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Mixed Stepping / Scanning Mode Control of Stick-Slip
SEM-integrated Nano-robotic Systems
Raouia Oubellil, Alina Voda, Mokrane Boudaoud, Stéphane Régnier
To cite this version:
Raouia Oubellil, Alina Voda, Mokrane Boudaoud, Stéphane Régnier. Mixed Stepping / Scanning
Mode Control of Stick-Slip SEM-integrated Nano-robotic Systems. Sensors and Actuators A: Physical
, Elsevier, 2019, 285, pp.258-268. �10.1016/j.sna.2018.08.042�. �hal-03225760�
Page 1 of 15
Accepted Manuscript
Mixed Stepping / Scanning Mode Control of Stick-Slip SEM-integrated Nano-robotic
Systems
R. Oubellil
1,∗
,A.Voda
1
, M. Boudaoud
2
and S. R
´
egnier
2
1
GIPSA-lab, Control Systems department, ENSE3 bat B, BP 46, Domaine Universitaire,
38400 Saint Martin d’Heres, France
2
Sorbonne Universit´e, Institut des Syst`emes Intelligents et de Robotique, UMR 7222, ISIR, F-75005 Paris, France
Abstract
The ability to do dexterous automated and semi-automated tasks at the micro- and nano-meter scales inside a Scanning Electron
Microscope (SEM) is a critical issue for nanotechnologies. SEM-integrated nano-robotic systems with several Degrees Of Freedom
(DOF) and one or several end-effectors have therefore widely emerged in research laboratories and industry. The Piezoelectric Stick-
Slip (PSS) is one of the best actuation principle for SEM-integrated nano-robotic systems as it has two operating modes, namely a
coarse positioning mode with long travel range, and a fine positioning mode with a resolution of the order of the nanometer. The
main contribution of this paper is the design of a switch control strategy to deal efficiently and in a transparent way from the user’s
point of view, with the transition between the coarse and the fine operating modes of PSS actuators. The aim is to be able to perform
positioning tasks with a millimeter displacement range and a nanometer resolution without worrying about the mode of operation
of the actuator. The coarse mode and the fine mode are respectively controlled with a frequency/voltage proportional control and
a H
∞
control. The switch control is based on an internal model of the actuator. Experimental results show the effectiveness of the
new mixed coarse/fine mode control strategy to satisfy closed-loop stability and bumpless specifications at the switching time. For
the best knowledge of the authors, this result is the first demonstration of such a control capability for PSS actuators.
1. Introduction
SEM-integrated nano-robotic systems have widely emerged
in recent years to address the issue of automated and semi-
automated tasks for nanotechnologies. The SEM is particularly
interesting because it provides a visual feedback with nanome-
ter resolution and a depth of field better than that of light mi-
croscopes. Nano-robotics inside the SEM enables in-situ tasks
at the nanometer scale such as nano-manipulation [1, 2], nano-
assembly [3, 4] as well as electrical [5] and mechanical charac-
terization [6] of materials and biological samples at the small
scales. SEM integrated nano-robotic systems have to be able
to generate two motion modes, namely a coarse positioning
with a displacement range of several micrometers or millime-
ters to bring an end effector close to the micro/nano-object to
be manipulated, and a fine positioning with a resolution in the
nanometer range to locally characterize and/or manipulate the
object. According to the literature, such robots are generally
actuated by piezoelectric inertial actuators in the coarse and the
fine modes independently [3,7,5,4,1]. Particularly, the ba-
sic architecture of Piezoelectric Stick-Slip (PSS) type actuator
[3,7,5]is composed of a Piezoelectric Element (PE), a slider,
and a friction material between the PE and the slider. It operates
in scanning mode when there is no slip between the PE and the
✩
This work was not supported by any organization.
∗
Corresponding author
Email address: raouia.oubellil@gmail.com (R. Oubellil)
slider, and in stepping mode when several sequences of stick
and slip phases occur. In scanning mode, the PSS actuator can
perform a fine positioning with a nanometer resolution but the
displacement range is limited by the maximal deformation of
the PE (∼ few micrometers). In stepping mode, a coarse posi-
tioning with a millimeter displacement range can be achieved,
but with a poor resolution. In this mode, the input voltage is
usually a sawtooth signal.
The state of art has shown that PSS actuators have a real
potential for nano-robotics. Design issues have been deeply in-
vestigated [8]. However, several control issues related to the
nonlinear behavior and the hybrid operating mode of these ac-
tuators still require studies in order to satisfy the demanding
performance in nanotechnologies. Existing control strategies
can be classified into control in scanning mode and control in
stepping mode. The objective of the control in scanning mode
is to reduce the hysteresis effect and to damp the vibrations [9].
Hysteresis may induce open-loop positioning errors as high as
10%-15% of the displacement range [10]. Furthermore, signif-
icant oscillations of a hundred nanometers at the fundamental
resonance frequency can be observed in the slider displacement
[11]. These mechanical vibrations present a major problem in
nano-robotics. For instance, for in situ stiffness measurements
on membranes of 200 nm thickness [12], an oscillation of 100
nm of the end-effector can produce the membrane destruction.
Open-loop strategies can be used for hysteresis compensation
[13, 14] [15, 16, 17] and vibration damping [18, 19]. However,
Preprint submitted to Sensors and Actuators September 28, 2018
Page 2 of 15
Accepted Manuscript
in practice, it is difficult to obtain precise compensators, and
hence to guarantee positioning accuracy. Also, these methods
are not robust against hysteresis variations and shifts in the reso-
nance frequency. For these reasons, numerous closed-loop con-
trol strategies have been studied in the literature, including pole-
placement [20], PID control [21], H
∞
control [22, 23] [24], slid-
ing mode control [25], LQG control [26], and so on. On the
other hand, few techniques exist in the literature to control PSS
actuators in stepping modes. A frequency proportional con-
troller is proposed in [27] where the frequency of the sawtooth
control voltage is chosen based on the tracking error. A cascade
controller is designed via dehybridization in [28] using a hybrid
model of the actuator. In the inner-loop, a hybrid controller is
designed to impose a time-scale separation between continuous
and discrete states. In the outer-loop, a continuous proportional
derivative controller is developed using an approximated con-
tinuous model of the inner-loop in order to satisfy closed-loop
stability. A frequency/amplitude proportional controller is pre-
sented in [29] to control the amplitude and the frequency of
the sawtooth control signal separately. The proportional gains
are determined in the same way as for classical proportional
controllers. None of the existing controllers has dealt with the
stepping/scanning switch problem of PSS actuators. In fact,
this switch generally leads to closed-loop instability and signif-
icant vibrations at switching time, which compromises the use
of these actuators for fully-automated tasks inside a SEM.
This paper focuses on a new control strategy able to drive
a PSS actuator in closed loop in both stepping and scanning
modes while guaranteeing an efficient bumpless switch between
these two operating modes. The experimental setup used to val-
idate the proposed strategy is a nano-robotic platform made up
of a Cartesian structure actuated by PSS actuators (Fig. 1). In
our approach, these actuators are initially controlled separately
in scanning mode and in stepping mode. The hybrid controller
involves a H
∞
scanning mode controller, a frequency/ ampli-
tude ( f /u) proportional stepping mode controller, and a switch-
ing strategy using an internal model of the actuator. Experimen-
tal results demonstrate the effectiveness of the new hybrid con-
troller and its ability to achieve millimeter range motion with
a resolution of the order of the nanometer. The closed-loop
system enables automated coarse/fine positioning which opens
new perspectives on the use of PSS actuators in nano-robotics,
particularly to perform precise automated tasks inside a SEM.
The paper is structured as follows. In Section 2, the exper-
imental setup used in this study is described. Sections 3 and
4 deal respectively with the scanning control and the stepping
control strategies. In section 5, the new mixed stepping/scanning
mode controller is presented. Section 6 concludes the paper.
2. Experimental setup
The experimental setup of the laboratory enables SEM ma-
nipulation and characterization tasks [12]. It consists of a SEM,
a multi-Degrees Of Freedom (DOF) nano-robotic system in-
cluding the 3 axes serial nanorobot that is studied in this paper
Z axis
X axis
Y axis
x
y
z
Figure 1: The 3-DOF Cartesian nano-robotic structure. It is composed of three
axes X, Y and Z. Each axis is actuated by a piezoelectric stick slip actuator
(SmarAct SLC-1720-S-HV).
(Fig. 1), a processor board and a human-robot interface. The
processor board features a QorlQ P5020 dual-core processor
running at 2 GHz. The serial nano-robotic system is actuated by
PSS actuators of the same reference (SLC-1720-S-HV). Each
actuator integrates an optical encoder sensor with a resolution
of 20 μm. Digital interpolators with an interpolation factor of
4096 are used to obtain a measurement resolution of 5 nm.
The allowable input voltage for each PSS actuator is 0-100
V. In scanning mode, the maximum displacement of the actu-
ators is around 2 μm, whereas it is around 12 mm in stepping
mode. The hypotheses of the study are that the PE is attached to
the base of the actuator, there is a friction material without lu-
bricant between the PE and the slider and each axis (i.e. slider +
the supported robot axis) is guided by a linear guideway, which
allows only a translational motion [11].
3. Robust control in scanning mode
The scanning mode controller has to deal with hysteresis
and undamped resonant modes. The standard H
∞
control strat-
egy is designed for X, Y, and Z axes of the Cartesian structure
based on the models presented in the work [30].
The desired closed-loop multi-criteria performance is three-
fold: (i) A closed-loop response time of few milliseconds only
to deal with the need to perform fast positioning tasks in nano-
robotics. To do so, the closed-loop bandwidth must be very
close to the fundamental open-loop resonance frequency. (ii) A
high resolution positioning with a static error of few nanometers
only. This performance is fundamental in several micro/nano-
robotic tasks such as nano-assembly and nanomaterial charac-
terization. (iii) A closed-loop stability robustness against the
hysteresis and the uncertain measurement time delay varying in
a defined interval.
2
Page 3 of 15
Accepted Manuscript
Piezo stick-slips
+ hysteresis
Static hysteresis Linear dynamics
Vx (t)
V
y (t)
V
z (t)
Xs(t)
Y
s(t)
Z
s(t)
Vx (t)
V
y (t)
V
z (t)
Xs(t)
Y
s(t)
Z
s(t)
G(s)
H
Optical encoder
sensors
(a)
(b)
Optical encoder
sensors
Figure 2: (a) Block diagram of the open-loop input/output transfers of X (resp.
Y, Z) axis in scanning mode. (b) Using the Hammerstein model, a PSS ac-
tuator in scanning mode is equivalent to a static hysteresis followed by linear
presliding dynamics.
3.1. Scanning mode dynamic modeling
The block diagram of Fig. 2(a) describes the open-loop sys-
tem, where V
x
(resp. V
y
, V
z
) is the input voltage and X
s
(t) (resp.
Y
s
(t), Z
s
(t)) is the slider displacement in X (resp. Y, Z) axis.
Each input/output transfer includes a hysteresis and a pres-
liding dynamic between the PE and the slider. The hysteresis
is the nonlinear relationship between the input voltage and the
slider displacement. The Hammerstein model is used to de-
scribe the nonlinear dynamic in scanning mode as a static hys-
teresis H followed by a linear dynamic model G(s)asshown
120
80
40
0
-40
X axis displacement
(nm)
Time (ms)
024
68
Experimental data
Simulation data
Experimental data
Simulation data
X axis PSD
( )
μm
2
/Hz
Frequency (kHz)
10
0
10
-5
10
-10
0 5 10 15 20 25
Experimental data
Simulation data
Y axis displacement (nm)
Time (ms)
120
80
40
0
-40
02468
Y axis PSD
( )
μm
2
/Hz
Frequency (kHz)
10
0
10
-4
10
-8
10
-12
0 5 10 15 20 25
Experimental data
Simulation data
Experimental data
Simulation data
Z axis displacement (nm)
200
100
0
-100
Time (ms)
0246
8
Z axis PSD
( )
μm
2
/Hz
Experimental data
Simulation data
10
0
10
-4
10
-8
10
-12
Frequency (kHz)
0 5 10 15 20 25
(a) (b)
(c) (d)
(e) (f)
Figure 3: Experimental and identified linear presliding dynamics: (a) PRBS
response of X axis, (b) Power Spectral Density (PSD) of X axis response , (c)
PRBS response of Y axis, (d) PSD of Y axis response, (e) PRBS response of Z
axis, (f) PSD of Z axis response [30].
in Fig. 2(b) [31]. This approximation is valid because the hys-
teresis does not affect the dynamic parameters such as the reso-
nance frequencies and the damping.
3.1.1. Linear presliding dynamic modeling
The presliding dynamics are identified for each actuator us-
ing Pseudo-Random Binary Sequence (PRBS) signals, and mod-
eled considering a linear parametric (an autoregressive-moving
average with exogenous terms (ARMAX)) model. The model
parameters are identified from the experimental data using the
Matlab Identification ToolboxTM.
Fig. 3 shows experimental data and simulation data of the
PRBS responses of X (resp. Y, Z) axis. Fig. 3(b) (resp. Fig. 3(d),
Fig. 3(f))) shows that the PSS actuator in X (resp. Y, Z) axis has
three resonance frequencies at 2061 Hz, 3652 Hz, and 6761 Hz
(resp. 1684 Hz and 2870 Hz and 4397 Hz, 5819 Hz and 6760
Hz and 9613 Hz).
For an easy readability of the paper, in the sequel, the block
diagrams will be presented for X axis only. Those of Y and Z
axes can be obtained by replacing X by Y and Z, respectively.
3.1.2. MPI model of hysteresis
The modified Prandtl Ishlinskii (MPI) model is chosen be-
cause it is suitable for asymmetric hysteresis.
Unlike classical Prandtl Ishlinskii (PI) model which is com-
posed of only backlash operators, the MPI model uses another
type of operators, namely one-sided dead-zones, to catch the
asymmetry [32]. This model is a superposition of weighted
backlash operators followed by a superposition of dead-zone
operators, where each backlash (resp. dead-zone) is character-
ized by a threshold r
X
Si
(resp. r
X
Hi
) and a weighting coefficient
w
X
Hi
(resp. w
X
Si
) as shown in Fig .4.
Backlash Dead zone
Vx(t)
Gain Gain
xs (t)
-rXH1
rXH1
wXH1
-rXH2
rXH2
wXH2
-rXHn
rXHn
wXHn
-rXs1
rXs1
-rXs2
rXs2
-rXsm
rXsm
wXs1
wXs2
wXsm
Figure 4: Block diagram of the MPI model.
To identify the MPI model parameters, sinusoidal voltage
signals of different amplitudes and 50 Hz frequency are ap-
plied to the PSS actuators. The frequency is chosen so that
the displacement is performed only in scanning mode. A num-
ber n = 16 of elementary backlashes and m = 16 of elemen-
tary dead-zone operators are defined. The thresholds have been
initialized, and the weighting coefficients have been thereafter
3
Page 4 of 15
Accepted Manuscript
Experimental data
Simulation data
X axis displacement (nm)
Input voltage (V)
0204060801
00
0
500
1000
1500
2000
I
nput voltage (V)
010203040
0
200
400
600
700
Y axis displacement (nm)
I
nput voltage (V)
020406080100
0
500
1000
1500
2
000
Input voltage (V)
0102030
40
0
200
40
0
600
Z
ax
i
s d
i
splacement
(
nm
)
Input voltage (V)
020406080
100
0
500
1000
1500
2000
Z axis displacement (nm)
Input voltage (V)
0102030
4
0
0
200
400
600
800
(a) (b)
(c) (d)
(e) (f)
Y ax
i
s d
i
splacement
(
nm
)
Experimental data
Simulation data
Experimental data
Simulation data
Experimental data
Simulation data
Experimental data
Simulation data
Experimental data
Simulation data
X axis displacement (nm)
Figure 5: Experimental and identified MPI hysteresis. X axis for input signals
of amplitudes: (a) 100 V, (b) 50 V. Y axis for input signals of amplitudes: (c)
100 V, (d) 50 V. Z axis for input signals of amplitudes: (e) 100 V, (f) 50 V [30].
identified using the Quadratic Programming Algorithm of the
Matlab Optimization ToolboxTM.
Fig. 5 shows a good agreement between experimental and
simulated hysteresis curves of the X, Y and Z axes, despite the
small numbers of m and n.
3.1.3. Multi-linear approximation of hysteresis
The Multi-linear approximation of hysteresis is very suit-
able for the control design because it leads to a model with very
few parameters [33].Inthe[V, X] plane, the hysteresis curve is
X axis displacement (μm)
Experimental hysteresis data
Affine approximation
2
1.5
1
0.5
0
Input voltage (V)
aMx=0.0382 μm/V
a
mx=0.0124 μm/V
0 20 40 60 80 100
Figure 6: Multilinear approximation of hysteresis, and parameters estimation
on X axis [30].
+
+
x (t)
s
v
x
(t)
dead-zone
b0x
a0x
a0x
Gnx(s)
Gx(s)
Figure 7: Block diagram of the PSS actuator with the multilinear approximation
of hysteresis.
divided into several piecewise affine functions [34]. Fig. 6 il-
lustrates this approximation using straight lines, where a
Mx
and
a
mx
are the maximal and the minimal hysteresis slopes, respec-
tively. Each hysteresis slope can be used for the control design.
The mean slope a
0x
= 0.0253 μm//V is chosen to repre-
sent the static gain of the nominal model G
nx
of the actuator as
shown in Fig .7. As such, G
nx
is the model whose frequency re-
sponse is shown in Fig. 3 (b) but with a static gain equal to a
0x
.
In Fig .7, the ratio of b
0x
on a
0x
is an input disturbance [35].
The H
∞
control strategy, developed in the following section, is
based on this model.
3.2. Scanning mode control
The scanning mode controller has to satisfy the following
closed-loop specifications:
maximal closed loop response time lower than 5 ms,
vibrations damping with no overshoot,
maximal static error lower than 2%.
These control specifications are introduced through the fol-
lowing weighting functions:
W
1x
to satisfy the tracking performances in terms of fast
response time and low tracking error.
W
2x
to keep the control voltage lower than 100 V.
W
dx
to reduce the effect of the input disturbance
b
0
a
0
.
W
tx
to reject the measurement noise n(t).
3.2.1. H
∞
principle
The H
∞
optimization problem can be illustrated using the
block diagram of Fig. 8, where P(s) is the generalized plant
model (i.e. the nominal model augmented by the weighting
functions), K(s)istheH
∞
controller, i are the exogenous inputs
(e.g. reference signals, disturbances, noises,...etc), o are the
exogenous outputs (e.g. errors or signals used in the optimiza-
tion), are the available measurements, and u are the control
signals.
4
![Figure 5: Experimental and identified MPI hysteresis. X axis for input signals of amplitudes: (a) 100 V, (b) 50 V. Y axis for input signals of amplitudes: (c) 100 V, (d) 50 V. Z axis for input signals of amplitudes: (e) 100 V, (f) 50 V [30].](/figures/figure-5-experimental-and-identified-mpi-hysteresis-x-axis-bnfuskuv.webp)