WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --Piezo Tip/Tilt Systems
Design – Performance – Tuning

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --Contents
1

Overview

3

2

Design and Functional Principle

3

3

Condition on Delivery and Quality

44

Handling the Mirror

5

5Controlling Tip/Tilt Systems

5

5.1

Choosing the Matching Control Electronics

5

5.2

PIMikroMove: Easy Configuration and Startup

6

6

During Operation

6

6.1

Hysteresis

6

6.2

Resonant Frequencies

7

6.3

Step Response and Settling Time

7

6.4

Heat Generation During Continuous Operation

8

6.5

Position Drift9

6.6

Lifetime

97

OEM Engineering and Solutions

10

8

FEM Optimization

10

9

Simulation of the Overall System

1010Author

About PI

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

1011

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --1 Overview
Piezo tip/tilt systems from Physik Instrumente (PI) areversatile positioning systems ─ they are ideal for dynamic
operation in applications such as scanning, tracking, forsuppressing drift oscillation or dynamic image stabilizing.
Piezo tip/tilt systems and scanners offer greater accelerationand dynamic bandwidth than similar actuators such as forexample, voice coil or galvanometer scanners. Piezo tip/tiltsystems developed by PI are also found in applications forquasistatic positioning of optics with high demands on"pointing stability".
All piezo tip/tilt systems manufactured by PI are equippedwith flexure guides for friction-free motion and therefore
provide excellent guiding accuracy. Resolutions into thenanoradian range are possible and at the same time, highangle stability. Optical deflection angles of up to 70 mrad canbe achieved with very short settling time (milliseconds tomicroseconds).

2 Design and Functional Principle!

Note: Despite their massive and robust
appearance, PI piezo tip/tilt mirrors are
sensitive precision systems. The effects offorces and torques on the tip/tilt platform
are particularly critical during assembly. This
needs to be minimized or avoided at all
times. PI provides the corresponding
instructions for assembly and adjustment.

Fig. 1

Schematic diagram of a piezo tip/tilt mirror with a piezo
actuator (left) and differential drive (right). The pivot point of
the differential drive piezo tip/tilt system can be obtained
from the technical drawing (image: PI)

The design of the piezo tip/tilt systems with differential driveis based on two piezo actuators (for this, see Fig. 1, righthand graphic) that drives the platform in push/pull mode. For
this purpose, both actuators are operated electrically in a
bridge circuit supplied with a fixed voltage and controlled by avariable voltage. The differential design allows the highest
angular stability over a wide temperature range because thechanges in temperature only affect one linear offset shift ofthe platform. The use of strain gauge sensors makes both
high linearity and excellent repeatability possible.

PI piezo tip/tilt systems are offered in single- and multi-axis
versions. In addition, differential piezo tip/tilt systems areequipped with two piezo actuators per axis.
The motion platform for systems with one piezo actuatorsuch as for Fig. 1 (left-hand graphic), is guided by a flexure.
The flexure forms the center of rotation (pivot point) and at
the same time, preloads the piezo actuator. Simple design,
low costs, and small installation space are among theadvantages of this version. A differential piezo drive isrecommended for applications that require high angularstability over a wide temperature range.

Fig. 2

Motion directions of parallel kinematics (left) and a comparable
serial setup (right) (image: PI)

Multi-axis piezo tip/tilt systems are designed as parallelkinematic systems (Fig. 2). This design has great advantages
compared to serial systems. The motion platform is displaced
only around one fixed center of rotation.

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --Therefore, the higher system resonant frequency results inhigher dynamics. In addition, parallel-kinematic systems
achieve much better linearity than serial systems. Serial
systems work by switching two single-axis system successively– e.g., galvanometer scanners.

The standard version of the piezo tip/tilt systems provides thebest performance and at the same time, conservative systemutilization. The system works reliably within the standard
specifications and allows stable operation in the majority ofcustomer-specific applications.

PI offers standard designs with two and three axes that are
driven by parallel kinematics. Altogether, four piezo actuators
are driven differentially in the case of two-axis systems. They
are arranged in pairs around 90° and both of them move thesame platform at the same time (parallel kinematics), which isdisplaced around a fixed center of rotation. The basic setup ofa three-axis, parallel-kinematic piezo tip/tilt system is
illustrated in Fig. 3.

PI offers system tuning tailored specifically to the application
for particular applications such as for example, extremely
high dynamics or extremely stable positioning requirements.
This makes it possible to optimize the servo control
parameters specifically in order to achieve the best result for
the respective application.
Of course, PI can also make customer-specific changes to thedesign of the standard product to match the exact customer's
requirements on the installation space.
Each and every product is measured and qualified before
dispatch. The system is subsequently supplied with the"Performance Test Protocol" as a further seal of quality – see
Fig. 4.

Fig. 3

Schematic diagram of parallel kinematics using the example
of a three-axis piezo tip/tilt system ─ the tripod (image: PI)

The multi-axis design in "tripod" form is driven by three piezo
actuators arranged with gaps of 120° in between. The
advantage of driving with three independent piezo actuators
means that, in addition to tilting, the platform is also capableof liner motion, which means for example, that the controller
can make use of optical phase differences.

3 Condition on Delivery andQuality
Very high standards are set for the reliability and quality of all
products from PI. The ISO certification, which not only focuses
on a product but also customer expectations and satisfaction,
was achieved back in 1994 and is recertified regularly.

Fig. 4

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws“Performance Test Protocol” of an S-335.2SH piezo tip/tilt
mirror (image: PI)

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --4 Handling the Mirror!

ATTENTION: Never remove the mirror by"levering" or applying mechanical force
because forces can be transferred directly tothe piezo actuators, which will react very
sensitively. Chemical solvents should also not
be used because they can easily penetrate
the inside of the tip/tilt mirror and cause
damage.

Excessive force increases the risk of damage to the seemingly
robust piezo tip/tilt system particularly for mirror applications
or when removing the mirror. The mirror should be mounted
by the user according to the instructions in the user manual
for the respective system.
A 3-point template is recommended for applying theadhesive. The template indicates the position the adhesive on
the tip/tilt platform and restricts the quantity of the adhesive
to be applied. This prevents applying too much adhesive,
which could then penetrate the housing. In order to achieve
the best possible adhesive bonding, an epoxy resin-based
two-component adhesive should be chosen that has ahardening temperature of approx. 20 °C.
It is recommended to position the mirror on the platform
with the help of a centering aid (Fig. 5). The template and thecentering aid can be ordered at PI under the following link:
https://www.physikinstrumente.com/en/products/accessories/adapter-plates-mounting-brackets/s-330xx-mirrorcentering-aids-for-the-s-330-and-s-331-412418450/

Fig. 5

S-335.2SH piezo tip/tilt systems with 3-D printed centeringaid (blue) for applying a 1-inch mirror (image: PI)

The dynamic properties of the piezo tip/tilt system andtherefore the respective servo control parameters in thecontroller react very sensitively to changes in the moment ofinertia. Changes to the load and inertia conditions for thosesystems tuned specifically for the respective application by PI,
will then not be able to fulfil the required specifications andwould have to be tuned again for the new situation.

5 Controlling Tip/Tilt Systems
5.1

Choosing the Matching Control
Electronics

PI offers analog and digital electronics for controlling thepiezo tip/tilt systems. However, digital electronics(Fig. 6) are recommended for applications where demands on
the system performance vary.

Alternatively, PI can also mount the mirror as part of theorder.
If the mirror has to be removed, PI recommends heating themirror carefully with a hot-air blow dryer to soften theadhesive. It should then be possible to remove the mirror
easily.
If a larger mirror or a greater mass such as a beam splitter, ismounted on the system for dynamic applications, it may
result in a decrease in performance or the characteristics
could deviate from those specified by PI.

Fig. 6

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

E-727 digital controller (image: PI)

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --The servo control parameters can be adapted in the
PIMikroMove software by simply pressing a button. The
integrated ID chip in the piezo tip/tilt systems makes it
possible to replace the controller or even the piezo tip/tiltsystem quickly and easily. The individual parameters of thepiezo tip/tilt systems are read out of the controller
automatically and the individual tuning data is thentransferred.

In addition to tuning, PIMikroMove provides the option ofanalyzing the system for errors. Integrated software tools test
each individual function of the system.
In this way, a graph of the current progression can berecorded during displacement. If there any changes in thecurrent characteristic curve, it is possible to draw conclusions
on the state of the system.

In conjunction with the PIMikroMove software, the digitalelectronics offer a large range of functions and options fordisplaying the measured values for diagnostics and processcontrol.
As a matter of course, PI also provides the entire measuring
and control logic as Dynamic Link Library (DLL) for fast andeasy integration into complex OEM and systems for the end
customer. In addition, the LabVIEW integration provides anoptional laboratory and prototype platform during the
introductory phase.
The use of analog electronics is recommended for
applications where the dynamic requirements are high andthe necessary controller performance is less expensive. On
top of that, it is planned to avoid time-consuming adaptationof the system properties in the future.

5.2

PIMikroMove: Easy Configuration andStartup!

Note: To avoid damage, a sound knowledgeof the system is necessary for tuning thepiezo tip/tilt mirror. If required, PI will takecare of tuning the piezo tip/tilt mirror
according to the customer application.

6 During Operation
6.1

Hysteresis

In the case of open-loop systems, the displacement curves
show strong hysteresis that results from ferroelectric
polarization effects of the piezo ceramics. The "opening" ofthe voltage displacement curve reaches 10-15 % of thedisplacement angle ─ see Fig. 7.

PIMikroMove is an integral part of the extensive software
package that is included as standard in the scope of deliveryof every digital PI controller. The software ensures easy andintuitive startup of the entire system.
Once the system has set up, the full range of functions isavailable to the user. In addition to easy position
specification, selection of step size, and acceleration etc., it isalso possible to implement macros for continuous motion
sequences. So-called "controller macros“ are available thatcan be used just as they are, or adapted accordingly.
"Host macros", which contain code for motion sequences, canbe created in PIMikroMove. It is recommended to make useof the various high-level languages for complex trajectories.
PIMikroMove supports several common high-level languages
and graphical software such as C, C++, C#, Python, LabVIEW
as well as MATLAB and Simulink.
System optimization and tuning are additional components of
PIMikroMove. The P and I parts of the servo controller areavailable to the software to get the best possible
performance from the system components. This means thatthe system can be optimized for the specific application.

Fig. 7

Hysteresis of an S-335.2SH in a voltage range of -20 to 120 V(image: PI)

Position-controlled piezo tip/tilt systems from PI minimize
this effect. That means that the systems achieve highabsolute accuracy, linearity, and repeatability in thenanoradian and subnanoradian range.

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --6.2

Resonant Frequencies

One of the most important technical characteristics of highdynamics applications is the stiffness of the mechanical piezo
tip/tilt system. The resonant frequency is derived as afunction of the stiffness and serves to qualify the system. The
general rule of thumb is: The higher the resonant frequency,
the higher the maximum operating frequency that can beused for operating the system. Normally, the resonant
frequency of positioning applications is considerably lower. In
closed-loop operation, the maximum safe operating
frequency is also limited by the phase and amplitude
response of the system. The following also applies in thiscase: The higher the resonant frequency of the mechanics,
the higher the control bandwidth can be set. The resonant
frequency is directly dependent on the weights that are
mounted on the piezo tip/tilt system. The dynamic
performance is reduced by large weights to be moved.
Resonant frequency of an ideal spring-mass system:

1𝑘𝑇
𝑓0 = � � �
2𝜋 𝑚𝑒𝑒𝑒

𝑓𝑜 = resonant frequency [Hz]𝑘 𝑇 = spring stiffness [N/m]𝑚𝑒𝑒𝑒 = effective mass [kg]The above equation shows that in order to double theresonant frequency of a spring-mass system, either the
stiffness must be increased by a factor of 4 or the effective
mass reduced by 25 % of its original value. In the case of
extremely low resonant frequencies, it is only possible torealize quasistatic applications.

Fig. 8Resonant frequencies of the S-335.2SH piezo tip/tilt system
without load, ½-inch mirror and 1-inch mirror (image: PI)

6.3

Step Response and Settling Time

Fast response behavior is a characteristic feature of piezo
actuators. A rapid change of the operating voltage causes a
rapid change in the position of the piezo actuator andtherefore a change in the tip/tilt platform's position.
If the control voltage increases suddenly, a piezo actuator canreach its nominal displacement in approx. 1/3 of the resonant
frequency period, inasmuch as the voltage source is able tosupply sufficient power. In this case, there is a strong
overshoot of the target position.

The system bandwidth can even limit the sensor bandwidthand servo controller performance (digital / analog electronics,
filter and control type, bandwidth).
Piezo tip/tilt systems from PI are optimized for applicationspecific masses (for example, 1“ mirror).
In Fig. 8, the first resonant frequencies are shown when using
a ½-inch and a 1-inch mirror when compared to an unloaded
system.

Fig. 9Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

Tuning an S-335.2SH piezo tip/tilt system for the fastest
possible displacement. A 1“ mirror is mounted (image: PI)

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --Fig. 9 shows several step responses of an S-335.2SH piezo
system, based on the standard performance (as delivered,without tuning). The step response of the system can be
influenced by tuning the servo controller.
Changing the load, for example, by changing the size of themirror, also influences system performance. Fig. 10 shows
how a change of mass influences a 50 % step (17:5 mrad,
open loop) of a S-335-2SH piezo system.

Fig. 10

Fig. 11

Left-hand graph: Measurement of the repeatability of an
S-335.2SH. Right-hand graph: Histogram with standard deviation(image: PI)

6.4

Heat Generation During Continuous
Operation

Behavior of an S-335.2SH piezo tip/tilt system, open loop;
without load, with ½-inch and 1-inch mirror (image: PI)!

The positioning repeatability depends on the actual
displacement of the piezo tip/tilt system and the type of
sensor used. Basically, the repeatability is considerably higher
for shorter than longer travel ranges.
Strain gauge sensors re installed into the most piezo tip/tiltsystems. An SGS provides sufficient resolution and can beaccommodated in the system to save space. BY evaluating thestrain gauge sensors, which are attached directly to the piezo
actuators, the actual position is continuously synchronized tothe target position. Residual errors result from indirect
position measuring and the strain gauge sensor technology
itself. The piezo displacement makes it possible to determine
the position of the platform.
On request, the repeatability of the system can be measure
by PI. 100 measured points are recorded and the deviation
between the target and actual position is acquired as"position error". The Fig. 11 (left-hand graphic) shows themeasurement of an S-335.2SH piezo tip/tilt system. All
deviations are compiled into a histogram shown on the right.

Note: Position-controlled piezo tip/tilt mirror
have better temperature stability comparedto open-loop systems. The highest accuracy isreached when the operating temperature andcalibration temperature are identical. Piezo
tip/tilt mirrors from PI are calibrated at 22 °C
unless otherwise specified.

During long-term operation, it is possible that heat generation
is limited by the operating frequency. Because piezo actuators
behave like capacitive loads, their charge and discharge
currents increase with the operating frequency. In addition tothe operating frequency, thermal power loss in the tip/tilt
mirror depends essentially on the voltage amplitude of thedisplacement, because this is squared in the power loss.

𝑃≈𝜋2∙ tan 𝛿 ∙ 𝑓 ∙ 𝐶 ∙ 𝑈𝑝𝑝
4

P= power converted to heat [W]δ= dielectric loss factor
f= operating frequency [Hz]C= actuator capacitance [F]Upp= voltage (peak-peak) [V]Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --The thermal power loss of the piezo ceramics is approx. 8 to
12% of the electrical power input. Therefore, cooling may benecessary at higher frequencies and amplitudes.
The change in the temperature over time of an S-331.2SL
piezo tip/tilt system at 100 V control voltage and 2000 Hz(sine) operating frequency is shown in Fig. 12. The change oftemperature was measured at the ceramics.

6.6

Lifetime

The lifetime of a piezo ceramic is not limited by wear andtear. Tests have shown that PICMA® piezo actuators that haveundergone at least 100 billion cycles do not exhibit any
measureable wear under appropriate ambient conditions andcontinue to operate according to specifications.
In PICMA® piezo actuators, the piezo ceramic is covered
entirely by a ceramic insulation layer that protects theactuators from humidity and failure resulting from increased
leakage current. The monolithic piezoceramic block of a
PICMA® actuator is very reliable even under extreme ambientconditions and this extends the lifetime considerably
Slots on the sides of PICMA® actuators effectively prevent anexcessive increase of mechanical tensile stress in the passive
regions of the stack as well uncontrolled cracking that would
lead to electrical breakdowns and therefore damage to theactuator.
The meander-shaped design of the external contact strips
ensures stable electrical contact to all inner electrodes, evenunder extreme dynamic loads (Fig. 13).

Fig. 12

Heating up of an S-331.2SL piezo tip/tilt system at a control
voltage of 100 V and a frequency of 2000 Hz (image: PI)

6.5

Position Drift

Drift or creeping describes the change of displacement overtime with unchanged control voltage.
The desired target position is controlled continuously inclosed-loop system systems. The actual position is detectedby strain gauge sensors and the difference between thetarget and actual value is minimized. Nevertheless, minimal
position deviations can still occur when for example,
fluctuations in the temperature of the surroundings cause
expansion of the material in the overall system.
Drifting occurs more strongly in open-loop systems because
the signals from the strain gauge sensors are not acquired.
The actual and target positions are not compared. This meansthat the difference in measuring is not compensated and thisresults in drifting.

Fig. 13

PICMA® actuators with patented outer electrodes for up to 20 A
charging current (image: PI)

There is no general formula for calculating the lifetime ofpiezo ceramics because many of the parameters such as forexample, temperature, humidity, voltage, acceleration, pushand pull forces, preload, operating frequency, and insulating
material exert a nonlinear influence.
PI piezo ceramics are not only optimized for maximum
displacement, but also for long lifetime under practicaloperating conditions.

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --7 OEM Engineering and Solutions
Joint development of solutions unites. This is the intention ofmembers of the customer service staff at PI. This starts withthe preliminary informative discussion and and extends far
beyond delivery.
Because a large part of the OEM business is based on
customer-specific products, the developer's know-how andlongstanding experience is an important requirement forsuccess.
Extensive testing and production equipment allow PI to react
quickly to the development and production requirements ofhighly complex custom products and assemblies. All
development procedures and production processes, from theidea to the final product, are controlled via a comprehensive
management system.
All systems manufactured by PI undergo endurance testing,where various types of load, operating and control conditions
were taken into consideration.

8 FEM Optimization

Development engineers at PI use the latest FEM (Finite
Elements Method) analytical tools as well as CAD software forsimulating and developing new mechanical systems. This
ensures the functionality, precision, and performance before
a prototype is set up.
For example, flexures, which serve as guide for the platform,
are optimized in this way during development of the piezo
tip/tilt systems. FEM optimization maximizes the stiffness
perpendicular to the direction of motion and therefore
reduces undesired creeping.
Modal analysis during FEM optimization helps to reveal later
resonant frequencies and other dynamic systemcharacteristics. Fig. 14shows the result of an FEM simulationof platform displacement of an S-335.2SH piezo tip/tilt system
at a control voltage of 100 V.

9 Simulation of the Overall
SystemThe resonant frequencies revealed by the modal analysis
represent one of the parameters for a holistic simulation
model. In addition, the electrical capacities of piezo ceramics,
servo control parameters, and system damping are relevant
as input data for simulating the overall system.
Therefore, the simulation model represents a step towards
the digital twin of the tip/tilt mirror in conjunction with theelectronics unit that in turn, provides a virtual representationof the performance of the real product. Feasibility analyses ofcustomer requirements and an early and sound risk analysis
for the product can be done very quickly. Development
engineers at PI use the latest FEM (Finite Element Method)
analytical tools as well as CAD software for simulating anddeveloping new mechanical systems. This ensures thefunctionality, precision, and performance before a prototype
is set up.

10 Author
Armin Karle is development engineer in the development
department for piezo systems at Physik Instrumente (PI)GmbH & Co. KG in Karlsruhe, Germany.

Fig. 14 FEM simulation of platform tilting at a specified control
voltage using the example of the S-335.2SH (image: PI)

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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WHITEPAPER – Piezo Tip/Tilt Systems-- Armin Karle --About PI
Well known for the high quality of its products, PI (Physik
Instrumente) has been one of the leading players in the global
market for precision positioning technology for many years. PI
has been developing and manufacturing standard and OEM
products with piezo or motor drives for more than 40 years.
WP4012E Piezo Tip/Tilt Systems 10/2018.0 subject to change. © Physik Instrumente (PI) GmbH & Co. KG 2018

Continuous development of innovative drive concepts,
products, and system solutions and more than 200
technology patents distinguish the company history today.
PI develops, manufactures, and qualifies all core technology
itself: From piezo components, -actuators, and motors as wellas magnetic direct drives through air bearings, magnetic andflexure guides to nanometrological sensors, control
technology, and software. PI is therefore not dependent oncomponents available on the market to offer its customers
the most advanced solutions. The high vertical range ofmanufacturing allows complete control over processes andthis allows flexible reaction to market developments and new
requirements.
By acquiring the majority shares in ACS Motion Control, aworldwide leading developer and manufacturer of modular
motion controllers for multi-axis drive systems, PI can also
supply customized complete systems for industrial
applications that make the highest demand on precision anddynamics. In addition to four locations in Germany, the PI
Group is represented internationally by fifteen sales andservice subsidiaries.

Physik Instrumente (PI) GmbH & Co. KG, Auf der Roemerstrasse 1, 76228 Karlsruhe, Germany
Phone +49 721 4846-0, Fax +49 721 4846-1019, Email info@pi.ws, www.pi.ws

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