WHITE PAPER – Performance of Stepper Motor Axes

– Joachim Oberfell, Birgit Schulze –Performance of Stepper Motor Axes
Optimization of Precision, Stability, and Repeatability

220,00200,00180,00160,00

Positionn [nm]140,00120,00100,00
80,00
60,00
40,00
20,00
0,00
-20,00

0

5

10

15

20

25

30

35

40

45

50

Time [sec]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

Page 1 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --1 Drive Technology Basics
Irrespective of the business sector or the market, a production process that is not based on moving components fromone position to the other is inconceivable.
Positioning tasks of this type are increasingly being taken overby machines and automated procedures ensure safety andreproducibility. Reliable drives with the corresponding lifetime are essential for this purpose. At the same time, thedemand on positioning precision in the industrial environment is also increasing.
On the following pages, it will be shown how positioning
systems with a stepper motor drive can be used in precision
positioning, and also what special properties they have.
Rotating electric motors are a typical and widespread solution
for drive technology in the industrial sector. Stepper motors
are usually preferred because they are considered to beparticularly robust and have a long lifetime. The have a hightorque even at low speed = velocity. They are also attractively
priced and can be operated by affordable controllers. Stepper
motors heat up during (continuous) operation and this must
be taken into account when designing a system.
Stepper motors take discrete positions within one revolution.
Because these steps have a constant distance, a position may
be commanded using the number of steps without the needfor a position sensor. Normally, there are 200 to 500 full steps
in each revolution. The actual achievable step size is determined by the stepper motor control, which, depending on theversion, electronically interpolates up to several thousand
microsteps between the full steps.
When holding a position, stepper motors are very stable,
particular the full steps. For this purpose, current must becontinually applied to stepper motors without a self-locking
gearhead.
PI uses smooth-running 2-phase stepper motors for the positioning axes in high-precision mechanics. A mechanicaldamper on the motor shaft, which also works as handwheel,
supports smooth running. A combination of suitable linear
measuring systems and high-resolution controllers increases
the positioning repeatability.
Fig. 1

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

Examples of PI precision axes with stepper motor: L-509 linear
axis (former PLS-85), L-511 linear axis (former LS-110), L-611 rotation stages (former PRS-110), L-310 Z-axis stage (former ES-100),
MCS XY stage (from above)

Page 2 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --2 Precision Positioning into the
Nanometer Range
A stepper motor with 200 full steps per revolution rotates at
an angle of 1.8° for each step. This results in a feed of 10 µm
in conjunction with a drive screw with a pitch of 1 mm. The
position resolution that could be theoretically achieved is
calculated (without further mechanical gear reduction) fromthe number of microsteps in each full step, which the motor
controller interpolates. A controller, with for example,
256 microsteps, achieves a design position resolution of
39 nm, which corresponds to 625 nm at 16 microsteps. The
steps that are commanded in the mechatronic system andcan be cleanly executed are limited to whole number multiples of this calculated resolution.

Fig. 2

Systems with these types of high-resolution stepper motor
controllers are therefore theoretically able to achieve position
resolutions into the nanometer range. This allows actual
measured and typical step sizes in the range of a few nanometers, which are only limited by the mechanical characteristics of the positioning axis. Due to the high design resolution, virtually any step sizes are possible. Fig. 3 and 4 areexamples of 100 nm and 25 nm steps of an L-509 axis with 1
mm spindle pitch.

Fig. 3100-nm steps of an L-509 linear stage with 2-phase stepper
motor, and without position control

Fig. 425-nm steps of an L-509 linear stage with 2-phase stepper
motor, and without position control

Steps of an L-511 linear stage with 2-mm drive screw, which iscontrolled by a motor controller with 16 microsteps per full step. 3µm steps (left), 0.6-µm steps (right)

Stepper motor controllers with more microsteps between thefull steps such as for example, the SMC Hydra (3000 microsteps), achieve a corresponding finer division of the motor
rotation angle. They allow virtually stepless position commanding, even in small and very small steps. This results inparticularly smooth-running motors, a very high position
resolution, uniform feed, and a higher dynamic velocity andacceleration range. The efficiency of these controllers is very
high, which suppresses heating up of the motors.

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

Page 3 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --3 Optimizing the Repeatability
with Position Control
A stepper motor executes uniform steps reliably with highprecision repeatability. The repeatability of a position that has
been reached once in an overall mechatronic system also
depends on the mechanical components and their interaction: The coupling and possibly the gearhead, drive screw,
drive screw nut, and the guidings used, determine the mechanical play. These mechanical effects of the construction
can never be completely eradicated.

Fig. 735-nm steps of an L-511 linear stage with 2-phase stepper
motor, and with position control

Fig. 820-nm steps of an L-511 linear stage with 2-phase stepper
motor, and with position control

Fig. 910-nm steps of an L-511 linear stage with 2-phasen stepper
motor, with position control. The 10-nm steps can still be differentiated, but are no longer executed cleanly

The accuracy, with which a position is reached each time, canbe improved by additional position feedback and evaluationin the controller. A direct-measuring linear or angle measuring system in the desired resolution effectively suppresses themechanical backlash/play. At the same time, the linearity of ameasuring system is normally higher than that of the motor
so even here, there is room for improvement.
Fig. 5 to 9 show the step sizes of an L-511 axis with 2-mm
spindle pitch, recorded during control. In this case, step sizes
up to 20 nm are easily verifiable.

Fig. 5

Fig. 6100-nm steps of an L-511 linear stage with 2-phase stepper
motor, and with position control (10 kHz sample frequency, unfiltered)

Detail view of Fig. 5 (zoom)

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

Page 4 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --3.1

Stability and Resolution in Control

Position-controlled stepper motor axes are distinguished by
an excellent position stability. Why is that the case?
Classical (DC) servo systems exhibit typical controller oscillation at amplitudes within the range of the resolution. Depending on the servo parameters, they can reach multiples of
the resolution and even lead to the total instability of thesystem. These effects do not occur with stepper motors.
Initially a stepper motor does not need control for position
stability. As soon as current is applied to the motor, it builds
up a moment while it is at a standstill. In contrast to (DC)servo systems, it has an intrinsic velocity servo control ("velocity feedforward"). These are the ideal requirements forexcellent stability. Common stepper motor controllers, withfor example, 256 microsteps per full step, allow smooth control of discrete step sizes. The commandable positions arelimited to whole number multiples of the theoretical resolution. Any step sizes within a range of a few tens of nanometers are however, not possible, and a disparity between the
motor and the encoder resolution leads to a quantization of
the achievable positions.

Fig. 101-mm steps, executed by an L-511 with position control(velocity 15 mm/s; acceleration 200 mm/s2)

Fig. 11
The enlarged view from fig. 10 shows the very low oscillationof less than 10 µm

Stepper motor controllers with more microsteps allow virtually stepless position commanding, even in small and very small
steps. The maximum accuracy is achieved when the position
signals are transmitted as analog sine-cosine signals with
1 Vpp and then digitized in the controller with a high resolution. The position resolution of such a positioning system isonly limited by the sensor.

3.2

Settling Behavior at the Position

The step-and-settle of an axis decisively affects the process
execution times. Initially, the control algorithms in the controller influence the step-and-settle at the target position.
SMC controllers suppress high frequencies and still allow
dynamic positioning with only minimal overshoot. The axis
therefore does not generate any oscillation that in return
could be registered by the overall system.

Fig. 12Further enlargements: It is clear to see that only one single
oscillation occurs. The target position was reached within a few
tenths of a second within a window of less than 20 nm

In order to achieve the shortest possible settling times, theoperating parameters must be optimized according to thespecifications of the application. The mass of the payload, theresulting moments, and the orientation of the motion axis
must definitely be taken into account. Further measures are
not necessary; the system is stable, and optimized dynamically.

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

Page 5 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --4 Constant Velocity at Low Velocity
Velocity is a decisive parameter for selecting a positioning
system. Often, the fastest possible motion and positioning are
the most important factors. However, some applications
require particularly slow and even feed motion. Particularly
the velocity constancy presents a challenge.
The required velocities can range from a few 100 µm/s toconsiderably less than 100 nm/s. This corresponds to a feedof a few millimeters per day. For optimum and even motion, a
positioning system is recommended with a high-resolution
measuring system and with position resolutions of around ananometer.

Fig. 15
Velocity constancy at 50 nm/s, measured using an L-511 withposition control

Fig. 16

Enlarged view of the measurement in fig. 15

Fig. 13
Velocity constancy at 1 µm/s, measured using an L-511 withposition control

Fig. 14
The measurement from fig. 13 in an enlarged view. The periodic position deviation shown in the range of only a few nanometers
can be attributed to the interferometerPhysik 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

Page 6 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --Background: How does the number of microsteps influence the positioning characteristics of an axis?
Velocity constancy
With only a few microsteps per full step, each step is particularly
noticeable at very slow velocities. This is illustrated initially in thepath-time diagram, where steps are clearly visible when suitably
enlarged (fig. 17 and 18).

Operating at 3000 microsteps per full step, the path-time
diagram shows very smooth almost perfect straighten (fig. 19
and 20) and therefore a considerably improved velocity constancy.

If measuring is repeated with position control, almost perfect straightness is visible in the path-time diagram. Position
deviation can be reduced to less than 100 nm by using theencoder (fig. 21 and 22)!

L-511 linear axis and C-663.11 Mercury Step motion controller(16 microsteps per full step). Velocity 5 µm/s

L-511 linear axis and SMC Hydra motion controller (3000 microsteps
per full step). Velocity 5 µm/s

L-511 linear axis with measuring system (linear encoder) and SMC Hydramotion controller (3000 microsteps per full step). Velocity 5 µm/s

Fig. 17 Without position control (open-loop)

Fig. 19 Without position control (open-loop)

Fig. 21 With position control (closed-loop)

Fig. 18 Detailed view of Fig. 17 shows a distinct step

Fig. 20 Detailed view of Fig. 19

Fig. 22 Detailed view of Fig. 21

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

Page 7 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --Background: How does the number of microsteps influence the positioning characteristics of an axis? (cont.)
Position deviation and frequency behavior
If an axis is operated by a controller with fewer microsteps per fullstep, a position deviation around 1 µm amplitude is shown (fig. 23).
Residual oscillation of the mechanics results in higher frequencies
and therefore increased resonance (fig. 24).

A controller with more microsteps per full step reduces boththe absolute position deviation and the frequency spectrum
considerably (fig. 25 and 26).

With the higher microstepping ratio, resonance now only occurs
with 100 nanometer amplitude, a reduction to less than 10 % (fig.
27 and 28).

L-511 linear axis and C-663.11 Mercury Step motion controller (16microsteps per full step). Velocity 5 µm/s

L-511 linear axis and SMC Hydra motion controller (3000 microsteps
per full step). Velocity 5 µm/s

L-511 linear axis with measuring system (linear encoder) and SMC Hydramotion controller (3000 microsteps per full step). Velocity 5 µm/s

Fig. 23 Position deviation

Fig. 25 Position deviation

Fig. 27 Position deviation

Fig. 24 Frequency spectrum

Fig. 26 Frequency spectrum

Fig. 28 Frequency spectrum

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

Page 8 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --5 Dynamic Position Correction(Mapping)
Optimization of the overall accuracy of a positioning axis canbe achieved by dynamic position correction. In particularly
with rotary axes, it is possible to considerably improve theabsolute accuracy, usually by a factor of 10.
For this purpose, the deviation from the target position at apredefined step size is initially determined with the help of areference measuring system. A system with an accuracy of±0.2 arcsec is available for this purpose at PI miCos. The
measured deviations are stored in the controller (SMC Hydra)
as a correction table.

Fig. 30
The measured values from fig. 29 were stored in the controller(SMC Hydra) and used for dynamic position correction. The symmetrical behavior independent of the direction of rotation is clearly visible. It was possible to considerable reduce the position deviationand is maximum ±0.0003°

Dynamic correction then takes place during operation because the values are already being used in the profile generator for calculation of the motion profile. That means all absolute errors are actually corrected during motion.

Fig. 31
The bidirectional repeatability is considerably and permanently improved by the stored error correction (mapping). The measurement shows several repetitions in steps of 10° in both the positive and negative direction of rotation

Fig. 29
The absolute accuracy of a PRS-110 (now L-611) rotation stage
with stepper motor and angle-measuring system. The deviationfrom the target position is determined in steps of 1°. The angular error can be up to ±0.004°

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

Page 9 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --6 Measurement Set-Up
6.1

6.2

Ambient conditions, and resources

All measurements were performed in a measurement laboratory under standard laboratory conditions, i.e., clean surroundings without cleanroom classification, room temperature 22°C ±1°C, air humidity 43% ±3%. The measurement setup is on a table isolated from vibration without further provision for isolation from thermal, acoustic or other external
influences.

Positioning Systems and Motion Controllers

Measuring was performed on standard linear and rotation
positioning systems, partly with additionally integrated measuring systems. Stages from series production were used.
The following positioning systems were tested:
L-511 (formerly LS-110)
L-509 (formerly PLS-85)

Measuring device, linear: Renishaw XL-80 interferometer

L-611 (formerly PRS-110)

Measuring device, rotational: Heidenhain RON-905

The motor controllers or motion controllers are also from the
PI portfolio.

Height of the reference mirror above the motion platform:
25 mm

Fig. 32
Noise measurements from the SMC Hydra controller. Axis at
rest, energized and controlled (sample frequency 10 kHz, unfiltered). The noise level is at approximately 3 nm (peak-peak), which
can be attributed to the interferometer

Basically, the ambient conditions influence the achievable
precision during positioning. A fluctuation of the ambient
temperature of only 0.01 °C already has an effect of around
10 nm on the thermal expansion of a stage made of aluminum. Stabilization of the surroundings is therefore a basic
requirement for precision and the repeatability of the results.
If required, ultraprecision axes with special material pairing
can be used, for example, on a granite base.

Fig. 33
SMC Hydra with integrated DeltaStar Eco encoder interface
module. 3000 microsteps per full step, evaluation from analog position signals (sin/cos, 1 Vpp)

Fig. 34
C-663.11 Mercury Step; 16 microsteps per full step, without
position control

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

Page 10 of 11

WHITE PAPER – Performance of Stepper Motor Axes-- Joachim Oberfell, Birgit Schulze --Authors

Joachim Oberfell has been working for the former miCos Gmbh, now
PI miCos GmbH, for more than 20 years

About PI

He is a specialist for complex positioning tasks and has frequently proved his particular talent for optimizing positioning
systems and motion controllers. A sympathetic ear for customer requirements and his profound knowledge on motion
control merge to produce the ideal solution for the respective
application. Of course, it goes without saying that the precise
knowledge of the operating conditions is an important requirement.

Over the past four decades, PI (Physik Instrumente) with
headquarters in Karlsruhe, Germany, has become the leading
manufacturer of positioning systems with accuracies in thenanometer range. The privately managed company is represented at four locations in Germany and internationally byfifteen sales and service subsidiaries. More than 850 highly
qualified employees all over the world enable the PI Group to
fulfill virtually any requirement in the field of innovative
precision positioning technology. All key technologies aredeveloped in-house. This allows the company to control every
step of the process, from design to shipment: The precision
mechanics and electronics as well as position sensors.

Joachim Oberfell attaches great importance to understanding
the way a motor controller works in order to exploit all possibilities that a positioning system has to offer, whether it be ahigh-precision application in basic research such as coordination of several axes in Beamline experiments, or an ideal
solution in the automation of production systems, whereindustry controllers with robust positioning axes are transformed to high-tech applications with future potential.

The required piezoceramic elements are manufactured by
PI Ceramic, our subsidiary in Lederhose, Germany, one of the
global leaders for piezo actuator and sensor products.
PI miCos GmbH in Eschbach near Freiburg, Germany, specializes in positioning systems for ultrahigh vacuum applications
and parallel-kinematic positioning systems with six degrees of
freedom as well as custom-made designs.

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

Page 11 of 11

WP4004 Performance of Stepper Motor Axes 06/2016.0 Subject to changes. © Physik Instrumen-

Birgit Schulze is product manager at Physik Instrumente (PI)