This paper introduces an improved indirect-driven self-sensing actuation circuit designed for effective vibration control of piezoelectrically-actuated flexible structures within mechatronic systems. The modified circuit functions as a high-pass filter, enhancing self-sensing performance and significantly reducing vibrations at critical resonant frequencies, achieving up to 75% improvement in suppression compared to traditional methods. The approach is validated through experiments on a dual-stage hard disk drive system.

1. ISA Transactions 51 (2012) 834–840
Contents lists available at SciVerse ScienceDirect
ISA Transactions
journal homepage: www.elsevier.com/locate/isatrans
Research Article
Robust vibration control at critical resonant modes using indirect-driven
self-sensing actuation in mechatronic systems
Fan Hong a, Chee Khiang Pang b,n
a
b
Data Storage Institute, A*STAR, 5 Engineering Drive 1 (Off Kent Ridge Crescent, NUS), Singapore 117608, Republic of Singapore
Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583, Republic of Singapore
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 29 November 2011
Received in revised form
19 May 2012
Accepted 7 June 2012
Available online 4 July 2012
This paper presents an improved indirect-driven self-sensing actuation circuit for robust vibration
control of piezoelectrically-actuated flexible structures in mechatronic systems. The circuit acts as a
high-pass filter and provides better self-sensing strain signals with wider sensing bandwidth and
higher signal-to-noise ratio. An adaptive non-model-based control is used to compensate for the
structural vibrations using the strain signals from the circuit. The proposed scheme is implemented in a
PZT-actuated suspension of a commercial dual-stage hard disk drive. Experimental results show
improvements of 50% and 75% in the vibration suppression at 5.4 kHz and 21 kHz respectively,
compared to the conventional PI control.
& 2012 ISA. Published by Elsevier Ltd. All rights reserved.
Keywords:
Piezoelectricity
Self-sensing actuation
Strain signal
Vibration control
Critical resonant mode
Mechatronics
1. Introduction
Mechatronic systems are highly compatible integration of
mechanics, electronics, control systems, and computer science [1],
which appear widely in industrial applications such as intelligent robots, aerospace crafts, and consumer electronics, etc. To
meet the growing demand for high-performance and low-cost
mechatronic products, continual improvements in R&D such as
servo evaluation and mechanical structure optimization are
essential [2], especially for portable devices requiring ultrahigh data capacities and ultra-strong disturbance rejection
capabilities [3,4].
In recent decades, lightweight flexible structures are widely
used in mechatronic systems to achieve high-speed and highaccuracy performance with low-energy consumption. These flexible structures can be found in a wide range of applications such
as high-density data storage devices [5,6], flexible robotic arms
[7,8], or high-speed nanopositioners [9,10], etc. However, due to
the inherent low structural damping and light weight, these
flexible structures may suffer from disturbance induced structural
vibrations at critical resonant modes [11]. These vibrations
would degrade the positioning accuracy severely and prolong
n
Corresponding author. Tel.: þ65 6516 7942; fax: þ65 6779 1103.
E-mail address: justinpang@nus.edu.sg (C.K. Pang).
the settling time, and therefore need to be properly compensated
for [12].
Active vibration control schemes were developed using additional sensors such as in [13–16]. Basically, sensors were attached
on the mechanical structures to measure the acceleration or
strain signals, and the measured signals were fed back to the
inner loop to actively compensate for the structural vibrations of
the flexible structures. In particular, active vibration control
incorporated with Pb–Zr–Ti (PZT) material as actuators/sensors
has attracted many research interests [17,18].
PZT material has become one of the popular choices in
vibration control and noise suppression applications due to their
efficiency in converting mechanical energy into electrical energy,
and vise versa [19]. In addition, it possesses favourable features
such as high sensitivity, high working bandwidth, and low-level
noise at high frequency range. In traditional approaches, PZT
material has been used solely as sensors or actuators [20–22],
where separated circuitries were required for sensors and actuators respectively. The idea of self-sensing actuation (SSA) was
concurrently proposed in [23,24], where the PZT elements were
used as sensors and actuators simultaneously to reduce implementation cost and complexity, achieving truly collocated control. In these works, conventional RC bridge circuits were used to
extract the strain signals from the PZT elements, with good
applications appeared in [25–27] where the strain signals were
used to provide active damping of the vibrations of PZT-actuated
suspension in dual-stage hard disk drives (HDDs).
0019-0578/$ - see front matter & 2012 ISA. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.isatra.2012.06.004

2. F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840
As the sensing voltage is much smaller than the driven voltage
applied on the PZT elements, the quality of the signal, i.e., the
signal-to-noise ratio (SNR) is a concern [28]. Conventional RC
bridge circuits suffer from poor common-mode signal rejection so
that the bridge is hard to be balanced. To tackle this problem, an
Indirect-Driven Self-Sensing Actuation (IDSSA) circuit was proposed in [29], where operational amplifiers were used to drive the
PZT actuators indirectly rather than by the input voltage (actuation voltage). By doing so, the SSA circuit has provided sensing
signals with higher SNR.
In this paper, the IDSSA circuit is further improved so that the
circuit acts as a high-pass filter, resulting in better self-sensing
performance in terms of wider sensing bandwidth and higher SNR
compared to conventional SSA circuits and its earlier version in
[29]. The improved circuit is then used to suppress the structural
vibrations at critical resonant modes of the PZT-actuated suspension of a commercial dual-stage HDD. Rather than directly feeding
back the strain signal, an adaptive non-model-based control [30]
is used to enhance the performance of vibration suppression.
The rest of the paper is organized as follows. Section 2 presents
the characteristics of the PZT elements and the schematic of the
improved IDSSA circuit. The controller with an add-on adaptive
strain feedback is designed in Section 3. The effectiveness of the
proposed adaptive control with IDSSA circuit is evaluated by
extensive experiments on a PZT-actuated suspension of a commercial dual-stage HDD in Section 4. Section 5 gives conclusive
remarks.
835
Fig. 1. Conventional SSA circuit.
2.2. Conventional SSA circuit
The structure of the conventional SSA circuit is shown in Fig. 1,
where the PZT element is modeled as a sensing voltage source vp
in series with an equivalent capacitor Cp. The driving voltage vin is
applied to the PZT element directly, and the sensing voltage vp
generated from the strain of PZT element can be extracted by
balancing the bridge circuit.
The circuit can be analyzed by deriving the Laplace transform
of v1 ðtÞ and v2 ðtÞ as
V 1 ðsÞ ¼
Cp
½V ðsÞÀV p ðsÞŠ
C p þC 1 in
V 2 ðsÞ ¼
C eq
V ðsÞ
C eq þ C 2 in
2. Indirect-driven self-sensing actuation (IDSSA) circuit
In this section, the characteristics of the PZT element and the
structure of conventional SSA circuit are briefly reviewed, followed by the IDSSA circuit design.
2.1. PZT element
The electromechanical equations of the PZT element can be
written as [23]
S ¼ sE T þdE
p
ð2Þ
P
where S, T, D, and E are the strain, the applied mechanical stress,
the charge density, and the uniform electric field of the PZT
element respectively. sE and E represent the elastic compliance
and the permittivity of the PZT element respectively. d and e are
the PZT constants. From Eq. (2), the uniform electric field Ep in the
PZT element can be written as
E
À
eS
ð3Þ
E
Assume that the PZT element is a rectangular solid with length lp,
width bp, and thickness hp. The voltage v measured across the PZT
element can be obtained by multiplying Eq. (3) by hp, i.e.,
v ¼ Ep hp ¼
If C 1 =C 2 ¼ C p =C eq , the sensing voltage Vp(s) can be decoupled from
the control input Vin(s) and is proportional to circuit output Vo(s) as
V o ðsÞ ¼
D ¼ eS þ EE
D
V o ðsÞ ¼ V 2 ðsÞÀV 1 ðsÞ
C eq
Cp
Cp
¼
À
V p ðsÞ
V in ðsÞ þ
C eq þ C 2 C p þ C 1
Cp þ C1
ð1Þ
p
Ep ¼
The circuit output Vo(s) is then calculated as
Dhp
E
À
eShp
E
9
qin qp
À 9vin Àvp
Cp Cp
ð4Þ
where D9qin =A is the charge density due to the applied voltage
vin with A ¼ lp  bp being the polarization area of the PZT element,
eS9qp =A is the polarization charge density due to the strain, and
C p 9ðEAÞ=hp is the capacitance of the PZT element. It can be seen
from Eq. (4) that the voltage measured across the PZT element is a
subtraction of the sensing voltage vp from the applied voltage vin.
An SSA circuit shall be designed to extract the sensing voltage vp
which is proportional to the strain of the PZT element.
Cp
V p ðsÞ
Cp þ C1
As pointed out in [26], the PZT actuators with conventional SSA
circuit require more power input for actuation than those without it.
To handle this problem, an IDSSA circuit was proposed in [29],
which employed op-amps to drive the PZT actuators indirectly so
that the load burden on the implementation hardware was lessened.
The IDSSA circuit is further improved in Section 2.3.
2.3. Improved IDSSA circuit design
Based on the original design in [29], the IDSSA circuit is further
improved by adding capacitors and resistors in the feedback loops
of op-amps such that the circuit acts as a high-pass filter as
shown in Fig. 2, resulting in better self-sensing performance in
terms of wider sensing bandwidth and higher SNR compared to
conventional SSA circuits.
The sensing voltage vp generated from the strain of the PZT
element can be decoupled from vin as shown in the following
derivations. The Laplace transform of v1 ðtÞ and v2 ðtÞ is derived as
C 1 C p R1 R2 s2 þ C 1 R2 s
V 1 ðsÞ ¼ 1 þ
V ðsÞ
C 1 C 2 R1 R2 s2 þðC p þ C 1 þ C 2 ÞR1 s þ 1 in
À
ðC p =C 2 Þs2
V p ðsÞ
s2 þðC p þ C 1 þ C 2 Þ=ðC 1 C 2 R2 Þs þ 1=ðC 1 C 2 R1 R2 Þ

3. 836
F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840
Fig. 2. Improved indirect-driven self-sensing actuation (IDSSA) circuit.
V 2 ðsÞ ¼ 1 þ
C 3 C eq R3 R4 s2 þ C 3 R4 s
V in ðsÞ
C 3 C 4 R3 R4 s2 þ ðC eq þ C 3 þ C 4 ÞR1 s þ1
The circuit output Vo(s) is given by
V o ðsÞ ¼
Fig. 3. Head suspension assembly of a commercial dual-stage HDD.
R6
R7 þ R8
R7
Á
V 2 ðsÞÀ V 1 ðsÞ
R5 þR6
R8
R8
The components are chosen to be
8
C 1 ¼ C 2 ¼ C 3 ¼ C 4 ¼ C eq ¼ C p
R1 ¼ R2 ¼ R3 ¼ R4
R5 ¼ R8
:
R6 ¼ R7 ¼ kR5
Therefore, the bridge circuit is balanced and Vp(s) is decoupled
from Vin(s) as
2
V o ðsÞ
ks
¼
V p ðsÞ
s2 þ 2zð2pf c Þs þ ð2pf c Þ2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where
f c ¼ 1=2p C 1 C 2 R1 R2 ,
z ¼ C 1 C 2 R1 R2 ðC 1 þC 2 þC p Þ=
2C 1 C 2 R2 , and k are the cut-off frequency, damping ratio, and gain
of the high-pass filter, respectively.
Neutral axis
PZT
3. Adaptive non-model-based controller design
The proposed IDSSA circuit is used for vibration control at the
critical resonant modes of the PZT-actuated suspension. Rather
than directly feeding back the strain signal, an adaptive nonmodel-based control is used to enhance the performance of
vibration suppression. In this section, the structure of the PZTactuated suspension is analyzed, followed by the adaptive algorithm with its stability proof.
3.1. PZT-actuated suspension
Fig. 3 shows the head suspension assembly of a commercial
dual-stage HDD, where the PZT-actuated suspension is mounted
on the base-plate of the Voice Coil Motor (VCM) actuator for fine
positioning. The suspension can be modeled as a flexible beam
with length l, width b, and thickness h as shown in Fig. 4, for
simplicity but without loss of generality.
Assume that the cross-section of the suspension is a symmetrical area (in y2z plane) which is perpendicular to the neutral
plane (in x2z plane). Therefore, the strain ex generated in the x2y
^
plane can be calculated as
2
^
ex ¼ Àz
^
^
d wðx,tÞ
^
dx
Fig. 4. PZT-actuated suspension modeled as a flexible beam (Top: top view;
bottom: side view).
The proposed IDSSA circuit is used to extract the strain signal
of the PZT-actuated suspension. The strain signal can then be used
for adaptive non-model-based controller design to compensate
for the structural vibrations at the critical resonant modes.
3.2. Adaptive non-model-based control
Fig. 5 shows the block diagram of the control system with the
add-on adaptive control, where the base-line control is composed
of a PI control and notch filters, and an adaptive non-model-based
control is used in the add-on strain feedback loop to enhance the
performance of vibration suppression at the critical resonant
modes of the PZT-actuated suspension.
The adaptive non-model-based control is derived based on an
energy function [30] as
½Ek ðtÞ þ Ep ðtÞŠÀ½Ek ð0Þ þEp ð0ÞŠ ¼
Z
t
_
vðtÞwðtÞ dt
ð5Þ
0
2
^
^
where wðx,tÞ is the displacement of in x2y plane and z is the
distance from the neutral axis to a point of interest in the beam as
shown in Fig. 4.
where Ek(t) and Ep(t) are the total kinetic and potential energy of
the system at time t, Ek ð0Þ and Ep ð0Þ are the initial kinetic and
_
potential energy of the system at time 0. vðtÞ and wðtÞ are the
external input and velocity respectively. The time derivative of

4. F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840
¼ ÀaÀ1 bY 2 ðtÞ r 0
s
837
ð12Þ
which is negative semi-definite, i.e., the closed-loop system is
energy dissipative and stable. Since the stability condition in (12)
is independent of system dynamics, the control system is robust
against plant uncertainties.
4. Performance evaluation
Fig. 5. Block diagram of the control system with the add-on adaptive control.
Eq. (5) is
_
_
_
E k ðtÞ þ E p ðtÞ ¼ vðtÞwðtÞ
ð6Þ
_
_
where E k ðtÞ and E p ðtÞ are the time derivatives of the kinetic and
potential energy respectively.
The adaptive non-model-based control v(t) is designed as the
combination of a PI control and an adaptive strain feedback term,
which is expressed as
Z t
Z t
vðtÞ ¼ Àkp wðtÞÀki
wðtÞ dtÀkf f ðtÞ
f ðtÞ dt
ð7Þ
0
0
where kp, ki 4 0 are proportional and integral gains respectively,
f(t) is a signal reflecting the deformation of the controlled
plant, e.g., the strain, which should be chosen such that it is zero
when the controlled plant is static without deformation. The gain
kf 4 0 is for the add-on strain feedback loop, where larger kf
leads to faster transient performance but undesired high-gain
control and more energy consumption, and vice versa. An adaptive tuning for kf can be achieved by setting kf ¼ Y 2 ðtÞ, and Ys(t) is
s
updated by
Z t
_
_
Y s ðtÞ ¼ aY s ðtÞwðtÞf ðtÞ
f ðtÞ dtÀbY s ðtÞ
ð8Þ
0
where a 40 sets the updating rate, b 40 is introduced to avoid
divergence of the integral gains in the presence of various
disturbances and plant uncertainties. With the b-term, Ys(t) acts
Rt
_
as a first order filter of the aY s ðtÞwðtÞf ðtÞ 0 f ðtÞ dt and thus it will
not diverge.
Note that PI control is used in Eq. (7) rather than PD control
in [30]. The integral term is used to eliminate the steady-state
error. To accommodate the extra term, the integral gain is chosen
2
as ki ¼ k0 ðtÞ, where k0 ðtÞ is adaptively tuned by
Z t
_
_
k 0 ðtÞ ¼ gk0 ðtÞwðtÞ
wðtÞ dt
ð9Þ
The adaptive control with the proposed IDSSA circuit is
implemented in the PZT-actuated suspension of a commercial
dual-stage HDD. The objective is to robustly suppress the structural vibrations at the critical resonant modes of the PZT-actuated
suspension.
The schematic of the experimental setup is shown in Fig. 6. A
PZT-actuated suspension from a dual-stage commercial HDD is
used in the experiment test. The effective stroke of the PZTactuated suspension is around 7150 nm with 710 V input
range. A Laser Doppler Vibrometer (LDV) from Polytec is used to
measure the lateral displacement of the slider without disk
rotation. The resolution of the LDV is set at 500 nm/V. Control
algorithms are implemented in dSPACE by setting the sampling
frequency at 60 kHz. Control signals are applied to the PZTactuated suspension through a Piezo Amplifier (amplification
 20, Piezo Systems, Inc.). Fig. 7 captures the actual experimental
setup placed on a vibration-free table.
4.1. Self-sensing performance of the IDSSA circuit
The proposed IDSSA circuit is implemented in a Printed Circuit
Board (PCB) as shown in Fig. 8, which is used to extract the strain
signal of the PZT-actuated suspension produced by PZT elements.
AD827JN with dual op-amps is chosen due to its high unity-gain
bandwidth and high performance. Both op-amps are connected in
the non-inverting configuration so that the PZT elements can be
driven indirectly by negative input terminal of op-amp rather
than by input voltage directly [29]. In addition, a difference
amplifier is implemented by another op-amp chip LF356N. A grid
0
where g 40 sets the updating rate of k0 ðtÞ.
The stability of the closed-loop system with the add-on
adaptive control is proven as follows. The Lyapunov function
candidate is chosen as
1
1
1
2
VðtÞ ¼ Ek ðtÞ þ Ep ðtÞ þ kp wðtÞ2 þ aÀ1 Y 2 ðtÞ þ gÀ1 k0 ðtÞ
s
2
2
2
ð10Þ
Using Eq. (6), the time derivative of V(t) is
_
_
_
_
_
V ðtÞ ¼ vðtÞwðtÞ þ kp wðtÞwðtÞ þ aÀ1 Y s ðtÞY s ðtÞ þ gÀ1 k0 ðtÞk 0 ðtÞ
ð11Þ
Substituting Eqs. (7)–(9) into (11) yields
Z t
Z t
_
_
V ðtÞ ¼ Àkp wðtÞÀki
wðtÞ dtÀkf f ðtÞ
f ðtÞ dt wðtÞ
0
0
Z t
_
f ðtÞ dtÀbY s ðtÞ
þ aÀ1 Y s ðtÞ aY s ðtÞwðtÞf ðtÞ
2
_
_
þkp wðtÞwðtÞ þ k0 ðtÞwðtÞ
Z
0
0
t
wðtÞ dt
Fig. 6. Schematic diagram of the self-sensing vibration control system.

5. 838
F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840
10
Gain (dB)
5
0
−5
−10
IDSSA
−15
103
104
Phase (deg.)
−80
−100
−120
−140
−160
−180
103
Fig. 7. Experimental setup on the vibration-free table.
104
Frequency (Hz)
Gain (dB)
Fig. 9. Frequency response of the proposed IDSSA circuit.
20
10
0
−10
−20
−30
−40
103
IDSSA
LDV
104
Phase (deg.)
100
0
−100
−200
−300
103
104
Frequency (Hz)
Fig. 8. PCB of the IDSSA circuit.
Fig. 10. Self-sensing performance of IDSSA circuit (solid-line: V IDSSA =V in ; dashedline: V LDV =V in ).
Table 1
Values of circuit components.
Component
Value
Cp
C 1 ¼ C 2 ¼ C 3 ¼ C 4 ¼ C eq
R1 ¼ R2 ¼ R3 ¼ R4
R5 ¼ R8
R6 ¼ R7
4.84 nF
4.84 nF
8 kO
1 kO
4:7 kO
of pin holes on the board is used for plugging in suitable passive
components to balance the circuit and adjust the circuit amplification gain. As most of the critical resonant modes of the PZTactuated suspension lie above 5 kHz and the circuit is designed to
act as a high-pass filter, the cut-off frequency, damping ratio, and
gain of the circuit are set as f c ¼ 4:5 kHz, z ¼ 1:5, and k¼4.7
respectively. The values of components are listed in Table 1. The
corresponding frequency response of the IDSSA circuit, i.e.,
V o ðsÞ=V p ðsÞ, is measured and plotted in Fig. 9. Note that the output
provides a quadruple amplification of the sensing voltage, i.e.,
vo ¼ 4vp in the effective working bandwidth 4.5–30 kHz.
The self-sensing performance of the proposed IDSSA circuit is
evaluated by conducting the experiments in an open-loop configuration. The suspension is actuated by PZT actuator by injecting swept sine signal vin through piezo amplifier, while the strain
signal vIDSSA is collected from the sensing circuit. The frequency
response of V IDSSA =V in is then obtained and benchmarked against
V LDV =V in , with V LDV being the lateral displacement of the slider
measured by LDV. The comparison is shown in Fig. 10, and
confirms that the proposed IDSSA circuit is able to detect almost
all the critical resonant modes of the PZT-actuated suspension.
4.2. Vibration suppression at critical resonant modes
Note that in this experiment, only the PZT actuation loop is
active and the VCM actuation loop is disabled.
A nominal controller, i.e., a PI controller in series with four
notch filters at 5.4 kHz, 16 kHz, 20.9 kHz and 25.6 kHz, is first
designed to stabilize the system. As can be seen from Fig. 11, the
resulting open-loop achieves the gain cross-over frequency at
around 1.5 kHz with sufficient gain margin and phase margin, as
well as the DC gain around 25 dB. Fig. 12 shows that the base-line
loop system is able to track a 25 Hz square wave.

6. F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840
0.4
Open−loop
Plant model
20
0
−20
−40
102
103
PES (500 nm/V)
40
Gain (dB)
839
104
Base−line PI
0.2
0
−0.2
−0.4
0
1
2
3
4
5
6
0
0.4
−200
−400
−600
−800
102
103
Frequency (Hz)
104
0.1
0.06
−0.2
0
1
2
3
4
Time (sec)
5
6
7
x 10−3
0.4
PES (500 nm/V)
0.04
0.02
0
−0.02
Base−line PI
0.2
0
−0.2
−0.4
−0.04
−0.06
0
1
2
3
4
5
0.02
0.04
0.06
Time (sec)
0.08
0.1
Fig. 12. Step response of the base-line loop system.
PES (500 nm/V)
0
Adaptive+IDSSA
0.2
0
−0.2
−0.4
Remark 1. In order to eliminate the steady-state tracking error,
the open-loop shall ideally have a DC gain of 40–50 dB. However,
for the plant model such as the PZT-actuated suspension with a
low DC gain of around À 10 dB, the controller should be designed
to have a DC gain as high as around 50–60 dB. With such a highgain control, the PZT actuator will saturate easily. To avoid
saturation, therefore, the controller is designed to have a comparatively lower DC gain.
Remark 2. To prevent saturation of the PZT actuator due to the
signal drifting of LDV measurement, a 50 Hz square wave with
amplitude of 0.025 mV is injected to the ‘‘trig-in’’ port. Note that
the spikes in Fig. 12 are due to the ‘‘trig in’’ signal, not the actual
displacement of the plant.
To show the vibration suppression capability of the adaptive
scheme, sinusoidal signals with amplitude of 0.01 V at two
frequencies, i.e., 5.4 kHz and 20.9 kHz are injected as disturbance
respectively at the output. Note that only kf is tuned for simplicity. The parameters in Eq. (8) are chosen as a ¼ 1 and b ¼ 5.
As can be seen from Fig. 13, the nominal control (top) is unable to
attenuate the disturbance, while more than 50% improvement can
be achieved by the adaptive control (bottom) with the settling
time being 6 Â 10 À 3 s. Similarly, the disturbance rejection
6
x 10−4
0.4
−0.08
−0.1
0
Fig. 13. Transient response of vibration suppression at 5.4 kHz.
Reference
Base−line PI
0.08
Adaptive+IDSSA
0.2
−0.4
Fig. 11. Frequency response of base-line open-loop transfer function.
Displacement (500 nm/V)
7
x 10−3
PES (500 nm/V)
Phase (deg.)
200
0
1
2
3
4
5
Time (sec)
6
x 10−4
Fig. 14. Transient response of vibration suppression at 20.9 kHz.
performance at the other frequency of 20.9 kHz is improved by
75% with the settling time of 5 Â 10 À 4 s as shown in Fig. 14.
To explore the effect of the adaptive control and IDSSA circuit
in the frequency range of interest, the sensitivity functions with
and without the adaptive control and IDSSA circuit are plotted in
Fig. 15. Note that the sensitivity function with the adaptive
control is measured at steady-state, i.e., after the adaptive law is
converged at each frequency. Fig. 15 shows that better gain
attenuation is achieved at the critical resonant modes by the
adaptive control, which confirms the improved disturbance rejection performance of the scheme in time domain.
Remark 3. In the mass production of PZT-actuated structures for
mechatronic systems, significant perturbations exist in the natural frequencies, damping ratios, and residues of the critical
resonant modes of the PZT-actuated structures. Compared to
conventional high gain control schemes such as peak filter
method, the adaptive control with IDSSA circuit is more robust
against these perturbations due to: (1) the strain signal is

7. 840
F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840
10
Base−line PI
Adaptive+IDSSA
Gain (dB)
5
0
−5
−10
−15
103
104
Frequency (Hz)
Fig. 15. Sensitivity functions with and without the adaptive control and IDSSA
circuit.
proportional to the mechanical deformation, i.e., the sensing
signal of the IDSSA circuit varies along with the perturbations of
the critical resonant modes of the PZT-actuated structures; and
(2) the adaptive control is independent of plant dynamics.
5. Conclusions
In this paper, an indirect-driven self-sensing actuation (IDSSA)
circuit has been proposed for robust vibration control at the critical
resonant modes of PZT-actuated structures in mechatronic systems.
The proposed circuit employed op-amps to act as a high-pass filter
and provide better self-sensing strain signals with wider sensing
bandwidth and higher signal-to-noise ratio. Rather than directly
feeding back the strain signal, an adaptive non-model-based control
was used to enhance the performance of robust vibration control.
The proposed IDSSA circuit with adaptive control was implemented
in the PZT-actuated suspension of a commercial HDD, and the
experimental results showed improved performance in vibration
suppression at the critical resonant modes.
Acknowledgments
This work was supported in part by Singapore MOE AcRF Tier 1
Grant R-263-000-564-133. The authors would like to thank
X. Wang and G. Dai in Department of Electrical and Computer
Engineering, National University of Singapore, for their help in the
experiments.
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