniteacceleration which, since it is physi-cally impossible, causes large follow-ing errors and overshoot. Use thesmallest acceleration the applicationcan tolerate to reduce overshoot andmake tuning the PID filter easier.
Tuning Procedures
Stabilizing Axis Oscillation
If an axis oscillates, this indicatesthat the gain Kp may be too large.Start by reducing the proportionalgain factor Kp by one order of mag-nitude (e.g., 0.2 to 0.02) and makingKi and Kd equal to zero.
If the oscillation does not stop,reduce Kp again.
When the axis stops oscillating, thesystem response is probably verysoft. The following error may bequite large during motion and non-zero at stop. You should continuetuning the PID with the stepsdescribed in the next paragraph.
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Servo tuning sets the Kp, Ki and Kd
and the feed forward parameters ofthe digital PID algorithm, also calledthe PID filter.
Always start the tuning process usingthe default values supplied with thecontroller. These values are usuallyvery conservative, favoring safe,oscillation-free operation for a tighter,
more responsive system that mini-mizes following error. To achieve thebest dynamic performance possible,the system must be tuned for thespecific application. Load, accelera-tion, stage orientation and perfor-mance requirements all affect howthe servo loop should be tuned forbest results.
Servo Tuning Principles
Improving Stable Performance
If the system is stable and you wantto improve the performance, startwith the current parameters. The goalis to reduce the following error duringmotion and to eliminate it at stop.
Depending on the performance start-ing point and the desired outcome,here are some guidelines for furthertuning.
Before you startProper tuning requires the
motor driver’s signal gain,
tachometer gain and DC offset
on each axis to be properly
adjusted. Please consult our
technical staff.
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Following Error Too LargeThis is a case of a soft loop. It isespecially common if you just per-formed the steps described underaxis oscillations. The proportionalgain Kp is probably too low and Ki
and Kd are zero.
Start by increasing Kp by a factor of1.5 to 2. Continue this operationwhile monitoring the following erroruntil it starts to exhibit excessiveringing characteristics (more than 3 cycles after stop). To reduce theringing, add some damping byincreasing the Kd parameter.
Start with a Kd value one order ofmagnitude smaller than Kp. Increaseit by a factor of 2 while monitoringthe following error. As Kd is increased,the overshoot and the ringing willdecrease almost to zero.
NOTERemember that if the acceleration isset too high, the overshoot cannotbe completely eliminated with Kd.
If Kd is further increased, at somepoint the oscillation will reappear,usually at a higher frequency. Avoidthis by keeping Kd at a high enoughvalue, but not so high as to reintro-duce oscillations.
Next, add more gain. Increase the Kp
value by 50% at a time until signs ofexcessive ringing appear again.
Alternately increase Kd and Kp untilKd cannot eliminate the overshootand ringing at stop. This indicates Kp
is larger than its optimal value andshould be reduced.
Ultimately, optimal values for Kp andKd depend on the stiffness of theloop and how much ringing theapplication can tolerate.
Errors After StopIf you are satisfied with the dynamicresponse of the PID loop but themotion device does not always stop
accurately, modify the integral gainfactor Ki. As described before, thisterm of the PID reduces the followingerror to near zero. Unfortunately, itcan also contribute to oscillationand overshoot. Always change thisparameter carefully and in conjunc-tion with Kd.
Start, if possible with a value for Ki
that is at least two orders of magni-tude smaller than Kp. Increase itsvalue by 50% at time and monitorthe overshoot and the final positionat stop.
If intolerable overshoot develops,increase the Kd factor. Continuealternately increasing Ki and Kd
until an acceptable loop responseis obtained. If oscillation develops,immediately reduce the Ki.
Remember that any finite value forKi will eventually reduce the error atstop. It is simply a matter of howmuch time is acceptable for theapplication. In most cases it ispreferable to wait a few extra milli-seconds to stop in position ratherthan have overshoot or run the riskof oscillations.
Following Error During MotionThis is caused by a Ki value that istoo low. Follow the steps in the pre-vious paragraph, keeping in mind thatit is desirable to increase the integralgain factor as little as possible.
Points to Remember• Use the lowest acceleration the
application can tolerate. Smalleracceleration generates less over-shoot.
• Use the default values providedwith the system for all standardmotion devices as a startingpoint.
• Use the minimum value for Ki
that gives acceptable performance.The integral gain factor can causeovershoot and oscillations.
