Identification and Control of a Piezoelectric Bender Actuator
Mohd Nazmin Maslan
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
81310 UTM Johor Bahru, Johor, Malaysia
irnazminm@gmail.com
Musa Mailah, Intan Z. Mat Darus
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
81310 UTM Johor Bahru, Johor, Malaysia
musa@fkm.utm.my, intan@fkm.utm.my
Abstract—This paper focuses on determining the transfer
function (TF) of a highly nonlinear and hysteretic piezoelectric
actuator and its inverse. A system identification (SI) technique
was employed based on the direct measurements of the input-
output data from a bender type piezoelectric actuator mounted
on a suitably designed platform equipped with appropriate
instrumentation. Eventually, the actuator TF models were
approximated through a rigorous analytical procedure.
Verification and validation of the results are performed to
ensure that the transfer functions obtained are practically
viable and implementable. An illustrative case study is also
carried out involving the control of the identified piezo
actuator using closed-loop control methods that employ a
conventional proportional-integral-derivative (PID) controller
and PID with active force control (PIDAFC). The outcome of
the study clearly indicates the effectiveness of the proposed
schemes.
Keywords-hysteretic behaviour; piezoelectric bender
actuator; transfer function; system identification; active force
control
I. INTRODUCTION
Actuators incorporating smart materials are competitive
choices for micro applications, but they are difficult to
control because of their inherent nonlinearity and hysteresis
[1]. Smart materials can be defined as materials that have
one or more properties that can be significantly changed in a
controlled manner upon the application of external stimuli,
such as temperature, stress, pH, moisture, electric or
magnetic fields. Examples are piezoelectric devices, shape
memory alloys, magneto-rheological fluids and pH sensitive
polymers. The ‘smart’ properties inherent in these materials
are typically extracted and exploited to serve many useful
applications such as in the development of sensors and
actuators for control of dynamical systems (piezoelectric
devices), active control of vehicle suspension systems
(magneto-rheological dampers), determining and identifying
parameters of interest from changes in colour (halochromic
materials) and host of others. In the proposed study, the
smart material related to a piezoelectric actuator is rigorously
investigated to capture its mathematical models via system
identification (SI) technique for the purpose of closed-loop
feedback control strategies.
II. BACKGROUND AND LITERATURE SURVEY
Smart material devices in the form of piezoelectric
actuators are quite common and obvious choices due to their
highly desirable features in actuating mechanisms in
multitude of emerging nano and bio technologies. As an
example, piezo actuator is used in atomic force microscopy
to image and manipulate samples at the nanoscale and also a
wide range of mechatronic applications like fuel injection to
the field of smart structures for micro positioning or noise
and vibration suppression [2]. The actuator works on the
principle of the piezo material in the actuator changes its
dimension (e.g., displacement) in response to the applied
voltage. This property can be used to generate motion or
force in electromechanical devices and micro machines [3].
However, their highly nonlinear hysteretical stimulus-
response characteristic fundamentally limits the accuracy of
the actuators. Smart actuators such as piezoelectric actuator
are also subject to creep and vibration dynamics which
further complicates the behavioural study of their internal
mechanisms [1]. A popular approach in the control of smart
materials is to linearise the system by incorporating the
inverse of the actuator model before the actuator. If the
model can be inverted, the system can be linearised. In [4],
Tan and Baras demonstrated that the actuator is linearised by
an inverse model and optimal control is used to provide
robust stability for the linearised system. A standards
committee of the IEEE has published a description of the
behaviour of piezoelectric ceramic element in terms of
linearised constitutive relations. In other words, it is
generally meant to describe the linear modelling of
piezoceramics [5]. However, for more precise and critical
applications, this linearization notion does not hold true and
is not representative of the actual system behaviour. Hence, a
systematic and appropriate method needs to be devised so
that the above problems could be effectively addressed and
resolved. The acquisition of the inverse models of the
actuators poses a more complex problem than the direct
counterpart. System identification (SI) technique has been
used for the purpose of building mathematical model of
dynamical system based on observed data and may provide a
useful tool to study the behaviour of the piezo actuators,
given the adverse and complex conditions pertaining to the
dynamic motion of their internal structures.
Conventionally, model identification requires the
knowledge of the input and output data of the system of
interest. Such data are typically obtained from the tests or
physical rules governing the systems (model-based system
identification) and later used to identify the system model. In
general, SI involves two main steps, namely, the selection of
a suitable model structure and estimation of model
parameters. In the first step, a priori knowledge is used to
determine a class of models to which the target system may
2012 Third International Conference on Intelligent Systems Modelling and Simulation
978-0-7695-4668-1/12 $26.00 © 2012 IEEE
DOI 10.1109/ISMS.2012.100
459
2012 Third International Conference on Intelligent Systems Modelling and Simulation
978-0-7695-4668-1/12 $26.00 © 2012 IEEE
DOI 10.1109/ISMS.2012.100
461