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