Designing with Piezoelectric...

Piezo • Nano • Positioning

designing with piezo actuators, piezoelectrics, piezoactuation, piezo motor, fundamentals, nanopositioning, PZT, piezo-electric, piezoelectricity

Designing with Piezoelectric Transducer s: Nanopositioning Fundamentals

Polarization

09/2005

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Piezoelectric transducer, piezoelectric actuator, piezo positioner

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2

Features and Applications of Piezoelectric Positioner s . . . . . . . . . . . . . . . . . . . . . 4-4

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5

Symbols and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9

Nanopositioning with Piezoelectric Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9Features of Piezoelectric Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9

Quick Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10

Actuator Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10Operating Characteristics of Piezoelectric Actuators . . . . . . . . . . . . . . . . . . . . . . . . 4-11

Fundamentals of Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13

Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13PZT Ceramics Manufacturing Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14Definition of Piezoelectric Coefficients and Directions . . . . . . . . . . . . . . . . . . . . . . 4-14Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15

Fundamentals of Piezomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16

Displacement of Piezo Actuators (Stack & Contraction Type) . . . . . . . . . . . . . . . . . 4-16Hysteresis (Open-Loop Piezo Operation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17Creep / Drift (Open-Loop Piezo Operation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18

Actuators and Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19

Metrology for Nanopositioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19Indirect (Inferred) Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19Direct Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19Parallel and Serial Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19High-Resolution Sensors—Strain Gauge Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19Linear Variable Differential Transformers (LVDTs) . . . . . . . . . . . . . . . . . . . . . . . . . 4-20Capacitive Position Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20

Fundamentals of Piezoelectric Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21

Forces and Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21Maximum Applicable Forces (Compressive Load Limit, Tensile Load Limit) . . . . . 4-21Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21Force Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22Displacement and External Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23

Dynamic Operation Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24

Dynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24Resonant Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25How Fast Can a Piezo Actuator Expand? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26

4-2

Contents Tutorial: Piezoelectric Transducers / Actuators in Positioning

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PIezo

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Piezo Actuator Electrical Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27

Electrical Requirements for Piezo Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27Static Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27Dynamic Operation (Linear) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28Dynamic Operating Current Coefficient (DOCC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29Dynamic Operation (Switched) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29Heat Generation in a Piezo Actuator in Dynamic Operation . . . . . . . . . . . . . . . . . . 4-30

Control of Piezo Actuators and Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31

Position Servo-Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31Open- and Closed-Loop Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32Piezo Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32Methods to Improve Piezo Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33InputShaping® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33Signal Preshaping / Dynamic Digital Linearization (DDL) . . . . . . . . . . . . . . . . . . . . 4-34Dynamic Digital Linearization (DDL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35

Environmental Conditions and Influences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36

Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36Linear Thermal Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36Temperature Dependency of the Piezo Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36Piezo Operation in High Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36Piezo Operation in Inert Gas Atmospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-37Vacuum Operation of Piezo Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-37Lifetime of Piezo Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38

Basic Designs of Piezoelectric Positioning Drives/Systems . . . . . . . . . . . . . . . . . . 4-39

Stack Design (Translators) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39Laminar Design (Contraction-Type Actuators) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39Tube Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-40Bender Type Actuators (Bimorph and Multimorph Design) . . . . . . . . . . . . . . . . . . 4-41Shear Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41Piezo Actuators with Integrated Lever Motion Amplifiers . . . . . . . . . . . . . . . . . . . . 4-42Piezo Flexure Nanopositioners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-43

Parallel and Serial Kinematics / Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-44

Direct and Indirect Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-44Parallel and Serial Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-45

PMN Compared to PZT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-46

Electrostrictive Actuators (PMN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-46

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47

Mounting and Handling Guidelines for Piezo Translators . . . . . . . . . . . . . . . . . . . 4-48

4-3


Active Optics / Steering Mirrors

Tutorium: Nanoposi-tionieren mit Piezos

Capacitive PositionSensors

Piezo Drivers & Nano-positioning Controllers

Hexapods /Micropositioning

Photonics AlignmentSolutions

Motion Controllers

Ceramic Linear Motors & Stages

Nanopositioning &Scanning Systems

Piezo Actuators

Index


Tutorial: Piezo-electrics in Positioning





Motion Controllers



Piezo Actuators

Index

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4-4

Data Storage

� MR head testing� Spin stands� Disk testing� Active vibration cancellation� Pole-tip recession test

Semiconductors, Microelectronics

� Nano & Microlithography� Nanometrologie� Wafer and mask positioning� Critical-dimension-test� Inspection systems� Active vibration cancellation

Precision Mechanics

� Fast tool servos� Non-circular grinding,

drilling, turning� Active vibration cancellation � Structural deformation� Tool adjustment

� Wear compensation� Needle-valve actuation� Micropumps� Linear drives� Knife edge control in extrusion

tools� Micro engraving systems� Shock wave generation

Life Science, Medical Technology

� Scanning microscopy� Patch clamp� Nanoliter pumps� Gene manipulation� Micromanipulation� Cell penetration� Microdispensers

Optics, Photonics,

Nanometrologie

� Scanning mirrors� Image stabilization,

pixel multiplication

� Scanning microscopy� Auto focus systems � Interferometry � Fiber optic alignment� Fiber optics switching � Adaptive and active optics � Laser tuning � Stimulation of vibrations

Applications for Piezoelectric Positioning Technology

Features of Piezoelectric Positioning System s

Unlimited Resolution

Piezoelectric actuator s convertelectrical energy directly to me-chanical energy. They make mo-tion in the sub-nanometer rangepossible. There are no movingparts in contact with each other tolimit resolution.

Fast Expansion

Piezo actuators react in a matter ofmicroseconds. Acceleration ratesof more than 10,000 g can be ob-tained.

High Force Generation

High-load piezo actuators capableof moving loads of several tons areavailable today. They can covertravel ranges of several 100 µmwith resolutions in the sub-na-nometer range (see examples likethe P-056, in the “Piezo Actuators”section).

No Magnetic Fields

The piezoelectric effect is related toelectric fields. Piezo actuators donot produce magnetic fields nor

are they affected by them. Piezodevices are especially well suitedfor applications where magneticfields cannot be tolerated.

Low Power Consumption

Static operation, even holdingheavy loads for long periods, con-sumes virtually no power. A piezoactuator behaves very much like anelectrical capacitor. When at rest,no heat is generated.

No Wear and Tear

A piezo actuator has no movingparts like gears or bearings. Its dis-placement is based on solid statedynamics and shows no wear andtear. PI has conducted endurancetests on piezo actuators in whichno measurable change in perform-ance was observed after severalbillion cycles.

Vacuum and Clean Room

Compatible

Piezoelectric actuators neithercause wear nor require lubricants.The new PICMA® actuators with

ceramic insulation have no poly-mer coating and are thus ideal forUHV (ultra-high vacuum) applica-tions.

Operation at Cryogenic

Temperatures

The piezoelectric effect continuesto operate even at temperaturesclose to 0 kelvin. PI offers speciallyprepared actuators for use at cryo-genic temperatures.

Selection of piezo nanopositioning stages

Piezoelectric nano positioner s, large(e.g. for precision machining), medium (e.g. forinterferometry), small (e.g. for data storagemedium testing)

Properties / Applications

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Piezoelectric transducer, piezoelectric actuator

Nanopositioning system featuring parallel kinematics and parallel metrology.

Piezoceramic layers in a monolithic actuator (LVPZT).

4-5


Equipment for fully automated screen printing of electrodes on piezoelectric and dielectric ceramics.

Glossary







Motion Controllers



Piezo Actuators

Index

Piezoceramic layers in a “classical” stack actuator (HVPZT).

See also the MicropositioningGlossary, p. 7-12.

Actuator:

A device that can produce force ormotion (displacement).

Blocked Force:

The maximum force an actuatorcan generate if blocked by an infi-nitely rigid restraint.

Ceramic:

A polycrystalline, inorganic mate-rial.

Closed-Loop Operation:

The displacement of the actuatoris corrected by a servo-controllercompensating for nonlinearity,hysteresis and creep. See also“Open-Loop Operation“.

Compliance:

Displacement produced per unitforce. The reciprocal of stiffness.

Creep:

An unwanted change in the dis-placement over time.

Curie Temperature:

The temperature at which thecrystalline structure changes froma piezoelectric (non-symmetrical)

to a non-piezoelectric (symmetri-cal) form. At this temperature PZTceramics looses the piezoelectricproperties.

Drift:

See “creep”

Domain:

A region of electric dipoles withsimilar orientation.

HVPZT:

Acronym for High-Voltage PZT(actuator).

Hysteresis:

Hysteresis in piezo actuators isbased on crystalline polarizationand molecular effects and occurswhen reversing driving direction.Hysteresis is not to be confusedwith backlash.

LVPZT:

Acronym for low-voltage PZT(actuator).

Monolithic Multilayer Actuator:

An actuator manufactured in afashion similar to multilayer ce-ramic capacitors. Ceramic andelectrode material are cofired inone step. Layer thickness is typi-cally on the order of 20 to 100 µm.

Open-Loop Operation:

The actuator is used without aposition sensor. Displacementroughly corresponds to the drivevoltage. Creep, nonlinearity andhysteresis remain uncompensat-ed.

Parallel Kinematics:

Unlike in serial kinematics de-signs, all actuators act upon thesame moving platform. Advan-tages: Minimized inertia, no moving cables, lower center of

gravity, no cumulative guidingerrors and more-compact con-struction.







Motion Controllers



Piezo Actuators

Index


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4-6

Design principle of a stacked XY piezo stage(serial kinematics).

Parallel Metrology:

Unlike in serial metrology designs,each sensor measures the positionof the same moving platform in therespective degree of freedom. Thiskeeps the off-axis runout of allactuators inside the servo-controlloop and allows it to be correctedautomatically (active guidance).

Piezoelectric Materials:

Materials that change their dimen-sions when a voltage is appliedand produce a charge when pres-sure is applied.

Poling / Polarization:

The procedure by which the bulkmaterial is made to take on piezo-electric properties, i.e. the electricalalignment of the unit cells in a pie-zoelectric material.

PZT:

Acronym for plumbum (lead) zir-conate titanate. Polycrystalline ce-ramic material with piezoelectricproperties. Often also used to referto a piezo actuator or translator.

Serial Kinematics:

Unlike in parallel kinematics de-signs, each actuator acts upon aseparate platform of its own. Thereis a clear relationship betweenactuators and axes. Advantages: Simpler to assemble;simpler control algorithm. Disadvantages: Poorer dynamiccharacteristics, integrated “Parallel

Metrology” is not possible, cumu-lative guiding errors, lower accura-cy.

Serial Metrology:

One sensor is assigned to eachdegree of freedom to be servo-con-trolled. Undesired off-axis motion(guiding error) from other axes inthe direction of a given sensor, gounrecognized and uncorrected (seealso “Parallel Metrology”).

Stiffness:

Spring constant (for piezoelectricmaterials, not linear).

Trajectory-Control:

Provisions to prevent deviationfrom the specified trajectory. Canbe passive (e.g. flexure guidance)or active (e.g. using additional ac-tive axes).

Translator:

A linear actuator.

Flatness of a nanopositioning stage with active trajectory control is better than 1 nanometer over a 100 x 100 µm scanning range.

Glossary

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Symbols and Units

A Surface area [m2] (meter2)

� Coefficient of Thermal Expansion (CTE) [K-1] (1 / kelvin)

C Capacitance (F) [A�s/V]

dij Piezo modulus (tensor components) [m/V] (meter/volt)

ds Distance, thickness [m] (meter)

� Dielectric constant [A�s/V�m] (ampere · second / volt · meter)

E Electric field strength [V/m] (volt/meter)

f Operating frequency [Hz] (hertz = 1/second)

F Force [N] (newton)

f0 Unloaded resonant frequency [Hz] (hertz = 1/second)

g Acceleration due to gravity: 9.81 m/s2 (meter/second2)

i Current [A] (ampere)

kS Stiffness of restraint (load) [N/m] (newton/meter)

kT Stiffness of piezo actuators [N/m] (newton/meter)

L0 Length of non-energized actuator [m] (meter)

�L Change in length (displacement) [m] (meter)

�L0 Nominal displacement with zero applied force, [m] (meter)

�Lt=0.1 Displacement at time t = 0.1 sec after voltage change, [m] (meter)

m Mass [kg] (kilogram)

P Power [W] (watt)

Q Charge [C] (coulomb = ampere x second)

S Strain [�L/L] (dimensionless)

t Time [s] (second)

TC Curie temperature [° C]

U Voltage [V] (volt)

Up-p Peak-to-peak voltage [V] (volt)







Motion Controllers



Piezo Actuators

Index







Motion Controllers



Piezo Actuators

Index



4-8

4-9


IntroductionNanopositioning with Piezoelectric Technology

Basics

The piezoelectric effect is often en-countered in daily life, for exam-ple in lighters, loudspeakers andbuzzers. In a gas lighter, pressureon a piezoceramic generates anelectric potential high enough tocreate a spark. Most electronicalarm clocks do not use electro-magnetic buzzers anymore,because piezoelectric ceramicsare more compact and more effi-cient. In addition to such simpleapplications, piezo technology hasrecently established itself in theautomotive branch. Piezo-driveninjection valves in diesel enginesrequire much lower transitiontimes than conventional electro-magnetic valves, providing qui-eter operation and lower emis-sions.

The term “piezo” is derived fromthe Greek word for pressure. In1880 Jacques and Pierre Curie dis-covered that an electric potentialcould be generated by applyingpressure to quarz crystals; theynamed this phenomenon the“piezo effect”. Later they ascer-tained that when exposed to anelectric potential, piezoelectricmaterials change shape. This theynamed the “inverse piezo effect”.The first commercial applicationsof the inverse piezo effect were forsonar systems that were used inWorld War I. A breakthrough wasmade in the 1940’s when scientistsdiscovered that barium titanatecould be bestowed with piezoelec-tric properties by exposing it to anelectric field.

Piezoelectric materials are used toconvert electrical energy to mech-anical energy and vice-versa. Theprecise motion that results whenan electric potential is applied to apiezoelectric material is of primor-dial importance for nanoposition-ing. Actuators using the piezoeffect have been commerciallyavailable for 35 years and in thattime have transformed the worldof precision positioning andmotion control.

Features of Piezoelectric

Actuators

� Piezo actuators can performsub-nanometer moves athigh frequencies becausethey derive their motionfrom solid-state crystalineeffects. They have no rotat-ing or sliding parts to causefriction

� Piezo actuators can movehigh loads, up to severaltons

� Piezo actuators presentcapacitive loads and dissi-pate virtually no power instatic operation

� Piezo actuators require nomaintenance and are notsubject to wear because theyhave no moving parts in theclassical sense of the term







Motion Controllers



Piezo Actuators

Index



4-10

Quick Facts

Note

This section gives a brief summaryof the properties of piezoelectricdrives and their applications. Fordetailed information, see “Funda-mentals of Piezoelectricity” begin-ning on p. 4-13.

Stack actuators are the most com-mon and can generate the highestforces. Units with travel ranges upto 500 µm are available. To protectthe piezoceramic against destruc-tive external conditions, they areoften provided with a metal casingand an integrated preload spring toabsorb tensile forces.

Piezo tube actuators exploit theradial contraction direction, andare often used in scanning micro-scopes and micropumps.

Bender and bimorph actuators

achieve travel ranges in the mil-limeter range (despite their com-pact size) but with relatively lowforce generation (a few newtons).

Shear elements use the inverse-piezo-effect shear component andachieve long travel and high force.

For more information, see pp. 4-39 ff.

Guided piezo actuators (1 to 6

axes) are complex nanopositionerswith integrated piezo drives andsolid-state, friction-free linkages(flexures). They are used whenrequirements like the followingneed be met:

� Extremely straight and flatmotion, or multi-axis motionwith accuracy requirements inthe sub-nanometer or sub-micro-radian range

� Isolation of the actuator fromexternal forces and torques, pro-tection from humidity and for-eign particles

Such systems often also includelever amplification of up to 20

times the displacement of the piezoelement, resulting in a travel rangeof several hundred µm.

Piezomotors are used where evenlonger travel ranges are required.Piezomotors can be divided intotwo main categories:

� Ultrasonic Motors (Fig. 2a)

� Piezo-Walk® Motors (Fig. 2b)

The motion of ultrasonic piezomo-tors is based on the frictionbetween parts oscillating withmicroscopic amplitudes. Linear

ultrasonic motors are very compactand can attain high speeds com-bined with resolutions of 0.1 µm orbetter. Rotary motors feature hightorques even at low rpm.

Piezo-Walk® linear drives (see p. 10-3 ff.) offer high positioning andholding forces (up to hundreds ofnewtons) with moderate speedsand resolutions in the subnanome-ter range.

All implementations are self-lock-ing when powered down.

Actuator Designs

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Fig. 1b. Selection of monolithic PICMA ® technology actuators.

Fig. 1a. Selection of classical piezo stack actuators, with adhesive used to join the layers.


4-11








Motion Controllers



Piezo Actuators

Index

Operating Voltage

Two types of piezo actuators havebecome established. Monolithic-sintered, low-voltage actuators(LVPZT) operate with potential dif-ferences up to about 100 V and aremade from ceramic layers from 20to 100 µm in thickness. Classicalhigh-voltage actuators (HVPZT),on the other hand, are made fromceramic layers of 0.5 to 1 mmthickness and operate with poten-tial differences of up to 1000 V.High-voltage actuators can bemade with larger cross-sections,making them suitable for largerloads than the more-compact,monolithic actuators.

Stiffness, Load Capacity, Force

Generation

To a first approximation, a piezoactuator is a spring-and-mass sys-tem. The stiffness of the actuatordepends on the Young’s modulusof the ceramic (approx. 25 % thatof steel), the cross-section andlength of the active material and anumber of other non-linearparameters (see p. 4-21). Typicalactuators have stiffnessesbetween 1 and 2,000 N/µm andcompressive limits between 10and 100,000 N. If the unit will beexposed to pulling (tensile) forces,

a casing with integrated preloador an external preload spring isrequired. Adequate measuresmust be taken to protect the piezo-ceramic from shear and bendingforces and from torque.

Travel Range

Travel ranges of Piezo Actuatorsare typically between a few tensand a few hundreds of µm (linearactuators). Bender actuators andlever amplified systems canachieve a few mm. Ultrasonicpiezomotors and Piezo-Walk®

drives can be used for longer trav-el ranges.

Resolution

Piezoceramics are not subject tothe “stick slip” effect and there-fore offer theoretically unlimitedresolution. In practice, the resolu-tion actually attainable is limitedby electronic and mechanical fac-tors:

a) Sensor and servo-control elec-tronics (amplifier): amplifier noiseand sensitivity to electromagneticinterference (EMI) affect the posi-tion stability.

b) Mechanical parameters: designand mounting precision issues

concerning the sensor, actuatorand preload can induce micro-fric-tion which limits resolution andaccuracy.

PI offers piezo actuators and posi-tioning systems that provide sub-nanometer resolution and stabili-ty. For more information, see pp. 4-15 ff.

Operating Characteristics of Piezoelectric Actuator s

Fig. 2b. Custom linear drive with integrated NEXLINE® Piezo-Walk® piezomotor.

Fig. 3. Example of a compact piezo nanopositioning andscanning system with integrated flexure guidance, sen-

sor and motion amplifier.Fig. 2a. Ultrasonic linear piezo-motors.



http://www.piezo-motor.net


4-12

Quick Facts (cont.)

Open- and Closed-Loop Operation

In contrast to many other types ofdrive systems, piezo actuators canbe operated without servo-control.The displacement is approximatelyequal to the drive voltage.Hysteresis, nonlinearity and creepeffects limit the absolute accuracy.For positioning tasks which requirehigh linearity, long-term stability,repeatability and absolute accuracy,closed-loop (servo-controlled) pi-ezo actuators and systems areused (see p. 4-31). With suitablecontrollers, closed-loop operationenables reproducibilities in thesub-nanometer range.

High-Resolution Sensors for

Closed-Loop Operation

LVDT (linear variable differentialtransformer), strain gauge andcapacitive sensors are the mostcommon sensor types used forclosed-loop operation. Capacitivesensors offer the greatest accuracy.For more information, see p. 4-19 ff.

Dynamic Behavior

A piezo actuator can reach its nom-inal displacement in approximatelyone third of the period of its reso-nant frequency. Rise times on theorder of microseconds and acceler-ations of more than 10,000 g arepossible. This feature makes piezoactuators suitable for rapid switch-ing applications such as controllinginjector nozzle valves, hydraulicvalves, electrical relays, opticalswitches and adaptive optics. Formore information, see pp. 4-24 ff.

Power Requirements

Piezo actuators behave as almostpure capacitive loads. Static opera-tion, even holding heavy loads,consumes virtually no power. Indynamic applications the energyrequirement increases linearly withfrequency and actuator capaci-tance. At 1000 Hz with 10 µmamplitude, a compact piezo trans-lator with a load capacity ofapprox. 100 N requires less than 10 W, while a high-load actuator

(> 10 kN capacity) would use severalhundred watts under the same con-ditions. For more information, seepp. 4-27 ff.

Protection from Mechanical

Damage

PZT ceramics are brittle and cannotwithstand high pulling or shearforces. The mechanical actuatordesign must thus isolate theseundesirable forces from the ceram-ic. This can be accomplished bymeasures such as spring preloads,use of ball tips, flexible couplings,etc. (for more mounting guidelines,see p. 4-48). In addition, the ceram-ics must be protected from mois-ture and the intrusion of foreignparticles. Close contact betweenthe piezo mechanics manufacturerand the user facilitates finding anoptimal match between the piezosystem and the application envi-ronment.

Fig. 4. Piezo actuator with water-proof case and connection for flushing/cooling air.

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Fundamentals of PiezoelectricityMaterial Properties

Fig. 5. PZT unit cell: 1) Perovskite-type lead zirconate

titanate (PZT) unit cell in the sym-metric cubic state above the Curietemperature.

2) Tetragonally distorted unit cell belowthe Curie temperature.

Fig. 6. Electric dipoles in domains; (1) unpoled ferroelectricceramic, (2) during and (3) after poling (piezoelectric ceramic).

Notes

The following pages give adetailed look at piezo actuatortheory and their operation. Forbasic knowledge read “QuickFacts”, p. 4-10. For definition ofunits, dimensions and terms,see “Symbols and Units”, p. 4-7 and “Glossary”, p. 4-5.

Since the piezo effect exhibitedby natural materials such asquartz, tourmaline, Rochellesalt, etc. is very small, polycrys-talline ferroelectric ceramicmaterials such as bariumtitanate and lead (plumbum)zirconate titanate (PZT) withimproved properties have beendeveloped.

PZT ceramics (piezoceramics)are available in many varia-tions and are still the mostwidely used materials for actu-ator applications today.Before polarization, PZT crys-tallites have symmetric cubicunit cells. At temperaturesbelow the Curie temperature,the lattice structure becomesdeformed and asymmetric. Theunit cells exhibit spontaneouspolarization (see Fig. 5), i.e. theindividual PZT crystallites arepiezoelectric.

Groups of unit cells with thesame orientation are calledWeiss domains. Because of therandom distribution of thedomain orientations in theceramic material no macro-scopic piezoelectric behavior isobservable. Due to the ferro-electric nature of the material,it is possible to force perma-nent alignment of the differentdomains using a strong electricfield. This process is called pol-ing (see Fig. 6). Some PZTceramics must be poled at anelevated temperature. The ma-terial now has a remnant polar-ization (which can be degradedby exceeding the mechanical,thermal and electrical limits of

the material). The ceramic nowexhibits piezoelectric proper-ties and will change dimen-sions when an electric potentialis applied.







Motion Controllers



Piezo Actuators

Index







Motion Controllers



Piezo Actuators

Index


http://www.pi-usa.us/products/PiezoActuators/PiezoActuators.htm


4-14

Fundamentals of Piezoelectricity

PI develops and manufacturesits own piezo ceramic materialsat the PI Ceramic factory. Themanufacturing process forhigh-voltage piezoceramicstarts with mixing and ballmilling of the raw materials.Next, to accelerate reaction ofthe components, the mixture isheated to 75 % of the sinteringtemperature, and then milledagain. Granulation with thebinder is next, to improve pro-cessing properties. After shap-ing and pressing, the greenceramic is heated to about 750 °C to burn out the binder.The next phase is sintering, attemperatures between 1250 °Cand 1350 °C. Then the ceramicblock is cut, ground, polished,lapped, etc., to the desiredshape and tolerance. Elec-trodes are applied by sputter-ing or screen printing process-es. The last step is the polingprocess which takes place in a

heated oil bath at electricalfields up to several kV/mm.Only here does the ceramictake on macroscopic piezoelec-tric properties.

Multilayer piezo actuatorsrequire a different manufactur-ing process. After milling, aslurry is prepared for use in afoil casting process whichallows layer thickness down to20 µm. Next, electrodes arescreen printed and the sheetslaminated. A compactingprocess increases the densityof the green ceramics andremoves air trapped betweenthe layers. The final steps arethe binder burnout, sintering(co-firing) at temperaturesbelow 1100 °C , wire lead ter-mination and poling.

All processes, especially theheating and sintering cycles,must be controlled to very tight

tolerances. The smallest devia-tion will affect the quality andproperties of the PZT material.One hundred percent final test-ing of the piezo material andcomponents at PI Ceramicguarantees the highest possi-ble product quality.

Sputtering facility at PI Ceramic.

PZT Ceramics Manufacturing Process

Because of the anisotropicnature of PZT ceramics, piezo-electric effects are dependenton direction. To identify direc-tions, the axes 1, 2, and 3 willbe introduced (correspondingto X, Y, Z of the classical right-hand orthogonal axis set). Theaxes 4, 5 and 6 identify rota-tions (shear), �X, �Y, �Z (alsoknown as U, V, W.)

The direction of polarization(axis 3) is established duringthe poling process by a strongelectrical field applied betweentwo electrodes. For linear actu-ator (translator) applications,the piezo properties along thepoling axis are the most impor-tant (largest deflection). Piezoelectric materials arecharacterized by several coeffi-cients.

Examples are:� dij: Strain coefficients [m/V]

or charge output coefficients[C/N]: Strain developed[m/m] per unit of electricfield strength applied [V/m]or (due to the sensor / actua-tor properties of PZT materi-al) charge density developed[C/m2] per given stress[N/m2].

� gij: Voltage coefficients orfield output coefficients[Vm/N]: Open-circuit electricfield developed [V/m] perapplied mechanical stress[N/m2] or (due to the sensor /actuator properties of PZTmaterial) strain developed[m/m] per applied chargedensity [C/m2].

� kij: Coupling coefficients[dimensionless]. The coeffi-cients are energy ratios

describing the conversionfrom mechanical to electricalenergy or vice versa. k2 is theratio of energy stored(mechanical or electrical) toenergy (mechanical or elec-trical) applied.

Other important parametersare the Young’s modulus Y(describing the elastic proper-ties of the material) and �r therelative dielectric coefficients(permittivity).Double subscripts, as in dij, areused to describe the relation-ships between mechanical andelectrical parameters. The firstindex indicates the direction ofthe stimulus, the second thedirection of the reaction of thesystem.

Example: d33 applies when theelectric field is along the polar-ization axis (direction 3) and

the strain (deflection) is alongthe same axis. d31 applies if theelectric field is in the samedirection as before, but thedeflection of interest is thatalong axis 1 (orthogonal to thepolarization axis).

In addition the superscripts S,T, E, D can be used to describean electrical or mechanicalboundary condition.

Definition:S for strain = constant (mecha-

nically clamped)T for stress = constant (not

clamped)E for field = 0 (short circuit)D for charge displacement (cur-

rent) = 0 (open circuit)

The individual piezoelectriccoefficients are related to eachother by systems of equationsthat will not be explained here.

Definition of Piezoelectric Coefficients and Directions

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Polarisation

Fig. 7. Orthogonal system describing theproperties of a poled piezoelectric ceramic.Axis 3 is the poling direction.

Fig. 8. Smooth response of a P-170 HVPZT translator to a 1 V, 200 Hz triangu-lar drive signal. Note that one division is only 2 nanometers.

4-15


Notes

The piezoelectric coefficientsdescribed here are often pre-sented as constants. It shouldbe clearly understood that theirvalues are not invariable. Thecoefficients describe materialproperties under small-signalconditions only. They vary withtemperature, pressure, electricfield, form factor, mechanicaland electrical boundary condi-tions, etc. Compound compo-nents, such as piezo stack actu-ators, let alone preloaded actu-ators or lever-amplified sys-tems, cannot be described suf-ficiently by these materialparameters alone. This is why

each component or systemmanufactured by PI is accom-panied by specific data such asstiffness, load capacity, dis-placement, resonant frequen-cy, etc., determined by individ-ual measurements. The param-eters describing these systemsare to be found in the technicaldata table for the product. Important: There are no inter-national standards for definingthese specifications. Thismeans that claims of differentmanufacturers can not neces-sarily be compared directlywith one another.

Since the displacement of apiezo actuator is based on ionicshift and orientation of the PZTunit cells, the resolutiondepends on the electrical fieldapplied. Resolution is theoreti-cally unlimited. Because thereare no threshold voltages, thestability of the voltage source iscritical; noise even in the µVrange causes position changes.When driven with a low-noiseamplifier, piezo actuators canbe used in tunneling and atom-ic force microscopes providingsmooth, continuous motionwith sub-atomic resolution (seeFig. 8).

Amplifier Noise

One factor determining theposition stability (resolution) ofa piezo actuator is noise in thedrive voltage. Specifying thenoise value of the piezo driverelectronics in millivolts, how-ever, is of little practical usewithout spectral information. Ifthe noise occurs in a frequencyband far beyond the resonantfrequency of the mechanicalsystem, its influence onmechanical resolution and sta-

bility can be neglected. If itcoincides with the resonant fre-quency, it will have a far moresignificant influence on the sys-tem stability.

Therefore, meaningful infor-mation about the stability andresolution of a piezo position-ing system can only beacquired if the resolution of thecomplete system—piezo actua-tor and drive electronics—ismeasured in terms of nanome-ters rather than millivolts. Forfurther information see p. 2-8and p. 4-31 ff.

Notes

The smooth motion in the sub-nanometer range shown in Fig. 8 can only be attained byfrictionless and stictionlesssolid state actuators and guid-ance such as piezo actuatorsand flexures. “Traditional”technologies used in motionpositioners (stepper or DCservo-motor drives in combina-tion with dovetail slides, ballbearings, and roller bearings)all have excessive amounts offriction and stiction. This fun-







Motion Controllers



Piezo Actuators

Index

damental property limits reso-lution, causes wobble, hystere-sis, backlash, and an uncertain-ty in position repeatability.Their practical usefulness isthus limited to a precision ofseveral orders of magnitudebelow that obtainable with PIpiezo nanopositioners.

Resolution







Motion Controllers



Piezo Actuators

Index



4-16

Fundamentals of Piezomechanics

Commonly used stack actua-tors achieve a relative displace-ment of up to 0.2 %.Displacement of piezoceramicactuators is primarily a func-tion of the applied electric fieldstrength E, the length L of theactuator, the forces applied to itand the properties of the piezo-electric material used. Thematerial properties can bedescribed by the piezoelectricstrain coefficients dij. Thesecoefficients describe the rela-tionship between the appliedelectric field and the mechani-cal strain produced.

The change in length, �L, of anunloaded single-layer piezoactuator can be estimated bythe following equation:

(Equation 1)

Where:

S = strain (relative lengthchange �L/L, dimen-sionless)

L0 = ceramic length [m]E = electric field strength

[V/m]dij = piezoelectric coeffi-

cient of the material [m/V]

d33 describes the strain parallelto the polarization vector of theceramics (thickness) and isused when calculating the dis-placement of stack actuators;d31 is the strain orthogonal tothe polarization vector (width)and is used for calculating tubeand strip actuators (see Fig. 9).d33 and d31 are sometimesreferred to as “piezo gain”.

Notes

For the materials used in stan-dard PI piezo actuators, d33 ison the order of 250 to 550pm/V, d31 is on the order of

-180 to -210 pm/V. The highestvalues are attainable withshear actuators in d15 mode.These figures only apply to theraw material at room tempera-ture under small-signal condi-tions.

The maximum allowable fieldstrength in piezo actuators isbetween 1 and 2 kV/mm in thepolarization direction. In thereverse direction (semi-bipolaroperation), at most 300 V/mmis allowable (see Fig. 10). Themaximum voltage depends onthe ceramic and insulationmaterials.

Exceeding the maximum volt-age may cause dielectric break-down and irreversible damageto the piezo actuator.

With the reverse field, negativeexpansion (contraction) occurs,giving an additional 20 % of thenominal displacement. If boththe regular and reverse fieldsare used, a relative expansion(strain) up to 0.2 % is achiev-able with piezo stack actuators.This technique can reduce theaverage applied voltage with-out loss of displacement andthereby increase piezo lifetime.

Stacks can be built with aspectratios up to 12:1 (length:diame-ter). This means that the maxi-mum travel range of an actua-tor with 15 mm piezo diameteris limited to about 200 µm.Longer travel ranges can beachieved by mechanical ampli-fication techniques (see “LeverMotion Amplifiers” p. 4-42).

Polarisation

Fig. 9. Expansion and contraction of a piezoelectric disk in response to an appliedvoltage. Note that d31, which describes the lateral motion, �D, is negative.

V

Fig. 10. Typical response of a “soft PZT” actuator to a bipolar drivevoltage. When a certain threshold voltage negative to the polarizationdirection is exceeded, reversal of polarization can occur.

Displacement of Piezo Actuators (Stack & Contraction Type)

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4-17


Note:

PI piezo actuators and stagesare designed for high reliabilityin industrial applications. Thetravel, voltage and load rangesin the technical data tables canactually be used in practice.They have been collected overmany years of experience inpiezo actuator production andin numerous industrial applica-tions.

In contrast to many other piezosuppliers, PI has its own piezoceramic development and pro-duction facilities together withthe necessary equipment andknowhow. The goal is alwaysreliability and practical useful-ness. Maximizing isolatedparameters, such as expansionor stiffness, at the cost of piezolifetime might be interesting toan experimenter, but has noplace in practical application.

When selecting a suitablepiezo actuator or stage, consid-er carefully the fact that “maxi-mum travel” may not be theonly critical design parameter.

Hysteresis

(Open-Loop Piezo Operation)

Hysteresis is observable inopen-loop operation; it can bereduced by charge control andvirtually eliminated by closed-loop operation (see pp. 4-31 ff.).

Open-loop piezo actuatorsexhibit hysteresis in theirdielectric and electromagneticlarge-signal behavior. Hys-teresis is based on crystallinepolarization effects and molec-ular effects within the piezo-electric material.The amount of hysteresisincreases with increasing volt-age (field strength) applied tothe actuator. The “gap” in thevoltage/displacement curve(see Fig. 11) typically beginsaround 2 % (small-signal) and

widens to a maximum of 10 %to 15 % under large-signal con-ditions. The highest values areattainable with shear actuatorsin d15 mode.

For example, if the drive volt-age of a 50 µm piezo actuatoris changed by 10 %, (equiva-lent to about 5 µm displace-ment) the position repeatabili-ty is still on the order of 1 % offull travel or better than 1 µm.

The smaller the move, thesmaller the uncertainty.Hysteresis must not be con-fused with the backlash of con-ventional mechanics. Backlashis virtually independent of trav-el, so its relative importanceincreases for smaller moves.

For tasks where it is not theabsolute position that counts,hysteresis is of secondaryimportance and open-loopactuators can be used, even ifhigh resolution is required.

In closed-loop piezo actuatorsystems hysteresis is fullycompensated. PI offers thesesystems for applications re-

quiring absolute position infor-mation, as well as motion withhigh linearity, repeatability andaccuracy in the nanometer andsub-nanometer range (see pp.4-31 ff.).

Example: Piezoelectrically driv-en fiber aligners and trackingsystems derive the control sig-nal from an optical powermeter in the system. There, thegoal is to maximize the opticalsignal level as quickly as possi-ble, not to attain a predeter-mined position value. An open-loop piezo system is sufficientfor such applications. Ad-vantages like unlimited resolu-tion, fast response, zero back-lash and zero stick/slip effectare most welcome, even with-out position control.







Motion Controllers



Piezo Actuators

Index

V

L

Fig. 11. Hysteresis curves of an open-loop piezo actuator for variouspeak voltages. The hysteresis is related to the distance moved, notto the nominal travel range.







Motion Controllers



Piezo Actuators

Index



4-18

Creep / Drift (Open-Loop Piezo

Operation)

The same material propertiesresponsible for hysteresis alsocause creep or drift. Creep is achange in displacement withtime without any accompany-ing change in the control volt-age. If the operating voltage ofa piezo actuator is changed,the remnant polarization (piezogain) continues to change,manifesting itself in a slowchange of position. The rate ofcreep decreases logarithmical-ly with time (see Fig. 12). Thefollowing equation describesthis effect:

(Equation 2)

Creep of PZT motion as a func-tion of time.

Where:

t = time [s]�L(t) = change in position

as a function of time

�Lt= 0.1 = displacement 0.1 seconds after the voltage change is complete [m].

� = creep factor, which is depend-ent on the proper-ties of the actua-tor (on the order of 0.01 to 0.02, which is 1 % to 2 % per time decade).

In practice, maximum creep(after a few hours) can add upto a few percent of the com-manded motion.

Aging

Aging refers to reduction inremnant polarization; it can bean issue for sensor or charge-generation applications (direct

piezo effect). With actuatorapplications it is negligible,because repoling occurs everytime a higher electric field isapplied to the actuator materialin the poling direction.

Note

For periodic motion, creep andhysteresis have only a minimaleffect on repeatability.

Fundamentals of Piezomechanics

Fig. 12. Creep of open-loop PZT motion after a 60 µm change in length as a functionof time. Creep is on the order of 1 % of the last commanded motion per time decade.

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Piezo Actuators

Index

Metrology for Nanopositioning Systems

There are two basic techniquesfor determining the position ofpiezoelectric motion systems:Direct metrology and indirectmetrology.

Indirect (Inferred) Metrology

Indirect metrology involvesinferring the position of theplatform by measuring posi-tion or deformation at the actu-ator or other component in thedrive train. Motion inaccuracieswhich arise between the driveand the platform can not beaccounted for.

Direct Metrology

With direct metrology, howev-er, motion is measured at the

point of interest; this can bedone, for example, with aninterferometer or capacitivesensor.Direct metrology is more accu-rate and thus better suited toapplications which needabsolute position measure-ments. Direct metrology alsoeliminates phase shiftsbetween the measuring pointand the point of interest. Thisdifference is apparent in high-er-load, multi-axis dynamicapplications.

Parallel and Serial Metrology

In multi-axis positioning sys-tems parallel and serial metrolo-gy must also be distinguished.

With parallel metrology, allsensors measure the positionof the same moving platformagainst the same stationary ref-erence. This means that allmotion is inside the servo-loop,no matter which actuatorcaused it (see Active TrajectoryControl). Parallel metrologyand parallel kinematics can beeasily integrated.

With serial metrology the refer-ence plane of one or more sen-sors is moved by one or moreactuators. Because the off-axismotion of any moving refer-ence plane is never measured,it can not be compensated. See also p. 2-5 ff.

High-Resolution Sensors

Strain Gauge Sensors

SGS sensors are an implemen-tation of inferred metrologyand are typically chosen forcost-sensitive applications. AnSGS sensor consists of a resis-tive film bonded to the piezostack or a guidance element;the film resistance changeswhen strain occurs. Up to fourstrain gauges (the actual con-figuration varies with the actu-ator construction) form aWheatstone bridge driven by aDC voltage (5 to 10 V). Whenthe bridge resistance changes,the sensor electronics convertsthe resulting voltage changeinto a signal proportional to thedisplacement.

A special type of SGS is knownas a piezoresistive sensor. Ithas good sensitivity, butmediocre linearity and temper-ature stability. See also p. 2-5 ff.

Resolution: better than 1 nm(for short travel ranges, up toabout 15 µm)

Bandwidth: to 5 kHz

Advantages

� High Bandwidth � Vacuum Compatible� Highly Compact

Other characteristics:

� Low heat generation (0.01 to0.05 W sensor excitationpower)

� Long-term position stabilitydepends on adhesive quality

� Indirect metrology

Examples

Most PI LVPZT and HVPZT actu-ators are available with straingauge sensors for closed-loopcontrol (see the “PiezoActuators” section p. 1-8 ff.).

Note

The sensor bandwidth for thesensors described here shouldnot be confused with the band-width of the piezo mechanicsservo-control loop, which isfurther limited by the electronicand mechanical properties ofthe system.

4-19

Fig. 13. Strain gauge sensors. Paperclip for size comparison.

4-19







Motion Controllers



Actuators and Sensors




4-20

Actuators and Sensors

Linear Variable Differential

Transformers (LVDTs)

LVDTs are well suited for directmetrology. A magnetic core,attached to the moving part,determines the amount ofmagnetic energy induced fromthe primary windings into thetwo differential secondarywindings (Fig. 15). The carrierfrequency is typically 10 kHz.

Resolution: to 5 nm

Bandwidth: to 1 kHz

Repeatability: to 5 nm

Advantages:

� Good temperature stability� Very good long-term

stability� Non-contacting

� Controls the position of themoving part rather than theposition of the piezo stack

� Cost-effective


� Outgassing of insulationmaterials may limit applica-tions in very high vacuum

� Generates magnetic field

Examples

P-780, p. 2-32; P-721.LLQ, p. 2-20.

Capacitive Position Sensors

Capacitive sensors are themetrology system of choice forthe most demanding applica-tions.

Two-plate capacitive sensorsconsist of two RF-excitedplates that are part of a capaci-tive bridge (Fig. 17). One plateis fixed, the other plate is con-nected to the object to be posi-tioned (e.g. the platform of astage). The distance betweenthe plates is inversely propor-tional to the capacitance, fromwhich the displacement is cal-culated. Short-range, two-platesensors can achieve resolutionon the order of picometers.See the “Capacitive Displa-cement Sensors” section pp. 5-2 ff. for details.

Resolution: Better than 0.1 nmpossible

Repeatability: Better than 0.1 nm possible

Bandwidth: Up to 10 kHz

Advantages:

� Highest resolution of allcommercially available sen-sors

� Ideally suited for parallelmetrology

� Non-contacting� Excellent long-term stability� Excellent frequency response� No magnetic field � Excellent linearity


� Ideally suited for integrationin flexure guidance systems,which maintain the neces-sary parallelism of the pla-tes. Residual tip/tilt errorsare greatly reduced by theILS linearization system (seep. 5-6) developed by PI.

Fig. 15. Working principle of an LVDT sensor Fig. 17. Working principle of two-plate capacitive position sensors

Fig. 16. Capacitive sensors canattain resolution 10,000 times

better than calipers. Fig. 14. LVDT sensor, coil and core. Paper

clip for size comparison.

Examples

P-733 parallel kinematic nano-positioning system with paral-lel metrology, see p. 2-64. P-753 LISA NanoAutomation®

actuators, see p. 2-26; addition-al examples in the “Nanoposi-tioning & Scanning Systems”section.

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Fundamentals of Piezoelectric Actuator sForces and Stiffness

Maximum Applicable Forces

(Compressive Load Limit,

Tensile Load Limit)

The mechanical strength val-ues of PZT ceramic material(given in the literature) areoften confused with the practi-cal long-term load capacity of apiezo actuator. PZT ceramicmaterial can withstand pres-sures up to 250 MPa (250 x 106

N/m2) without breaking. Thisvalue must never beapproached in practical appli-cations, however, becausedepolarization occurs at pres-sures on the order of 20 % to 30 % of the mechanical limit.For stacked actuators andstages (which are a combina-tion of several materials) addi-tional limitations apply. Para-meters such aspect ratio, buck-ling, interaction at the inter-faces, etc. must be considered.

The load capacity data listedfor PI actuators are conserva-tive values which allow longlifetime.

Tensile loads of non-preloadedpiezo actuators are limited to5% to 10% of the compressiveload limit. PI offers a variety ofpiezo actuators with internalspring preload for increasedtensile load capacity. Preloadedelements are highly recom-mended for dynamic applica-tions.

The PZT ceramic is especiallysensitive to shear forces; theymust be intercepted by exter-nal measures (flexure guides,etc.).

Stiffness

Actuator stiffness is an impor-tant parameter for calculatingforce generation, resonant fre-quency, full-system behavior,etc. The stiffness of a solidbody depends on Young’smodulus of the material. Stiff-

ness is normally expressed interms of the spring constant kT,which describes the deforma-tion of the body in response toan external force.

This narrow definition is of lim-ited application for piezoce-ramics because the cases ofstatic, dynamic, large-signaland small-signal operationwith open and shorted elec-trodes must all be distin-guished. The poling process ofpiezoceramics leaves a rem-nant strain in the materialwhich depends on the magni-tude of polarization. The pola-

rization is affected by both theapplied voltage and externalforces. When an external forceis applied to poled piezoceram-ics, the dimensional changedepends on the stiffness of theceramic material and thechange of the remnant strain(caused by the polarizationchange). The equation �LN =F/kT is only valid for smallforces and small-signal condi-tions. For larger forces, anadditional term, describing theinfluence of the polarizationchanges, must be super-

imposed on the stiffness (kT). Since piezo ceramics are activematerials, they produce anelectrical response (charge)when mechanically stressed(e.g. in dynamic operation). Ifthe electric charge cannot bedrained from the PZT ceramics,it generates a counterforceopposing the mechanicalstress. This is why a piezo ele-ment with open electrodesappears stiffer than one withshorted electrodes. Commonvoltage amplifiers with theirlow output impedances looklike a short circuit to a piezo actuator.

Mechanical stressing of piezoactuators with open electrodes,e.g. open wire leads, should beavoided, because the resultinginduced voltage might damagethe stack electrically.

4-21


Fig. 18. Quasi-static characteristic mechanical stress/strain curves for piezo ceramic actua-tors and the derived stiffness values. Curve 1 is with the nominal operating voltage on theelectrodes, Curve 2 is with the electrodes shorted (showing ceramics after depolarization)







Motion Controllers



Piezo Actuators

Index

Note

There is no international stan-dard for measuring piezo actu-ator stiffness. Therefore stiff-ness data from different manu-facturers cannot be comparedwithout additional information.







Motion Controllers



Piezo Actuators

Index



4-22

Fundamentals of Piezoelectric Actuators

Force Generation

In most applications, piezoactuators are used to producedisplacement. If used in arestraint, they can be used togenerate forces, e.g. for stamp-ing. Force generation is alwayscoupled with a reduction in dis-placement. The maximumforce (blocked force) a piezoactuator can generate dependson its stiffness and maximumdisplacement (see also p. 4-23).At maximum force generation,displacement drops to zero.

(Equation 3)

Maximum force that can begenerated in an infinitely rigidrestraint (infinite spring con-stant).

Where:

�L0 = max. nominal displace-ment without externalforce or restraint [m]

kT = piezo actuator stiffness[N/m]

In actual applications thespring constant of the load canbe larger or smaller than thepiezo spring constant. Theforce generated by the piezoactuator is:

(Equation 4)

Effective force a piezo actuatorcan generate in a yieldingrestraint

Where:



kS = stiffness of externalspring [N/m]

Example

What is the force generation ofa piezo actuator with nominaldisplacement of 30 µm andstiffness of 200 N/µm? Thepiezo actuator can produce amaximum force of 30 µm x 200N/µm = 6000 N When forcegeneration is maximum, dis-placement is zero and viceversa (see Fig. 19 for details).

Example

A piezo actuator is to be usedin a nano imprint application.At rest (zero position) the dis-tance between the piezo actua-tor tip and the material is 30microns (given by mechanicalsystem tolerances). A force of500 N is required to embossthe material.

Q: Can a 60 µm actuator with astiffness of 100 N/µm be used?

A: Under ideal conditions this actuator can generate aforce of 30 x 100 N = 3000 N (30 microns are lost motiondue to the distance between

the sheet and the piezo actua-tor tip). In practice the forcegeneration depends on thestiffness of the metal and thesupport. If the support were asoft material, with a stiffness of10 N/µm, the piezo actuatorcould only generate a force of300 N onto the metal whenoperated at maximum drivevoltage. If the support werestiff but the material to beembossed itself were very softit would yield and the piezoactuator still could not gener-ate the required force. If boththe support and the metal werestiff enough, but the piezo actu-ator mount was too soft, theforce generated by the piezowould push the actuator awayfrom the material to beembossed.

The situation is similar to liftinga car with a jack. If the ground(or the car’s body) is too soft,the jack will run out of travelbefore it generates enoughforce to lift the wheels off theground.

Fig. 19. Force generation vs. dis-placement of a piezo actuator (dis-placement 30 µm, stiffness 200N/µm). Stiffness at various operat-ing voltages. The points where thedashed lines (external springcurves) intersect the piezo actua-tor force/displacement curvesdetermine the force and displace-ment for a given setup with anexternal spring. The stiffer theexternal spring (flatter dashedline), the less the displacementand the greater the force gener-ated by the actuator. Maximumwork can be done when the stiff-ness of the piezo actuator andexternal spring are identical.

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Displacement and

External Forces

Like any other actuator, a piezoactuator is compressed when aforce is applied. Two casesmust be considered when oper-ating a piezo actuator with aload:

a) The load remains constantduring the motion process.

b) The load changes during themotion process.

Note

To keep down the loss of travel,the stiffness of the preloadspring should be under 1/10that of the piezo actuator stiff-ness. If the preload stiffnesswere equal to the piezo actua-tor stiffness, the travel wouldbe reduced by 50 %. For prima-rily dynamic applications, theresonant frequency of the pre-load must be above that of thepiezo actuator.

aConstant Force

Zero-point is offset

A mass is installed on thepiezo actuator which appliesa force F = M · g (M is themass, g the acceleration dueto gravity).The zero-point will be shiftedby �LN ≈ F/kT, where kT is thestiffness of the actuator.If this force is below the spe-cified load limit (see producttechnical data), full displace-ment can be obtained at fulloperating voltage (see Fig. 20).

(Equation 5)

Zero-point offset with con-stant force

Where:

�LN = zero-point offset [m]F = force (mass x accel-

eration due to gravi-ty) [N]

kT = piezo actuator stiff-ness [N/m]

Example

How large is the zero-pointoffset of a 30 µm piezo actua-tor with a stiffness of 100N/µm if a load of 20 kg is

applied, andwhat is themaximum dis-placement withthis load?

The load of 20 kg generatesa force of 20 kgx 9.81 m/s2 =196 N. With a stiffness of

100 N/µm, the piezo actuatoris compressed slightly lessthan 2 µm. The maximumdisplacement of 30 µm is notreduced by this constantforce.

Example

Q: What is the maximum dis-placement of a 15 µm piezotranslator with a stiffness of50 N/µm, mounted in an elas-tic restraint with a spring constant kS (stiffness) of 100 N/µm?

A: Equation 6 shows that thedisplacement is reduced in anelastic restraint. The springconstant of the externalrestraint is twice the value ofthe piezo translator. Theachievable displacement istherefore limited to 5 µm (1/3 of the nominal travel).

b Changing Force

Displacement is reduced

For piezo actuator operationagainst an elastic load differ-ent rules apply. Part of thed i s p l a c e -ment gene-rated by the piezo effectis lost dueto the elas-ticity of thepiezo ele-ment (Fig.21). The to-tal avail-able displa-cement canbe related to the spring stiff-ness by the following equa-tions:

(Equation 6)

Maximum displacement of apiezo actuator acting againsta spring load.

(Equation 7)

Maximum loss of displace-ment due to external springforce. In the case where therestraint is infinitely rigid (ks

= ∞), the piezo actuator canproduce no displacement butacts only as a force generator.

Where:

�L = displacement with ex-ternal spring load [m]

�L0 = nominal displacementwithout external forceor restraint [m]

�LR = lost displacementcaused by the exter-nal spring [m]

ks = spring stiffness [N/m]

kT = piezo actuator stiff-ness [N/m]

Fig. 21. Case b: Effective displacement of a piezo actua-

tor acting against a spring load.

M

Fig. 20. Case a: Zero-point offsetwith constant force.



4-24

Dynamic Operation Fundamentals

Dynamic Forces

Every time the piezo drive volt-age changes, the piezo elementchanges its dimensions. Due tothe inertia of the piezo actuatormass (plus any additionalload), a rapid move will gener-ate a force acting on (pushingor pulling) the piezo. The maxi-mum force that can be generat-ed is equal to the blocked force,described by:

(Equation 8)

Maximum force available toaccelerate the piezo mass plusany additional load. Tensileforces must be compensated,for example, by a spring pre-load.

Where:

Fmax = max. force [N]



The preload force should bearound 20% of the compressiveload limit. The preload shouldbe soft compared to the piezoactuator, at most 10% the actu-ator stiffness. In sinusoidal operation peakforces can be expressed as:

(Equation 9)

Dynamic forces on a piezoactuator in sinusoidal opera-tion at frequency f.

Where:

Fdyn = dynamic force [N]meff = effective mass [kg],

see p. 4-25�L = peak-to-peak displace-

ment [m]f = frequency [Hz]

The maximum permissibleforces must be consideredwhen choosing an operatingfrequency.

Example:

Dynamic forces at 1000 Hz, 2 mpeak-to-peak and 1 kg loadreach approximately ±40 N.

Fig. 22. Recommended guiding for large masses.

Note

A guiding system (e.g.diaphragm type) is essentialwhen loads which are heavy orlarge (relative to the piezo actu-ator diameter) are moveddynamically. Without a guidingsystem, there is a potential fortilt oscillations that may dam-age the piezoceramics.

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Fig. 23. Effective mass of an actuator fixed at one end.







Motion Controllers



Piezo Actuators

Index

Resonant Frequency

In general, the resonant fre-quency of any spring/mass sys-tem is a function of its stiffnessand effective mass (see Fig.23). Unless otherwise stated,the resonant frequency givenin the technical data tables foractuators always refer to theunloaded actuator with oneend rigidly attached. For piezopositioning systems, the datarefers to the unloaded systemfirmly attached to a significant-ly larger mass.

(Equation 10)

Resonant frequency of an idealspring/mass system.

Where:

fO = resonant frequency ofunloaded actuator [Hz]


meff = effective mass (about1/3 of the mass of theceramic stack plus anyinstalled end pieces)[kg]

Note:

In positioning applications,piezo actuators are operatedwell below their resonant fre-quencies. Due to the non-idealspring behavior of piezoceram-ics, the theoretical result fromthe above equation does notnecessarily match the real-world behavior of the piezoactuator system under largesignal conditions. Whenadding a mass M to the actua-tor, the resonant frequencydrops according to the follow-ing equation:

(Equation 11)

Resonant frequency withadded mass.

m´eff = additional mass M + meff.

The above equations show thatto double the resonant fre-quency of a spring-mass sys-tem, it is necessary to eitherincrease the stiffness by a fac-tor of 4 or decrease the effec-tive mass to 25 % of its originalvalue. As long as the resonantfrequency of a preload spring

is well above that of the actua-tor, forces it introduces do notsignificantly affect the actua-tor’s resonant frequency.

The phase response of a piezoactuator system can be approx-imated by a second order sys-tem and is described by the fol-lowing equation:

(Equation 12)

Where:

� = phase angle [deg]

Fmax = resonant frequency [Hz]

f = operating frequency[Hz]







Motion Controllers



Piezo Actuators

Index



4-26

How Fast Can a Piezo

Actuator Expand?

Fast response is one of thecharacteristic features of piezoactuators. A rapid drive voltagechange results in a rapid posi-tion change. This property isespecially welcome in dynamicapplications such as scanningmicroscopy, image stabiliza-tion, switching of valves/shut-ters, shock-wave generation,vibration cancellation systems,etc.

A piezo actuator can reach itsnominal displacement inapproximately 1/3 of the periodof the resonant frequency, pro-vided the controller can deliverthe necessary current. If notcompensated by appropriatemeasures (e.g. notch filter,InputShaping®, see p. 4-33) in

the servo-loop, such rapidexpansion will be accompaniedby significant overshoot.

(Equation 13)

Minimum rise time of a piezoactuator (requires an amplifierwith sufficient output currentand slew rate).

Where:

Tmin = time [s]

f0 = resonant frequency[Hz]]

Example: A piezo translatorwith a 10 kHz resonant frequen-cy can reach its nominal dis-placement within 30 µs.

Dynamic Operation Fundamentals

Fig. 24. Response of an undamped, lever-amplified piezo actuator (low resonant frequency) to a rapid drive-voltage change. Thisbehavior can be prevented by intelligent control techniques or position servo-control.

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Piezo Actuator Electrical Fundamentals







Motion Controllers



Piezo Actuators

Index

Fig. 25. Design of a piezo stack actuator.

Electrical Requirements for Piezo Operation







Motion Controllers



Piezo Actuators

Index

General

When operated well below theresonant frequency, a piezoactuator behaves as a capaci-tor: The actuator displacementis proportional to stored charge(first order estimate). Thecapacitance of the actuatordepends on the area and thick-ness of the ceramic, as well ason its material properties. Forpiezo stack actuators, whichare assembled with thin, lami-nar wafers of electroactiveceramic material electricallyconnected in parallel, thecapacitance also depends onthe number of layers.

The small-signal capacitance ofa stack actuator can be estimat-ed by:

(Equation 14)

Where:

C = capacitance [F (As/V)]

n = number of layers =

�33T = dielectric constant[As/Vm]

A = electrode surface areaof a single layer [m2]

dS = distance between theindividual electrodes(layer-thickness) [m]

I0 = actuator length

The equation shows that for agiven actuator length, thecapacitance increases with thesquare of the number of layers.Therefore, the capacitance of apiezo actuator constructed of100 µm thick layers is 100 timesthe capacitance of an actuatorwith 1 mm layers, if the twoactuators have the samedimensions. Although the actu-ator with thinner layers draws

100 times as much current, thepower requirements of the twoactuators in this example areabout the same. The PI high-voltage and low-voltage ampli-fiers in this catalog are de-signed to meet the require-ments of the respective actua-tor types.

Static Operation

When electrically charged, theamount of energy stored in thepiezo actuator is E = (1/2) CU2

Every change in the charge(and therefore in displacement)of the PZT ceramics requires acurrent i:

(Equation 15)

Relationship of current andvoltage for the piezo actuator

Where:

i = current [A]

Q = charge [coulomb (As)]

C = capacitance [F]

U = voltage [V]

t = time [s]

For static operation, only theleakage current need be sup-plied. The high internal resist-ance reduces leakage currentsto the micro-amp range or less.Even when suddenly discon-nected from the electricalsource, the charged actuatorwill not make a sudden move,but return to its unchargeddimensions very slowly.

For slow position changes,only very low current isrequired.

Example: An amplifier with anoutput current of 20 µA canfully expand a 20 nF actuator in

one second. Suitable amplifierscan be found using the “Con-trol Electronics SelectionGuide” on p. 6-8.

Note

The actuator capacitance val-ues indicated in the technicaldata tables are small-signal val-ues (measured at 1 V, 1000 Hz,20 °C, unloaded) The capaci-tance of piezoceramics chan-ges with amplitude, tempera-ture, and load, to up to 200 % ofthe unloaded, small-signal,room-temperature value. Fordetailed information on powerrequirements, refer to theamplifier frequency responsecurves in the “Piezo Drivers &Nanopositioning Controllers”section.



4-28

Dynamic Operation (Linear)

Piezo actuators can provideaccelerations of thousands ofg’s and are ideally suited fordynamic applications.

Several parameters influencethe dynamics of a piezo posi-tioning system:

� The slew rate [V/s] and themaximum current capacityof the amplifier limit theoperating frequency of thepiezo system.

� If sufficient electrical poweris available from the amplifi-er, the maximum drive fre-quency may be limited bydynamic forces (see “Dyna-mic Operation”, p. 4-24).

� In closed-loop operation, themaximum operating fre-quency is also limited by thephase and amplituderesponse of the system. Ruleof thumb: The higher thesystem resonant frequency,the better the phase andamplitude response, and thehigher the maximum usablefrequency. The sensor band-width and performance ofthe servo-controller (digitaland analog filters, controlalgorithm, servo-bandwidth)determine the maximumoperating frequency of apiezoelectric system.

� In continuous operation, heat generation can alsolimit the operating frequency.

The following equationsdescribe the relationshipbetween amplifier output cur-rent, voltage and operating fre-quency. They help determinethe minimum specifications ofa piezo amplifier for dynamicoperation.

(Equation 16)

Long-term average currentrequired for sinusoidal opera-tion

(Equation 17)

Peak current required for sinu-soidal operation

(Equation 18)

Maximum operating frequencywith triangular waveform, as afunction of the amplifier outputcurrent limit

Where:

ia* = average amplifiersource/sink current [A]

imax* = peak amplifiersource/sink current [A]

fmax = maximum operatingfrequency [Hz]

C** = piezo actuator capaci-tance [Farad (As/V)]

Up-p = peak-to-peak drivevoltage [V]


The average and maximumcurrent capacity for each PIpiezo amplifier can be found inthe product technical datatables.

Example

Q: What peak current isrequired to obtain a sinewavedisplacement of 20 µm at 1000Hz from a 40 nF HVPZT actua-tor with a nominal displace-ment of 40 µm at 1000 V?

A: The 20 µm displacementrequires a drive voltage ofabout 500 V peak-to-peak. WithEquation 17 the required peakcurrent is calculated at ≈ 63 mA.For appropriate amplifiers, seethe “Piezo Drivers & Nano-positioning Controllers” sec-tion, p. 6-8.

The following equationsdescribe the relationship be-tween (reactive) drive power,actuator capacitance, operatingfrequency and drive voltage.

The average power a piezodriver has to be able to providefor sinusoidal operation isgiven by:

(Equation 19)

Peak power for sinusoidaloperation is:

(Equation 20)

Where:

Pa = average power [W]

Pmax = peak power [W]

C** = piezo actuator capaci-tance [F]


Up-p = peak-to-peak drivevoltage [V]

Umax = nominal voltage ofthe amplifier [V]

It is also essential that thepower supply be able to supplysufficient current.

* The power supply must be able to pro-vide enough current.

** For large-signal conditions a margin of70% of the small-signal value should beadded.


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Dynamic Operating Current

Coefficient (DOCC)

Instead of calculating therequired drive power for agiven application, it is easier tocalculate the drive current,because it increases linearlywith both frequency and volt-age (displacement). For thispurpose, the DynamicOperating Current Coefficient(DOCC) has been introduced.The DOCC is the current thatmust be supplied by the ampli-fier to drive the piezo actuatorper unit frequency (Hz) andunit displacement. DOCC val-ues are valid for sinewaveoperation in open-loop mode.In closed-loop operation thecurrent requirement can be upto 50% higher.

The peak and long-term aver-age current capacities of thedifferent piezo amplifiers canbe found in the technical datatables for the electronics, theDOCC values in the tables forthe piezo actuators.

Example: To determinewhether a selected amplifiercan drive a given piezo actua-tor at 50 Hz with 30 µm peak-to-peak displacement, multiplythe actuator’s DOCC by 50 x 30and compare the result withthe average output current ofthe selected amplifier. If thecurrent required is less than orequal to the amplifier output,then the amplifier has suffi-cient capacity for the applica-tion.

Dynamic Operation

(Switched)

For applications such as shockwave generation or valve con-trol, switched operation (on/off) may be sufficient. Piezoactuators can provide motionwith rapid rise and fall timeswith accelerations in the thou-sands of g’s. For informationon estimating the forces

involved, see “DynamicForces,” p. 4-24).

The simplest form of binarydrive electronics for piezoapplications would consist of alarge capacitor that is slowlycharged and rapidly dis-charged across the PZT ceram-ics.

The following equation relatesapplied voltage (which corre-sponds to displacement) totime.

(Equation 21)

Voltage on the piezo afterswitching event.

Where:

U0 = start voltage [V]

Up-p = source output voltage(peak-to-peak) [V]

R = source output resist-ance [ohm]

C = piezo actuator capaci-tance [F]

t = time [s]

The voltage rises or falls expo-nentially with the RC time con-stant. Under quasi-static condi-tions, the expansion of the PZTceramics is proportional to thevoltage. In reality, dynamicpiezo processes cannot bedescribed by a simple equa-tion. If the drive voltage risestoo quickly, resonance occurs,causing ringing and overshoot.Furthermore, whenever thepiezo actuator expands or con-tracts, dynamic forces act onthe ceramic material. Theseforces generate a (positive ornegative) voltage in the piezoelement which is superim-posed on the drive voltage. A

piezo actuator can reach itsnominal displacement inapproximately 30 % of the peri-od of the resonant frequency,provided the controller candeliver the necessary current.(see p. 4-26).

The following equation appliesfor constant-current charging(as with a linear amplifier):

(Equation 22)

Time to charge a piezoceramicwith constant current. Withlower-capacity electronics,amplifier slew rate can be alimiting factor.

Where:

t = time to charge piezoto Up-p [s]

C = piezo actuator capaci-tance [F]

Up-p = voltage change(peak-to-peak) [V]

imax = peak amplifiersource/sink current [A]

For fastest settling, switchedoperation is not the best solu-tion because of the resultingovershoot. Modern techniqueslike InputShaping® (see p. 4-33)solve the problem of reso-nances in and around the actu-ator with complex signal pro-cessing algorithms.

Note

Piezo drives are becomingmore and more popularbecause they can deliverextremely high accelerations.This property is very importantin applications such as beamsteering and optics stabiliza-tion. Often, however, the actua-tors can accelerate faster thanthe mechanics they drive can







Motion Controllers



Piezo Actuators

Index







Motion Controllers



Piezo Actuators

Index



4-30

follow. Rapid actuation ofnanomechanisms can causerecoil-generated ringing of theactuator and any adjacent com-ponents. The time required forthis ringing to damp out can bemany times longer than themove itself. In time-criticalindustrial nanopositioningapplications, this problemobviously grows more seriousas motion throughputsincrease and resolutionrequirements tighten.

Classical servo-control tech-niques cannot solve this prob-lem, especially when reso-nances occur outside theservo-loop such as when ring-ing is excited in a sample on afast piezo scanning stage as itreverses direction. A solution isoften sought in reducing thescanning rate, thereby sacrific-ing part of the advantage of apiezo drive.

A patented real-time feedfor-ward technology calledInputShaping® nullifies reso-nances both inside and outsidethe servo-loop and thus elimi-nates the settling phase. Formore information see p. 4-33 orvisit www.Convolve.com.

Heat Generation in a Piezo

Actuator in Dynamic

Operation

PZT ceramics are (reactive)capacitive loads and thereforerequire charge and dischargecurrents that increase withoperating frequency. The ther-mal active power, P (apparentpower x power factor, cos �),generated in the actuator dur-ing harmonic excitation can beestimated with the followingequation:

(Equation 23)

Heat generation in a piezo actu-ator.

Where:

P = power converted toheat [W]

tan � = dielectric factor (≈ powerfactor, cos �, for smallangles � and �)


C = actuator capacitance[F]

Up-p = voltage (peak-to-peak)

For the description of the losspower, we use the loss factortan � instead of the power fac-tor cos �, because it is themore common parameter forcharacterizing dielectric materi-als. For standard actuatorpiezoceramics under small-sig-nal conditions the loss factor ison the order of 0.01 to 0.02. Thismeans that up to 2 % of theelectrical “power” flowingthrough the actuator is convert-ed into heat. In large-signalconditions however, 8 to 12 %of the electrical power pumpedinto the actuator is convertedto heat (varies with frequency,

temperature, amplitude etc.).Therefore, maximum operatingtemperature can limit the piezoactuator dynamics. For largeamplitudes and high frequen-cies, cooling measures may benecessary. A temperature sen-sor mounted on the ceramics issuggested for monitoring pur-poses. For higher frequency operationof high-load actuators withhigh capacitance (such asPICA™-Power actuators, see p.1-20), a special amplifiersemploying energy recoverytechnology has been devel-oped. Instead of dissipating thereactive power at the heatsinks, only the active powerused by the piezo actuator hasto be delivered.

The energy not used in theactuator is returned to theamplifier and reused, as shownin the block diagram in Fig. 26.The combination of low-loss,high-energy piezoceramics andamplifiers with energy recov-ery are the key to new high-level dynamic piezo actuatorapplications.

For dynamic applications withlow to medium loads, the newly developed PICMA® actu-

ators are also quite well suited.With their high Curie tempera-ture of 320 °C, they can beoperated with internal temper-atures of up to 150 °C.

Fig. 26. Block diagram of an amplifier with energy recovery forhigher frequency applications.


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Control of Piezo Actuators and Stages







Motion Controllers



Piezo Actuators

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Position Servo-Control

Fig. 28. Block diagram of a typical PI closed-loop piezo positioning system. Fig. 29. Closed-loop position servo-control. For optimum performance, the sensoris mounted directly on the object to be positioned (direct metrology).

Fig. 27. Variety of digital piezo controllers.

Position servo-control elimi-nates nonlinear behavior ofpiezoceramics such as hystere-sis and creep and is the key tohighly repeatable nanometricmotion.

PI offers the largest selection ofclosed-loop piezo mechanismsand control electronics world-wide. The advantages of posi-tion servo-control are:

� High linearity, stability,repeatability and accuracy

� Automatic compensation forvarying loads or forces

� Virtually infinite stiffness(within load limits)

� Elimination of hysteresisand creep effects

PI closed-loop piezo actuatorsand systems are equipped withposition measuring systems

providing sub-nanometer reso-lution, linearity to 0.01 %, andbandwidths up to 10 kHz. Aservo-controller (digital or ana-log) determines the outputvoltage to the PZT ceramics bycomparing a reference signal(commanded position) to theactual sensor position signal(see Fig. 28).

For maximum accuracy, it isbest if the sensor measures themotion of the part whose posi-tion is of interest (direct metrol-ogy). PI offers a large variety ofpiezo actuators with integrateddirect-metrology sensors.Capacitive sensors provide thebest accuracy (see section 5,“Capacitive Position Sensors”).Simpler, less accurate systemsmeasure things like strain indrive elements.







Motion Controllers



Piezo Actuators

Index



4-32

Open- and Closed-Loop

Resolution

Position servo-controlled piezodrives offer linearity and re-peatability many times betterthan that of open-loop systems.The resolution (minimum in-cremental motion) of piezoactuators is actually better foropen-loop than for closed-loopsystems. This is because piezoresolution is not limited by fric-tion but rather by electronicnoise. In open-loop, there is nosensor or servo-electronics toput additional noise on the con-trol signal. In a servo-controlledpiezo system, the sensor andcontrol electronics are thus ofconsiderable importance. Withappropriate, high-quality sys-tems, subnanometer resolutionis also possible in closed-loopmode, as can be seen in Fig. 30and 31. Capacitive sensorsattain the highest resolution,linearity and stability.

Piezo Calibration Data

Each PI piezo position servo-controller is calibrated with thespecific closed-loop piezo posi-tioning system to achieve opti-mum displacement range, fre-quency response and settlingtime. The calibration is perfor-med at the factory and a reportwith plotted and tabulated po-sitioning accuracy data is sup-plied with the system (see p. 2-8, p. 3-7). To optimize calibra-tion, information about the spe-cific application is needed. Fordetails see p. 6-53 in the “PiezoDrivers & NanopositioningControllers” section.

Digital controllers can automat-ically read important calibra-tion values from an ID-chipintegrated in the piezo me-chanics. This feature facilitatesusing a controller with variousstages/actuators and viceversa.

Control of Piezo Actuator s and Stages

Fig. 30. Response of a closed-loop PI piezo actuator (P-841.10, 15 µm, strain gaugesensor) to a 3 nm peak-to-peak square-wave control input signal, measured withservo-control bandwidth set to 240 Hz and 2 msec settling time. Note the crisp,backlash-free behavior in the nanometer range.

Fig. 31. PI piezo actuators with capacitive position sensors can achieve ex-tremely high resolutions, as seen in the above result of a 250 picometerstep by a S-303 phase corrector (Controller: E-509.C1A servo-controller andE-503 amplifier). The measurements were made with an ultra-sensitivecapacitive sensor having a resolution of ±0.02 nm.

Ctrl Input /V

L

Fig. 32. Open-loop vs. closed-loop performance graph of a typical PI piezo actuator.

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Methods to Improve Piezo Dynamics

The dynamic behavior of apiezo positioning systemdepends on factors includingthe system’s resonant frequen-cy, the position sensor and thecontroller used. Simple con-troller designs limit the usableclosed-loop tracking band-width of a piezoelectric systemto 1/10 of the system’s reso-nant frequency. PI offers con-trollers that significantly in-crease piezo actuator systemdynamics (see table). Two ofthe methods are describedbelow; additional informationis available on request.

InputShaping® Stops

Structural Ringing Caused by

High-Throughput Motion

A patented, real-time, feedfor-ward technology calledInputShaping® nullifies reso-

nances both inside and outsidethe servo-loop and virtuallyeliminates the settling phase.The procedure requires deter-mination of all critical resonantfrequencies in the system. Anon-contact instrument like aPolytec Laser Doppler Vibro-meter is especially well-suitedfor such measurements. Thevalues, most importantly theresonant frequency of the sam-ple on the platform, are thenfed into the InputShaping®

Signal processor. There thesophisticated signal process-ing algorithms assure thatnone of the undesired reso-nances in the system or its aux-illary components is excited.Because the processor is out-side the servo-loop, it works inopen-loop operation as well.The result: the fastest possiblemotion, with settling within a

time equal one period of thelowest resonant frequency.InputShaping® was developedbased on research at theMassachusetts Institute ofTechnology and commercial-ized by Convolve, Inc.(www.convolve.com). It is anoption in several PI digitalpiezo controllers.







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Piezo Actuators

Index

Various Methods to Improve Piezo Dynamics

Method Goals

Feedforward Reduce phase difference between output and input (tracking error)

Signal preshaping (software) Increase operating frequency of the system, correct amplitude and phaseresponse. Two learning phases required; only for periodic signals.

Adaptive preshaping (hardware) Increase operating frequency of the system, correct amplitude and phaseresponse. No learning phase, but settling phase required; only for periodic signals.

Linearization (digital, in DSP) Compensate for piezo hysteresis and creep effects

InputShaping® Cancel recoil-generated ringing, whether inside or outside the servo-loop. Reduce the settling time. Closed- and open-loop.

Dynamic Digital Linearization (DDL) Increase operating frequency of the system, correct amplitude and phase response. Integrated in digital controller.No external metrology necessary, for periodic signals only.

Fig. 33. InputShaping® eliminates therecoil-driven resonant reaction of loadsand neighboring components due torapid nanopositioner actuation. Top: Polytec Laser Vibrometer revealsthe resonant behavior of an undampedfixture when the nanomechanism isstepped. Bottom: Same setup, same step, butwith InputShaping®. Structural ringingis eliminated. With no excitation ofvibration in the moved components,the target position is attained in a timesmaller than one period of the resonantfrequency.

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http://www.convolve.com


Fig. 34 a. Signal preshaping, phase 1.

Fig. 34 b. Signal preshaping, phase 2.

Signal Preshaping / Dynamic

Digital Linearization (DDL)

Signal Preshaping, a patentedtechnique, can reduce rolloff,phase error and hysteresis inapplications with repetitive(periodic) inputs. The result isto improve the effective band-width, especially for trackingapplications such as out-of-round turning of precisionmechanical or optical parts.Signal Preshaping is imple-mented in object code, basedon an analytical approach inwhich the complex transferfunction of the system is calcu-lated, then mathematicallytransformed and applied in afeedforward manner to reducethe tracking error.

Signal Preshaping is moreeffective than simple phase-shifting approaches and canimprove the effective band-width by a factor of 10 and inmulti-frequency applications.

Frequency response and har-monics (caused by nonlinearityof the piezo-effect) are deter-mined in two steps using FastFourier Transformation (FFT),and the results are used to cal-culate the new control profilefor the trajectory. The new con-trol signal compensates for thesystem non-linearities.

Methods to Improve Piezo Dynamics

For example, it is possible toincrease the command ratefrom 20 Hz to 200 Hz for a piezosystem with a resonant fre-quency of 400 Hz without com-promising stability. At the sametime, the tracking error isreduced by a factor of about 50.

Fig. 35. No preshaping. A: Control input signal (expected motion). B: Actual motion of system.C: Tracking error.

Fig. 36. Signal after preshaping phase 2.A: Expected Motion (old control signal). B: Actual motion of system. C: New control input (producted by preshaping). D: Tracking error.

4-34

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4-35

Dynamic Digital Linearization

(DDL)

DDL is similar in performanceto Input Preshaping, but is sim-pler to use. In addition, it canoptimize multi-axis motionsuch as a raster scan or tracingan ellipse. This methodrequires no external metrologyor signal processing, but isfully integrated in E-710 and E-711 digital controllers. DDLuses the position informationfrom capacitive sensors inte-grated in the piezo mechanics(requires direct metrology) tocalculate the optimum controlsignal. As with preshaping, theresult is an improvement in lin-earity and tracking accuracy ofup to 3 orders of magnitude.







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Fig. 37 a. Elliptical scan in a laser micro-drilling application with XYpiezo scanning stage, conventional PID controller. The outer ellipsedescribes the target position, the inner ellipse shows the actualmotion at the stage.

Fig. 37 b. Same scan as before, with a DDL controller. Targetand actual data can hardly be discerned. The tracking error hasbeen reduced to a few nanometers.

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4-36

Note

Closed-loop piezo positioningsystems are less sensitive totemperature changes thanopen-loop systems. Optimumaccuracy is achieved if theoperating temperature is iden-tical to the calibration tempera-ture. If not otherwise specified,PI piezomechanics are calibrat-ed at 22 °C.

Environmental Conditions and InfluencesTemperature Effects

Two effects

must be considered:

� Linear Thermal Expansion� Temperature Dependency of

the Piezo Effect

Linear Thermal Expansion

Thermal stability of piezoce-ramics is better than that ofmost other materials. Fig. 38ashows the behavior of severaltypes of piezoceramics used byPI. The curves only describethe behavior of the piezoce-ramics. Actuators and position-ing systems consist of a combi-nation of piezoceramics andother materials and their over-all behavior differs accordingly.

Temperature Dependency of

the Piezo Effect

Piezo translators work in awide temperature range. Thepiezo effect in PZT ceramics isknown to function down toalmost zero kelvin, but themagnitude of the piezo coeffi-cients is temperature depend-ent.

At liquid helium temperaturepiezo gain drops to approxi-mately 10–20 % of its room-temperature value.

Piezoceramics must be poledto exhibit the piezo effect. Apoled PZT ceramic may depolewhen heated above the maxi-mum allowable operating tem-perature. The “rate” of depol-ing is related to the Curie tem-perature of the material. PIHVPZT actuators have a Curietemperature of 350 °C and canbe operated at up to 150 °C.LVPZT actuators have a Curietemperature of 150 °C and canbe operated at up to 80 °C. Thenew monolithic PICMA® ceram-ics with their high Curie tem-perature of 320 °C allow oper-ating at temperatures of up to150 °C.

Piezo Operation

in High Humidity

The polymer insulation materi-als used in piezoceramic actua-tors are sensitive to humidity.Water molecules diffusethrough the polymer layer and

can cause short circuiting ofthe piezoelectric layers. Theinsulation materials used inpiezo actuators are sensitive tohumidity. For higher humidityenvironments, PI offers specialsystems with waterproofedenclosed stacks, or integrateddry-air flushing mechanisms.A better solution are PICMA®

actuators (see Fig. 39a), whichhave ceramic-only insulationwithout any polymer coveringand are thus less sensitive towater diffusion (see Fig. 39c).

Fig. 38 a. Linear thermal expansion of different PZT ceramics.

Fig. 38 b. The expansion of PICMA® piezoceramics is only slightly tem-perature dependent. This, and their low heat generation, makes themideal for dynamic applications.

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Piezo Operation in Inert Gas

Atmospheres

Ceramic-insulated PICMA®

actuators are also recommend-ed for use in inert gases, suchas helium. To reduce the dan-ger of flashover with high-volt-age piezos, the maximum oper-ating voltage must be reduced.Semi-bipolar operation is rec-ommended, because the aver-age operating voltage can bekept very low.

Vacuum Operation

of Piezo Actuators

All PI piezo actuators can beoperated at pressures below100 Pa (~1 torr). When piezoactuators are used in a vacu-um, two factors must be con-sidered:

I. Dielectric stability

II. Outgassing

I. The dielectric breakdown volt-age of a sample in a specificgas is a function of the pres-sure p times the electrode dis-tance s. Air displays a highinsulation capacity at atmos-pheric pressure and at very lowpressures. The minimumbreakdown voltage of ~300 Vcan be found at a ps-product of1000 mm Pa (~10 mm torr).

That is why PICMA® actuatorswith a maximum operatingvoltage of 120 V can be used inany vacuum condition. How-ever, the operation of HVPZTactuators with dielectric layerthicknesses of 0.2 – 1.0 mm andnominal voltages to 1000 V isnot recommended in the pres-sure range of 100 – 50000 Pa(~1 – 500 torr).

II. Outgassing behavior variesfrom model to model depend-ing on design. Ultra-high-vacu-um options for minimum out-gassing are available for manystandard low-voltage and high-voltage piezo actuators. Bestsuited are PICMA® ceramics(see Fig. 39a), because theyhave no polymers and canwithstand bakeout to 150 °C(see also “Options” in the“Piezo Actuators” sections, p.1-44 ff).

All materials used in UHV-com-patible piezo nanopositioners,including cables and connec-tors, are optimized for minimaloutgassing rates (see Fig. 39b).Materials lists are available onrequest.

Fig. 39 a. PICMA® actuators are made with ceramic-only insulation and candispense with any polymer coating. Result No measurable outgasing, insen-

sitive to atmospheric humidity and a wider operating temperature range.

Fig. 39 b. P-733.UUD UHV-compatible XY stage for scanning microscopyapplications. PICMA® ceramics are used here too. All materials used are

optimized for minimal outgassing. Materials lists are available on request.







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4-38

The lifetime of a piezo actuatoris not limited by wear and tear.Tests have shown that PI piezoactuators can perform billions(109) of cycles without anymeasurable wear.

As with capacitors, however,the field strength does have aninfluence on lifetime. The aver-age voltage should be kept aslow as possible. Most PI piezoactuators and electronics aredesigned for semi-bipolaroperation.

There is no generic formula todetermine the lifetime of apiezo actuator because of themany parameters, such as tem-perature, humidity, voltage,acceleration, load, preload,operating frequency, insulationmaterials, etc., which have(nonlinear) influences. PI piezoactuators are not only opti-mized for maximum travel, butalso designed for maximumlifetime under actual operatingconditions.

The operating voltage rangevalues in the technical datatables are based on decades ofexperience with nanomech-anisms and piezo applicationsin industry. Longer travel canonly be obtained with highervoltages at the cost of reducedreliability.

Example:

An P-842.60 LVPZT actuator(see p. 1-36 in the “PiezoActuators” section) is to oper-ate a switch with a stroke of100 µm. Of its operating time, itis to be open for 70 % andclosed for 30 %.

Optimum solution: The actua-tor should be linked to theswitch in such a way that theopen position is achieved withthe lowest possible operatingvoltage. To reach a displace-ment of 100 µm, a voltage

amplitude of approximately110 volts is required (nominaldisplacement at 100 V is only90 µm).

Since the P-842.60 can be oper-ated down to -20 volts, theclosed position should beachieved with 90 V, and theopen position with -20 volts.When the switch is not in use atall, the voltage on the piezoactuator should be 0 volts.

Statistics show that most fail-ures with piezo actuators occurbecause of excessive mechani-cal stress. Particularly destruc-tive are tensile and shearforces, torque and mechanicalshock. To protect the ceramicfrom such forces PI offers avariety of actuators with pre-loads, ball tips, flexible tips aswell as custom designs.

Failures can also occur whenhumidity or conductive materi-als such as metal dust degradethe PZT ceramic insulation,leading to irreparable dielectricbreakdown. In environmentspresenting these hazards,PICMA® actuators with theirceramic-only insulation arestrongly recommended. PI alsooffers hermetically sealed actu-ators and stages.

Lifetime of Piezo Actuators

Environmental Conditions and Influences

Fig. 39 d. P-885.50 PICMA® actuators with 15 MPa preload in dynamic motion test at 116 Hz. No observable wear after 1.2 billion (109) cycles.

Fig. 39 c. PICMA® piezo actuators (lower curve) compared with conventional multi-layer piezo actuators with polymer insulation. PICMA® actuators are insensitve tohigh humidity in this test. In conventional actuators, the leakage current begins to rise after only a few hours—an indication of degradation of the insulation andreduced lifetime. Test conditions: U = 100 VDC, T = 25 °C, RH = 70%.

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Basic Designs of Piezoelectric PositioningDrives/SystemsStack Design (Translators)

The active part of the position-ing element consists of a stackof ceramic disks separated bythin metallic electrodes. Themaximum operating voltage isproportional to the thickness ofthe disks. Most high-voltageactuators consist of ceramiclayers measuring 0.4 to 1 mmin thickness. In low-voltagestack actuators, the layers arefrom 25 to 100 µm in thicknessand are cofired with the elec-trodes to form a monolithicunit.

Stack elements can withstandhigh pressures and exhibit thehighest stiffness of all piezoactuator designs. Standarddesigns which can withstandpressures of up to 100 kN areavailable, and preloaded actua-tors can also be operated inpush-pull mode. For furtherinformation see “MaximumApplicable Forces”, p. 4-21.

Displacement of a piezo stackactuator can be estimated bythe following equation:

(Equation 24)

where:

�L = displacement [m]

d33 = strain coefficient (fieldand displacement inpolarization direction)[m/V]

n = number of ceramic layers

U = operating voltage [V]

Example:

P-845, p. 1-36, etc. (see the“Piezo Actuators” section)

Laminar Design

(Contraction-Type Actuators)

The active material in the lami-nar actuators consists of thin,laminated ceramic strips. Thedisplacement exploited inthese devices is that perpendi-cular to the direction of polar-ization and electric field appli-cation. When the voltage isincreased, the strip contracts.The piezo strain coefficient d31(negative!) describes the rela-tive change in length. Itsabsolute value is on the orderof 50 % of d33.

The maximum travel is a func-tion of the length of the strips,while the number of stripsarranged in parallel determinesthe stiffness and force genera-tion of the element.

Displacement of a piezo con-traction actuator can be esti-mated by the following equa-tion:

(Equation 25)

where:

�L = displacement [m]

d31 = strain coefficient (displacement normal to polarization direction)[m/V]

L = length of the piezoce-ramics in the electricfield direction [m]


d = thickness of one ceramiclayer [m]

Examples:

Laminar piezos are used in theP-280 and P-282 nanoposition-ing systems, (see pp. 2-30 and2-31).

Fig. 41. Mechanical design of a stack translator.







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Index

Fig. 40. Electrical design of a stack translator.

Fig. 42. Laminar actuator design.







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4-40

Fig. 44. Piezo scanner tube working principle.

Tube Design

Monolithic ceramic tubes areyet another form of piezo actu-ator. Tubes are silvered insideand out and operate on thetransversal piezo effect. Whenan electric voltage is appliedbetween the outer and innerdiameter of a thin-walled tube,the tube contracts axially andradially. Axial contraction canbe estimated by the followingequation:

(Equation 26 a)

where:

d31 = strain coefficient (dis-placement normal topolarization direction)[m/V]

L = length of the piezoceramic tube [m]


d = wall thickness [m]

The radial displacement is theresult of the superposition ofincrease in wall thickness(Equation 26 b) and the tangen-tial contraction:

(Equation 26 b)

r = tube radius

(Equation 26 c)

where:

�d = change in wall thickness[m]

d33 = strain coefficient (fieldand displacement inpolarization direction)[m/V]


When the outside electrode ofa tube is separated into four90° segments, placing differen-tial drive voltages ±U onopposing electrodes will leadto bending of one end. Suchscanner tubes that flex in X andY are widely used in scanning-probe microscopes, such asscanning tunneling micro-scopes.

The scanning range can beestimated as follows:

(Equation 27)

where:

�x = scan range in X and Y(for symmetrical electro-des) [m]

d31 = strain coefficient (dis-placement normal topolarization direction)[m/V]

U = differential operatingvoltage [V]

L = length [m]

ID = inside diameter [m]

d = wall thickness [m]

Tube actuators cannot gener-ate or withstand large forces.Application examples: Micro-dosing, nanoliter pumping,scanning microscopy, ink jetprinters.

Examples:

PT120, PT130, PT140 (p. 1-26).

Fig. 43. Tube actuator design.

Basic Designs of Piezoelectric PositioningDrives/Systems

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Bender Type Actuators

(Bimorph and Multimorph

Design)

A simple bender actuator(bimorph design) consists of apassive metal substrate gluedto a piezoceramic strip (seeFig. 45a). A piezo bimorphreacts to voltage changes theway the bimetallic strip in athermostat reacts to tempera-ture changes. When the ceram-ic is energized it contracts orexpands proportional to theapplied voltage. Since themetal substrate does notchange its length, a deflectionproportional to the appliedvoltage occurs. The bimorphdesign amplifies the dimen-sion change of the piezo, pro-viding motion up to severalmillimeters in an extremelysmall package. In addition tothe classical strip form,bimorph disk actuators wherethe center arches when a volt-age is applied, are also avail-able.

PZT/PZT combinations, whereindividual PZT layers are oper-ated in opposite modes (con-traction/expansion), are alsoavailable.

Two basic versions exist: thetwo-electrode bimorph (serialbimorph) and the three-elec-trode bimorph (parallelbimorph), as shown in Fig. 45b.In the serial type, one of thetwo ceramic plates is alwaysoperated opposite to the direc-tion of polarization. To avoiddepolarization, the maximumelectric field is limited to a fewhundred volts per millimeter.Serial bimorph benders arewidely used as force and accel-eration sensors.

In addition to the two-layerbenders, monolithic multilayerpiezo benders are also avail-able. As with multilayer stackactuators, they run on a lower

operating voltage (60 to 100 V).Bender type actuators providelarge motion in a small pack-age at the cost of low stiffness,force and resonant frequency.

Examples:

P-286 - 289 disk translators (seep. 1-28), PL122 multilayer ben-der actuators (p. 1-14).

Shear Actuators

Shear actuators can generatehigh forces and large displace-ments. A further advantage istheir suitability for bipolaroperation, whereby the mid-position corresponds to a drivevoltage of 0 V. In shear mode,unlike in the other modes, theelectric field is applied perpen-dicular to the polarizationdirection. (see Fig. 46). The cor-responding strain coefficient,d15, has large-signal values ashigh as 1100 pm/V, providingdouble the displacement of lin-ear actuators of comparablesize based on d33.

Shear actuators are suitable forapplications like piezo linearmotors, and are available asboth single-axis and two-axispositioning elements.

Examples:

PX155 (p. 1-24), P-363 (p. 2-72),N-214 NEXLINE® Piezo-Walk®

motor (p. 10-12).







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Fig. 45 a. Bimorph design (strip and disk translator).

Fig. 45 b. Bender Actuators: Serial and parallel bimorphs.

Fig. 46. Material deformation in a shear actuator.

metal

.







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4-42

Piezo Actuators with

Integrated Lever Motion

Amplifiers

Piezo actuators or positioningstages can be designed in sucha way that a lever motionamplifier is integrated into thesystem. To maintain sub-nanometer resolution with theincreased travel range, thelever system must be extreme-ly stiff, backlash- and friction-free, which means ball or rollerbearings cannot be used.Flexures are ideally suited aslinkage elements. Using flex-ures, it is also possible to design multi-axis position-ing systems with excellent guidance characteristics (see p. 4-43).

PI employs finite elementanalysis (FEA) computer simu-lation to optimize flexurenanopositioners for the bestpossible straightness and flat-ness (see Fig. 49 and Fig. 51).

Piezo positioners with integrat-ed motion amplifiers have bothadvantages and disadvantagescompared to standard piezoactuators:

Advantages:

� Longer travel� Compact size compared to

stack actuators with equaldisplacement

� Reduced capacitance (= reduced drive current)

Disadvantages:

� Reduced stiffness � Lower resonant frequency

The following relations applyto (ideal) levers used to amplifymotion of any primary drivesystem:

where:

r = lever transmissionratio

�L0 = travel of the primarydrive [m]

�LSys = travel of the lever-amplified system [m]

ksys = stiffness of the lever-amplified system[N/m]

k0 = stiffness of the pri-mary drive system(piezo stack andjoints) [N/m]

fres-sys = resonant frequency ofthe amplified system[Hz]

fres-0 = resonant frequency ofthe primary drive sys-tem (piezo stack andjoints) [Hz]

Note:

The above equations are basedon an ideal lever design withinfinite stiffness and zero mass.They also imply that no stiff-ness is lost at the couplinginterface between the piezostack and the lever. In realapplications, the design of agood lever requires long expe-

rience in micromechanics andnanomechanisms. A balancebetween mass, stiffness andcost must be found, whilemaintaining zero-friction andzero-backlash conditions.

Coupling the piezo stack to thelever system is crucial. Thecoupling must be very stiff inthe pushing direction butshould be soft in all otherdegrees of freedom to avoiddamage to the ceramics. Evenif the stiffness of each of thetwo interfaces is as high as thatof the piezo stack alone, a 67 %loss of overall stiffness stillresults. In many piezo-drivensystems, the piezo stiffness isthus not the limiting factor indetermining the stiffness of themechanism as a whole.

PI piezomechanics are opti-mized in this regard as a resultof more than 30 years experi-ence with micromechanics,nanopositioning and flexures.

Basic Designs of Piezoelectric PositioningDrives/Systems

Fig. 47. Simple lever motion amplifier.

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Piezo Flexure Nanopositioners

For applications whereextremely straight motion inone or more axes is neededand only nanometer or micro-rad deviation from the idealtrajectory can be tolerated,flexures provide an excellentsolution.

A flexure is a frictionless, stic-tionless device based on theelastic deformation (flexing) ofa solid material (e.g. steel).Sliding and rolling are entirelyeliminated. In addition, flexuredevices can be designed withhigh stiffness, high load capac-ity and do not wear. They arealso less sensitive to shock andvibration than other guidingsystems. They are also mainte-nance-free, can be fabricatedfrom non-magnetic materials,require no lubricants or con-sumables and hence, unlike aircushion bearings, are suitablefor vacuum operation.

Parallelogram flexures exhibitexcellent guidance characteris-tics. Depending on complexityand tolerances, they havestraightness/flatness values inthe nanometer range or better.Basic parallelogram flexurescause arcuate motion (travel inan arc) which introduces anout-of-plane error of about0.1% of the travel range (seeFig. 48). The error can be esti-mated by the following equa-tion:

(Equation 28)

where:

�H = out-of-plane error [m]

�L = distance traveled [m]

H = length of flexures [m]

For applications where thiserror is intolerable, PI hasdesigned a zero-arcuate-errormulti-flexure guiding system.This special design, employedin most PI flexure stages,makes possible straightness/flatness in the nanometer or microradian range (see Fig. 49).

Note:

Flexure positioners are farsuperior to traditional position-ers (ball bearings, crossedroller bearings, etc.) in terms ofresolution, straightness andflatness. Inherent friction andstiction in these traditionaldesigns limit applications tothose with repeatability re-quirements on the order of 0.5to 0.1 µm. Piezo flexurenanopositioning systems haveresolutions and repeatabilitieswhich are superior by severalorders of magnitude.

Fig. 48. Basic parallelogram flexure guiding system with motion ampli-fication. The amplification r (transmission ratio) is given by (a+b)/a.

Fig. 49. Zero-arcuate-error multi-flexure guiding system.







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4-44

Parallel and Serial Kinematics / Metrology

Direct and Indirect Metrology

Non-contact sensors are usedto obtain the most accurateposition values possible forposition servo-control systems.Two-plate capacitive sensorsinstalled directly on the movingplatform and measuring on theaxis of motion offer the bestperformance. Resolution andrepeatability can attain 0.1nanometer in such systems.Indirect metrology—measuringstrain at some point in the drivetrain—cannot be used in sys-tems with the highest accuracyrequirements.

Fig. 50 b. Working principle of a nested XY piezo stage (serial kinematics).Lower center of gravity and somewhat better dynamics compared withstacked system, but retains all the other disadvantages of a stacked system,including asymmetric dynamic behavior of X and Y axes.

Fig. 50 c. Working principle of a monolithic XY�Z parallel kinematics piezo stage. Allactuators act directly on the central platform. Integrated parallel metrology keeps allmotion in all controlled degrees of freedom inside the servo-loop. The position of thecentral, moving platform is measured directly with capacitive sensors, permitting alldeviations from the prescribed trajectory to be corrected in real-time. This feature,called active trajectory control, is not possible with serial metrology.

Fig. 50 a. Working principle of a stacked XY piezo stage (serial kinematics).Advantages: Modular, simple design. Disadvantages compared with parallelkinematics: More inertia, higher center of gravity, moving cables (can causefriction and hysteresis). Integrated parallel metrology and active trajectorycontrol (automatic off-axis error correction) are not possible.

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Parallel and

Serial Kinematics

There are two basic ways todesign multi-axis positioningsystems: Serial kinematics andparallel kinematics. Serial kine-matics are easier to design andbuild and can be operated withsimpler controllers. They do,however, have a number of dis-advantages compared to high-er-performance and more ele-gant parallel kinematics sys-tems. In a multi-axis serial kine-matics system, each actuator isassigned to exactly one degreeof freedom. If there are inte-grated position sensors, theyare also each assigned to onedrive and measure only themotion caused by that driveand in its direction of motion.All undesired motion (guidingerror) in the other five degreesof freedom are not seen andhence cannot be corrected inthe servo-loop, which leads tocumulative error.

In a parallel kinematics multi-axis system, all actuators actdirectly on the same movingplatform.

Only in this way can the sameresonant frequency anddynamic behavior be obtainedfor the X and Y axes. It is alsoeasy to implement parallelmetrology in parallel kinemat-ics systems. A parallel metrolo-gy sensor sees all motion in itsmeasurement direction, notjust that of one actuator, sorunout from all actuators canbe compensated in real-time(active trajectory control). Theresults are significantly lessdeviation from the ideal trajec-tory, better repeatability andflatness, as shown in Fig. 51.

Examples:

P-734, P-561, p. 2-68 ff. in the“Piezo Nanopositioners &Scanning Systems” section.

Fig. 51. Flatness (Z-axis) of a 6-axis nanopositioning system with active trajectorycontrol over a 100 x 100 µm scanning range. The moving portion of this parallelmetrology positioner is equipped with ultra-precise parallel metrology capacitivesensors in all six degrees of freedom. The sensors are continually measuring theactual position against the stationary external reference.

A digital controller compares the six coordinates of the actual position with therespective target positions. In addition to controlling the scanning motion in the X and Y directions, the controller also ensures that any deviations that occur inthe other four degrees of freedom are corrected in real-time.

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Motion Controllers



Piezo Actuators

Index



4-46

PMN Compared to PZT

Electrostrictive Actuators

(PMN)

Electrostrictive actuators oper-ate on a principle similar to thatof PZT actuators. The elec-trostrictive effect can beobserved in all dielectric mate-rials, even in liquids.

Electrostrictive actuators aremade of an unpolarized leadmagnesium niobate (PMN)ceramic material. PMN is aceramic exhibiting displace-ment proportional to thesquare of the applied voltageunder small-signal conditions.Under these conditions PMNunit cells are centro-symmetricat zero volts. An electrical fieldseparates the positively andnegatively charged ions,changing the dimensions of thecell and resulting in an expan-sion. Electrostrictive actuatorsmust be operated above theCurie temperature, which istypically very low when com-pared to PZT materials.

The quadratic relationshipbetween drive voltage and dis-placement means that PMNactuator are intrinsically non-linear, in contrast to PZT actua-tors. PMN actuators have anelectrical capacitance severaltimes as high as piezo actua-tors and hence require higherdrive currents for dynamicapplications. However, in a lim-ited temperature range, elec-trostrictive actuators exhibitless hysteresis (on the order of3 %) than piezo actuators. Anadditional advantage is theirgreater ability to withstandpulling forces.

PZT materials have greatertemperature stability than elec-trostrictive materials, especial-ly with temperature variationsof over 10 °C. As temperature increases,available travel is reduced; atlow temperatures where travel

is greatest hysteresis increases(see Fig. 53 b). PMN actuatorsare thus best for applicationswith little or no temperaturevariations of the ceramic, bethey caused by dynamic opera-tion or by environmental fac-tors.

PMN

PZT

V

L

Fig. 52. Comparison of PMN and PZT material: displacementas a function of field strength (generalized).

16

PMN

L

Fig. 53 a. Comparison of PMN and PZT material: displacementas a function of temperature.

Fig. 53 b. Comparison of PMN and PZT material: hysteresis as afunction of temperature.

PMN

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Summary

Piezoelectric actuators offer asolution to many positioningtasks that depend on highestaccuracy, speed and resolution.

Examples given in this tutorialindicate a selection of themany applications commontoday. The relentless push formore accuracy and speed—whether in the further miniatur-ization of microelectronics,production of optics and high-er-performance data storagedevices, precise positioning ofoptical fiber components fortelecommunications, or in thefabrication of micromech-

anisms—drives both the appli-cation and the further develop-ment of piezo technology. To use the advantages of piezopositioners to their full extent,it is important to carefully ana-lyze the system in which apiezo actuator is used as awhole. Close contact betweenuser and manufacturer is thebest recipe for success.

Piezoelectric actuators will inthe future partially replace, par-tially complement, convention-al drive technologies. They willwiden the realm of the possi-ble, and will usher in develop-

ments in areas like nanotech-nology which would beunthinkable with conventionaldrive technologies.







Motion Controllers



Piezo Actuators

Index







Motion Controllers



Piezo Actuators

Index



4-48

No pulling force without preload.

No lateral force or torque.

Ball tips or flexures to decouple lateral forces or bending forces.

Ball tips or flexures to decouple bending forces.

Bolting between plates is not recommended.

Adherence to the followingguidelines will help you obtainmaximum performance andlifetime from your piezo actu-ators: Do not use metal toolsfor actuator handling. Do notscratch the coating on the sidesurfaces. The following precau-tions are recommended duringhandling of piezoelectric actua-tors:

I. Piezoelectric stack actuatorswithout axial preload aresensitive to pulling forces. Apreload of up to 50% of theblocking force is generallyrecommended.

II. Piezoelectric stack actuatorsmay be stressed in the axialdirection only. The appliedforce must be centered verywell. Tilting and shearingforces, which can also be in-duced by parallelism errorsof the endplates, have to beavoided because they willdamage the actuator. Thiscan be ensured by the useof ball tips, flexible tips,adequate guiding mecha-nisms etc. An exception tothis requirement is made forthe PICA™-Shear actuators,because they operate in theshear direction.

III. Piezoelectric stack actuatorscan be mounted by gluingthem between even metalor ceramic surfaces by acold or hot curing epoxy,respectively. Ground sur-faces are preferred. Please,do not exceed the specifiedworking temperature rangeof the actuator during curing.

IV. The environment of all actu-ators should be as dry aspossible. PICMA® actuatorsare guarded against humid-ity by their ceramic coating.Other actuators must be pro-tected by other measures(hermetic sealing, dry airflow, etc).

The combination of long-term high electric DC fieldsand high relative humidityvalues should be avoidedwith all piezoelectric actua-tors.

V. It is important to shortcir-cuit the piezoelectric stackactuators during any hand-ling operation. Temperaturechanges and load changeswill induce charges on thestack electrodes whichmight result in high electricfields if the leads are notshorted: Should the stackbecome charged, rapid dis-charging—especially with-out a preload—might dam-age the stack. Use a resistorfor discharging.

VI. Prevent any contaminationof the piezo ceramic sur-faces with conductive orcorrosive substances. Iso-propanol is recommendedfor cleaning. Avoid acetoneand excessive ultrasoniccleaning at higher tempera-tures.

Mounting and Handling Guidelines

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Program Overview

� Piezoelectric Actuators

� Piezo Nanopositioning Systems and Scanners

� Active Optics / Tip-Tilt Platforms

� Capacitive Sensors

� Piezo Electronics: Amplifiers and Controllers

� Hexapods

� Micropositioners

� Positioning Systems for Fiber Optics, Photonicsand Telecommunications

� Motor Controllers

� Piezo Ceramic Linear Motors

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