372 IEEE TRANSACTIONS ON EDUCATION, VOL. 53, NO. 3, …

372 IEEE TRANSACTIONS ON EDUCATION, VOL. 53, NO. 3, AUGUST 2010

Teaching Modules on Modeling and Control ofPiezoactuators for System Dynamics, Controls,

and Mechatronics CoursesKam K. Leang, Member, IEEE, Qingze Zou, and Gina Pannozzo

Abstract—Piezoelectric actuators (or piezoactuators) are knownfor their nanoresolution and high-speed positioning capabilities.Therefore, they are used in scanning probe microscopes and inthe design of innovative surgical tools and biomedical devices.The expected growth of engineering jobs in the nano- and bio-re-lated fields, in which piezoactuators will play a significant role,motivated the development of a suite of teaching modules (lectureand laboratory materials) for the undergraduate mechanicalengineering (ME) curriculum that focus on modeling and pre-cision control of piezoactuators. Four laboratory exercises weredesigned to provide students with hands-on experience in data ac-quisition, sensors, and controller implementation. The developedmodules were implemented in three undergraduate courses. Thehypothesis being tested is that students who interact with thesemodules will gain a better understanding of piezoactuators andtheir application in nanotechnology and biotechnology. Throughlinked pre- to post-module comparisons, it is shown that studentsdid, in fact, experience a positive change in their knowledge andunderstanding of the material.

Index Terms—Dynamics and control, hysteresis, mechatronics,nanopositioning, nanotechnology, piezoactuators.

I. INTRODUCTION

A RECENT projection notes that millions of new jobs willbe created in the nano and bio fields worldwide by 2015

[1]. The expected growth of such jobs suggests that adequatepreparation and training of the future workforce are needed.One of the most prevalent devices used in emerging nano- andbiotechnology are sensors and actuators made from piezoelec-tric materials [2]. These materials are often referred to as smartor active materials. The piezoelectric actuator (or piezoac-tuator), a solid-state device used for actuation, is importantbecause of its ability to displace or move with nanometer reso-lution. This unique ability for fine displacement is exploited inatomic force microscopy (AFM), where a piezoactuator is usedto position a tool relative to a sample’s surface for imaging,

Manuscript received July 18, 2008; revised April 07, 2009. First publishedSeptember 15, 2009; current version published August 04, 2010. This workwas supported by the National Science Foundation under grants DUE-0633098,DUE-0632908, and CMMI-0626417.

K. K. Leang is with the Department of Mechanical Engineering, Universityof Nevada-Reno, Reno, NV 89557 USA (e-mail: [email protected]).

Q. Zou is with the Department of Mechanical Engineering, Iowa State Uni-versity, Ames, IA 50011 USA.

G. Pannozzo is with the Department of Education, Virginia CommonwealthUniversity, Richmond, VA 23284 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TE.2009.2024930

as well as object manipulation at the nanometer scale [3].Likewise, piezoactuators are employed in the design of surgicaltools for minimally invasive surgery [4]. Piezoelectric-basedactuators and transducers play a critical role in nanosystemsand biotechnology similar to the role the electric motor hasin common macroscale systems such as automobiles, homeappliances, and entertainment devices. Therefore, training andpreparing the future workforce with the knowledge and skillsto design and engineer piezo-based systems is important.

The fundamental concepts in modeling and control of electricmotors are covered in popular textbooks such as [5] and [6]. Thesubject is also tightly woven into core mechanical engineering(ME) classes like system dynamics, controls, and mechatronics.However, the treatment of piezoactuators is not common in thecurrent ME curriculum, nor is it standardized. Specifically, mod-eling and control of piezoactuators have not been systematicallyintegrated into core ME courses. Therefore, student exposureto the fundamental concepts of piezoactuators is limited. Thecontribution of this paper is the development of teaching mod-ules that focus on modeling and control of piezoactuators forthe undergraduate ME curriculum. The objective is to integratethe subject matter systematically into core mechanical courses,where modules are designed as plug-in teaching units for systemdynamics, controls, and mechatronics courses.

The development of teaching modules is preferred over cre-ating a new course on the subject. One reason for this is that inte-grating a new course into an existing curriculum is challengingdue to required department- and university-level approval. Ad-ditionally, new courses must be carefully designed to considertheir impact on the overall curriculum, as well as satisfying ex-isting accreditation standards such as those of the AccreditationBoard for Engineering and Technology (ABET) [7]. Althougha technical elective course can be created with fewer restric-tions, such courses impact a smaller number of students com-pared to core courses. Rather than developing a new or technicalelective course, proposed herein are teaching modules that canbe integrated into applicable core courses where the study ofthe piezoactuator is relevant. Such courses include system dy-namics, controls, and mechatronics. The integration of teachingmodules into core courses helps to broaden participation andimpact. Additionally, the modules can be tailored to meet thespecific learning objectives of the course at hand.

Efforts to integrate emerging technologies into the engi-neering curriculum have been documented in the literature.In particular, embedded systems (i.e., microcontrollers) formechatronics and controls courses are described in [8]. Theuse of microcontrollers for open-ended student design projects

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LEANG et al.: TEACHING MODULES ON MODELING AND CONTROL OF PIEZOACTUATORS 373

TABLE I(A) MODELING AND (B) CONTROL OF PIEZOACTUATOR MODULES

in robotics is described in [9]. Likewise, the hardware andsoftware requirements for microcontroller education are ex-amined in [10], and the alternatives to embedded systems formechatronics are found in [11]. On the topic of smart materials,the development of a senior-level course is described in [12],which focuses on piezo- and pyroelectricity. The course wasdesigned to address practical applications and a project wasassigned. Likewise, the study of shape memory alloy (SMA)is introduced to first-year engineering students in [13]. In thatexample, a handful of demonstrations involving SMAs weredeveloped and presented to students. A Web-based experimentfor controlling a piezoactuator is described in [14]. Althoughprevious works have considered the integration of emergingtechnologies such as smart materials into the ME curriculum,the concepts of modeling and control of smart materials has notbeen systematically developed and implemented.

In contrast to previously developed educational materials onsmart or active materials, the focus herein is to develop moduleson the piezoactuator for integration into core ME courses and totest the hypothesis that students who interact with these mod-ules will gain a better understanding of piezoelectric devices andtheir application in nano- and biotechnology. In particular, themodules are developed to address the key concepts that include:1) transducers; 2) linear dynamic effects; 3) nonlinearity; 4) fre-quency response; 5) feedback control; 6) feedforward control;and 7) experimental design and implementation. Table I showsthe subject modules on modeling and control of piezoactuatorsthat address these concepts.

II. INTRO TO PIEZOACTUATORS AND APPLICATIONS

Before students were exposed to the details of modeling andcontrol of piezoactuators, a brief overview (approximately 15min) is provided to promote engagement and motivate learningthe modules shown in Table I. The introduction begins with adescription of the piezoactuator as a device made from piezo-electric material. It is pointed out that the material responds to anapplied voltage by changing its dimensions. Conversely, whenstress is applied to the material, it produces a measurable voltageacross its electrodes. It is also emphasized that the former be-havior is typically exploited for actuation and the latter is forsensing as well as for energy harvesting applications [15].

The applications of piezoactuators and their useful workingrange are illustrated via the diagram shown in Fig. 1. Thediagram compares the operating range of electric motors topiezoactuators. Piezoactuators are primarily used in the po-sitioning of objects at the 1-mm down to the subnanometerrange. Applications include scanning probe microscopes, mi-cromachining, microrobotics, and fine-positioning of optics.Fig. 1(b) shows a schematic of an AFM, where the sharp tip

Fig. 1. (a) The length scale and typical operating range of electric motors andpiezoactuators. (b) Schematic of AFM system and AFM image of letters “VCU”scratched on a polymer surface.

at the end of the micromachined cantilever is used to scratchletters on a polymer surface (left image). The AFM imagedemonstrates the ability for micro- and nanoscale machiningwhere a piezoactuator positions a sharp tool tip for scratchingthe tiny letters “VCU” at the micrometer scale. Other applica-tions of piezoelectric materials that are presented can be foundin [16].

III. MODELING PIEZOACTUATORS

Three lectures on modeling the response of piezoactuatorswere developed and designed for a 1-h class period. The firstlecture covers the piezoelectric effect, a behavior that enablespiezoelectric materials to be used as actuators and sensors. Thesubsequent two lectures focus on the input-to-output behavior ofpiezoactuators. In this case, the input is the applied voltage andthe output is the actuator’s displacement. The behaviors includecreep, hysteresis, and vibrational dynamic effects [17].

A. The Piezoelectric Effect and Constitutive Equations

The piezoelectric effect is presented by using the quartzcrystal model first developed by Lord Kelvin in 1893 [18].The simple 2D model is based on the unique characteristicof certain crystalline lattices that deform under pressure. Thepressure induces separation of the centers of gravity of thepositive and negative charges within the material creating

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Fig. 2. A 2D model of a unit cell for a quartz crystal illustrating the piezo-electric effect. The large solid circles in (a) and (b) represent positively chargedions, and the small solid circle represents their center of gravity. Likewise, largeopen circles represent negatively charged ions, and their center of gravity is rep-resented by the small open circle.

a dipole moment, which is the product of charge value andtheir separation. The resulting dipole moment produces anelectric charge. This behavior explains the sensing ability ofpiezoelectric material. Conversely, an applied voltage inducesa mechanical strain in the crystalline lattice [18]. Fig. 2 showsthe 2D model to illustrate the piezoelectric effect, where (a)represents the sensing and (b) represents the actuating ability ofthe piezoelectric material. The arrows next to the charges shownin the figure indicate the direction of motion of the charges.This discussion is also connected with concepts from physicsand material engineering, e.g., the concept of charged particlesand the crystalline structure of materials such as ceramics [19].

Next, the linear constitutive relationship describing theelectromechanical properties of the piezoelectric material ispresented. This discussion begins with Hooke’s Law relatingthe strain to the compliance and stress for everydaymetals and plastics, . Because piezoelectric materialshave electrical properties, the basic constitutive equation forcommon dielectrics is included. The equation that relates theelectric displacement to the permittivity and electricfield is given by . Combining these two basicconstitutive equations, the following set of equations describethe electromechanical properties of the piezoelectric material:

(1)

(2)

It is emphasized that (1) and (2) are in general matrix equationsbecause of the anisotropic nature of piezoelectric materials, andthe subscript indicates a zero, or constant, electric field; thesubscript indicates a zero, or constant, stress field; the super-script stands for transposition of a matrix; and is piezoelec-tric modulus, the ratio of strain to applied field or charge den-sity to applied mechanical stress [2]. Also, in order to describeor model piezoelectric materials, it is emphasized that one musthave knowledge of the material’s mechanical properties (com-pliance or stiffness), its electrical properties (permittivity), andits piezoelectric coupling properties (piezoelectric modulus).

B. Vibrational Dynamics and Creep Effect

When voltage is applied to a piezoactuator, it displaces andexhibits the combined effects of hysteresis, creep, and vibration.These three effects are coupled, and the degree by which theyappear in the output response depends on the input frequencyand the range of motion. The approach to model the three ef-fects is to decouple them into two main components: a hysteresiselement (input nonlinearity) cascaded with a linear dynamicselement that captures the creep and vibration effects [20]. Theblock diagram of the decoupled model in the frequency domainis illustrated in Fig. 3(a).

Hysteresis is significant when the range of motion of apiezoactuator is large. At high operating speeds, the effect ofthe vibrational dynamics becomes noticeable as the resonantmodes of the actuator are excited. On the other hand, whena piezoactuator operates over long periods of time, creep be-comes significant. Several combinations of these behaviors aredepicted in Fig. 3 and discussed in the lecture.

The creep and vibrational dynamics are modeled using thelumped-parameter method and transfer function (Laplacedomain) technique. It has been shown that the creepand vibrational dynamics effects can be modeled by amass-spring-damper system. This approach is described inclass, and the method goes hand-in-hand with key concepts inmodeling mechanical systems in the ME undergraduate cur-riculum [6]. Likewise, the behavior of the spring-mass-dampersystem is connected with the vibration modes of mechanicalsystems [21]. The transfer function model for the creep effectin terms of the spring and damper elements is given by [17]and [22]

(3)

where and are the spring and damper constants, respec-tively (see Fig. 4). Similarly, a simplified model of the vibra-tional dynamics is obtained by performing a force balance ona standard spring-mass-damper system. The transfer functionmodel is

(4)

where , , , are the effective mass, damping, and spring con-stant of a piezoactuator, and is a constant that relates the ap-plied input voltage and force generated by a piezoactuator (as-sumed to be linear). Both models are derived in the lecture.Using these models, students are asked to simulate the creepand dynamics behaviors in Matlab through a homework assign-ment where the coefficients are taken from [23]. Additionally, anassignment is given to investigate the piezo’s response to slowtime-varying signals (creep behavior) as well as to rapid signalslike a step, ramp, and triangle input at different timescales. Thehomework exercise gives students the opportunity to study in-dependently and to identify the slow drift effect caused by creepand the oscillations in the output due to the vibrational dynamicsat high frequency.



Fig. 3. The cascade model for creep � ��, hysteresis ��, and the vibrational dynamics � �� in piezoactuators: (a) the large-range, high-speedmotion; (b) the large-range, low-speed motion; and (c) the small-range motion.

Fig. 4. Input–output model for piezoelectric creep.

C. Hysteresis Effect

Unlike the electric motor, a piezoactuator’s response showshysteresis. This effect is also present in other active (or smart)materials such as shape memory alloys [24]. To teach the funda-mentals of hysteresis, it is first emphasized that the behavior isnonlinear and the effect depends on the input magnitude [25], incontrast to linear systems in which the output magnitude scalesproportionally with the input. Next, it is explained that the non-linearity is attributed to the energy loss caused by microscaledomain wall interactions within the material [26]. The discus-sion also draws an analogy with plastic deformation in mate-rials [19]. The basic properties of hysteresis such as the localmemory property and rate- and range-independency [27] areemphasized. Finally, various methods to quantify and charac-terize the hysteresis behavior, such as recording the maximumoutput variation relative to a linear behavior, are described.

IV. FEEDBACK AND FEEDFORWARD CONTROL

The following lecture modules focus on teaching controltechniques for precision-positioning with piezoactuators. Themodules emphasize the fundamentals of feedback [28], [29]and feedforward [17], [30] control techniques (see Fig. 5) forpiezoactuators.

A. Challenges With Positioning With Piezoactuators

Piezoactuators are widely used in the design of high-preci-sion positioning systems. It is emphasized that obtaining accu-rate models and implementing effective control strategies en-able successful application of piezoactuators [31]. Since theseactuators exhibit nonlinearity (i.e., hysteresis), accurate models

Fig. 5. Block diagram of (a) feedforward and (b) feedback approaches to con-trol a piezoactuator.

can be difficult to obtain in practice. However, it is pointed outthat a linear dynamics model, such as the second-order transferfunction model typically used to describe the dynamics of a dcmotor, can effectively model the dynamics of a piezoactuatorover a small range ( of total range). Such linear modelscan be used to design effective controllers for piezo systemswith good performance.

Tracking error caused by vibrational dynamics, hysteresis,and creep effects are emphasized as major challenges. Althoughadvanced control techniques have been proposed and effectivelyimplemented (e.g., [17], [28], [31], and [32]), covering suchtopics is beyond the scope of the undergraduate curriculum. In-stead, industry-standard feedback controllers including lead-lagand proportional-integral-derivative (PID) are taught using thepiezoactuator as an example system.

B. Feedback Control Design for Piezoactuators

Application of feedback control for piezoactuators involvesdesigning a notch filter to first improve system gain margin [20].It is shown that a notch filter limits the magnitude of the input atspecific frequencies to avoid exciting dominant modes and in-stability issues. With sufficient gain margin, the feedback gaincan be increased to minimize hysteresis effect at low frequencywithout instability. A brief discussion is presented pointing outthat low gain margin caused by the lightly damped vibrationalmodes (resonant peaks) as well as high-frequency dynamics canlimit the performance of traditional PID control. Therefore, thebasic idea of a notch filter is to use a pair of complex zeros,

(’ ’ denotes the complex conjugate), to cancel the res-onant peak of the piezoactuator. For casual implementation, a



Fig. 6. Two modular piezoactuator experiments for laboratory activities. (a) Setup machined from plastic and aluminum. (b) Setup made using a rapid prototypingmachine.

pair of complex poles, , is combined with the zeros. Fi-nally, the notch filter transfer function is given by

(5)

where is the gain of the notch filter. To illustrate gain marginimprovement, an example MATLAB program is presented thatcompares the gain margin of the original open-loop system withthe notch filter cascaded with the open-loop system. The gainmargin improvement can be over 20 dB (10 times). Finally,two practical methods to implement a notch filter are discussed:1) the analog method using op-amp circuits [33]; and 2) the dig-ital method using the MATLAB-Simulink environment.

The feedback controller with the notch filter, (seeFig. 5(b)) is , where denotes,for example, a standard lead-lag compensator or PID controller.This design has several benefits. First, since the notch filter en-ables high-gain feedback, at low frequency the hysteresis is min-imized. Second, not only is the controller applicable to piezoac-tuators, but it can also be applied to other lightly damped dy-namic systems such as flexible structures including cranes androbot manipulators.

Following the notch filter discussion, the classical lead-lagcompensator is introduced. This discussion also includes PID-type controllers, which are widely used in industry for piezo-based systems. The lead-lag compensator has the fol-lowing form:

(6)

where is the controller gain; are the zero and poleof the lag compensator, respectively; and are the zeroand pole of the lead compensator, respectively. A PID controlleris a special case of the above with transfer function

(7)

where , , and are the proportional, derivative, and integralgains, respectively.

To give students experience working with notch filters, ahomework assignment is assigned asking them to comparethe maximum controller gains, in (6) and in (7), for a

feedback controller with and without a notch filter in the loop.The assignment also provides students the opportunity to inves-tigate the role of the notch filter in controlling lightly-dampeddynamic systems, which includes a flexible robotic arm andpiezoactuator.

C. Feedforward Control for Hysteresis Compensation

Hysteresis effect is a complex nonlinear behavior, andwithout appropriate control (compensation), significant posi-tioning error limits the performance of piezoactuators [20].One approach to account for the hysteresis effect is feedfor-ward control. This method involves modeling the hysteresisbehavior and then using the model to compensate or anticipatefor the hysteresis effect [see diagram in Fig. 5(a)]. The modelis typically inverted to find an input for a given desired outputbehavior.

Several models for hysteresis are described, including theclassic Preisach model, polynomial models, and simple lookuptable models for feedforward control application [31]. ThePreisach model consists of a sum of basic relays that repre-sent, for example, the behavior of individual dipoles in thepiezoelectric material [34]. This model is complex, and onlythe geometric interpretation is presented to show its basicproperties.

The advantages of using feedforward control over feedbackare discussed. In particular, with a reasonably accurate model,the performance can exceed that of feedback control because offeedforward’s ability to anticipate deficit performance. By in-verting the linear dynamics, feedforward control can be used forvibration compensation to enable high-speed positioning [17].One disadvantage of feedforward control is lack of robustness,especially when the system parameter changes (for example,due to aging or temperature effects) [35], [36].

V. LABORATORY MODULES

Experiments provide students with hands-on experiencein observing, measuring, and controlling piezoactuators, thuspreparing them for the practical aspects of emerging areas innano- and biotechnology. The following laboratory modules aredeveloped to enhance students’ understanding of the conceptsin Fig. 1 and to complement the developed lecture modules.



Fig. 7. The MATLAB-Simulink block diagram for (a) and (b) measuring the frequency response of the piezobimorph actuator, and (c) feedback control of thepiezobimorph actuator using a notch filter and a PI controller.

A. Experimental Piezoactuator System

The two experimental systems shown in Fig. 6 were de-signed for the laboratory activities. Both experiments consistof a bimorph piezoactuator, an inductive displacement sensor(Kaman SMU0-9000-15N001), a low-cost infrared sensor (e.g.,Fairchild QRB1113) [37], a high-voltage amplifier (not shown)to drive the piezoactuator, and a PC with a data acquisition card(not shown). The experimental setup in Fig. 6(b) is made by arapid prototyping machine.

B. Prelab: Safety and High-Voltage Concerns

Piezoactuators are driven with high voltages; therefore,a short discussion to highlight certain safety issues is firstpresented before the students are allowed to work on theirexperiments. During the experiments, the instructor is requiredto check over students’ experimental setups before turning onthe main power. In the event of an emergency, the students areinstructed to inform the lab technician and instructor immedi-ately.

C. Lab 1: Vibrational Dynamics and Creep ModelingExperiment

In this experiment, students model the linear vibrational dy-namics using the swept-sine method, where a data acquisitioncard and the Matlab software are used to record and process themeasured data. The experiment calls for students to do the fol-lowing.

1. Build a Simulink block diagram to implement the swept-sine method using the Matlab command “verb1chirp1.”Fig. 7(a) and (b) show one example of the Matlab Simulinkmodel used for collecting data (with the dSPACE DAQcard). Other types of DAQ systems can be implementedin a similar manner, such as Matlab’s xPC Target environ-ment with National Instruments DAQ card.

2. Apply the chirp input signal while simultaneously mea-suring the output response of the piezobimorph actuator.

Fig. 8. The frequency responses (magnitude versus frequency) of the piezobi-morph actuator, comparing the measured data and model.

3. Write a Matlab program (M-code) to process the measuredinput and output data to create the frequency response.

4. Curve-fit the frequency response functions using theMatlab function “ ” to obtain the transfer func-tion model (4). An example of the frequency responseand a transfer function model obtained for this step arecompared in Fig. 8. The result shows good agreement.

5. Measure the step response of the piezobimorph for post-processing and analysis.

To instill the modeling concept further, post-lab work is giventhat asks students to compare the simulated step response ofthe transfer function model to the measured step response. Anexample of a Matlab program for this step is shown in Fig. 9.

D. Lab 2: Hysteresis Modeling Experiment

This experiment is designed to provide hands-on experi-ence with measuring, quantifying, and modeling hysteresis inpiezoactuators. The steps require students to do the following.

1. Build a Simulink diagram similar to the example shown inFig. 7(a) and (b). The Simulink module is used to measurethe input–output response of the experimental piezoactu-ator.

2. Apply a triangle signal with different amplitudes to actuatethe piezoactuator and then measure the piezoactuator’s re-sponse.



Fig. 9. The main portion of an example Matlab code for obtaining the transfer function model of the piezobimorph actuator.

3. Plot the measured output with respect to the applied inputsignal (hysteresis curves).

4. Quantify the amount of output hysteresis by calculating thedifference between the measured output between the as-cending and descending hysteresis curves. The calculatedvalue is then compared to the range of the actuator, and themaximum measured hysteresis in the output typically fallsbetween 10% and 20% of the total displacement range.

5. Construct two simple models for hysteresis: a polynomialmodel (e.g., quadratic model by curve fitting) and a lookuptable model that relates the input to the output signal. Thesemodels can then be used for feedforward hysteresis com-pensation [38], [39].

E. Lab 3: Feedback Control Design Experiment

The objective of this laboratory experiment is to teach theprocess of designing, simulating, implementing, and tuning afeedback controller for piezoactuators. The model of the dy-namics obtained in Section V-C is used in this experiment. Theprocedures require students to do the following.

1. Design the notch filter by following the above pre-vious discussion (see Section IV-B). The design involvestuning the parameters of the notch filter using MATLAB,and comparing the gain margin before and after by ana-lyzing the frequency response.

2. Design a feedback controller (PID, lead-lag, etc.) toimprove the transient and steady-state response of thepiezoactuator. The objective is to reduce the settlingtime (e.g., by over 70% reduction) and the steady-stateerror due to a step reference. An example of a Simulinkblock diagram and measured step response from studentwork are shown in Figs. 7(c) and 10, respectively. Notethat in Fig. 7(c), the dSpace DAQ system (the blocksDS1104DAC_C 1 and DS1103ADC_CS in the figure)and the PI controller (PI Control block) are shown asexamples. Also, a Butterworth low-pass filter (the blockLow-pass Filter) is used to remove the measurementnoise in the feedback loop, where the order of the filter isexperimentally tuned.

3. Evaluate the design by observing and measuring thetracking results for a reference triangle trajectory at bothlow speed (2 Hz) and high speed (20 Hz). As shown in

Fig. 10. Example results for the feedback control experiment. The plot com-pares the step responses of the open-loop and the closed-loop system with andwithout the notch filter.

Fig. 11. (Top) Comparison of the output-tracking of triangle signal at 20 Hz inopen-loop, closed-loop PI control and closed-loop control with notch filter anda PI controller. (Bottom) Comparison of the corresponding tracking errors.

Fig. 11 for the 20-Hz case, the tracking performance issignificantly improved by using the notch filter and a PIcontroller.



TABLE IICOURSES AND MODULES INVOLVED IN THE IMPLEMENTATION

F. Lab 4: Feedforward Control Design Experiment

This lab teaches a simple example of model-based feedfor-ward control to address hysteresis-caused positioning error inpiezoactuators. The experiment uses the hysteresis model ob-tained from the hysteresis modeling experiment discussed pre-viously. First, the measured input-versus-output data is inverted(lookup table approach) such that for a given desired outputvalue, a corresponding input value is found through interpola-tion. Then, the input is applied to the piezoactuator to compen-sate for the hysteresis effect. The uncompensated and compen-sated responses are measured and compared to evaluate the per-formance of the feedforward method.

VI. MODULE IMPLEMENTATION

The modules were implemented at Virginia CommonwealthUniversity (VCU), Richmond, and Iowa State University (ISU),Ames. At VCU, the core courses involved were Process andSystem Dynamics (PSD, ENGR 315, Spring 2007 and 2008),a junior-level course on system dynamics and control, andMechatronics (EGRM 410, Fall 2007), a senior-level coursefocusing on the integration of mechanical, electrical, and com-puter systems in design. The PSD course was a prerequisiteto Mechatronics. At VCU, approximately 210 students wereenrolled in the three classes. At ISU, several modules wereimplemented in the senior-level, technical elective coursetitled Automatic Controls (ME 411) during Fall 2007. In thiscourse, 20 students were exposed to the teaching modules.Table II shows the modules implemented in each course, thematerials either replaced or supplemented by the modules, andthe approximate time required to present each module.

Because of limited instruction time, some standard coursematerial was condensed to make room for the new material.For example, the dc motor is a commonly used example for de-scribing the modeling of an electromechanical system. In thiscase, the dc motor is introduced in condensed form to makeroom for modeling the vibrational dynamics and creep effect of

a piezoactuator in both the PSD and Automatic Controls class.The dc motor lecture is typically covered in two lectures, but itwas condensed into a one lecture period. Then, the modeling ofthe piezoactuator’s dynamic effects (vibration and creep) waspresented in approximately two lectures, and analogies weredrawn between the dc motor and piezoactuator.

The modules outlined in Table I can be implemented individ-ually or as a group. For instance, the modeling modules 1–3 canall be presented to replace a traditional discussion on modelingof electromechanical systems such as dc motors in a system dy-namics class, or one module (lecture or lab) can replace onespecific topic to broaden a discussion or to bring in new tech-nology into the classroom. However, it is recommended that anintroduction to piezoactuators be presented prior to introducingany of the modules to provide a background and to motivatestudents to learn the new material (see Table II). Additionally,it is recommended that the control modules be presented afterthe modeling modules. If considered without the modeling mod-ules, the instructor should ensure that students are familiar withbasic concepts in system dynamics, such as Laplace transforms,transfer functions, and dynamics modeling.

Laboratory activities are an integral part of courses likemechatronics and automatic control. The developed laboratoryexperiments are primarily suited for such courses with a labcomponent. The laboratory modules listed in Table II wereimplemented starting the tenth week of the semester. Studentswere grouped into teams of four to work on each activity. Oneweek after working on a lab activity, each team was required tosubmit a laboratory report describing what they learned and toexplain their results.

VII. ASSESSMENT RESULTS

The impact of the modules was assessed for the PSD andMechatronics course at VCU. The objective was to determinewhether students gained a better understanding of piezoactu-ators and applications in nano- and biotechnology after inter-



TABLE IIIPRE-/POST-MODULE ASSESSMENT RESULTS BY COURSE

acting with the modules. Of the 210 students who interactedwith the modules during class time and in the laboratory at VCU,95.0% consented to participate in the assessment. All assess-ment procedures followed IRB protocol to ensure participantanonymity and confidentiality. The results reported here comefrom three courses, PSD Spring 2007 and 2008 and Mecha-tronics Fall 2007. Because the modules were only implementedin one class at ISU with a relatively small number of students

and the class was substantially different than thecourses at VCU, those results are not discussed.

The assessment consisted of questionnaires and focusgroups. Questionnaires were administered to students inPSD and Mechatronics on four separate occasions acrossthe semester: beginning of the semester (first two weeks ofinstruction), immediately prior to the implementation of theteaching module (between weeks 4 and 10), immediatelyfollowing the end of the instructional module, and at the endof the semester (last two weeks of instruction). Questionnairesinclude both open-ended and Likert-type items, and they werecompleted anonymously by students, with the exception of PSDSpring 2008 where linking of students’ pre- and post-moduleresponses was done in order to determine if there had beenchanges in students’ knowledge. Questionnaire items askedstudents about their knowledge, understanding, and interestrelated to nano/biotechnology and piezoactuators. Open-endeditems were scored for correctness with a possible point rangeof 0 to 5. Likert-type item responses ranged from 0 to 10,with increasing numbers indicating higher levels of interest orimportance. Focus groups were conducted with students duringthe last three weeks of the semester in order to gain additionalinsight and feedback regarding students’ perceptions of theinstructional modules.

The results of the premodule questionnaires were formative,and the post-module questionnaires were summative. Addi-tional data collected included students’ homework, project,and exam scores (results omitted for brevity). These were used

as summative measures to examine students’ learning of thecontent covered in the modules. The formative results wereused to give a snapshot of students’ general understandingof the material to better prepare the delivery of the material.Across the implementation of the project, questionnaires andassessment procedures were revised to accommodate changesin the modules and strengthen the quality of the data collected.

The results of the open-ended questionnaire items (mean andstandard deviation) by course are reported in Table III. A subsetof the data from the PSD Spring 2008 linking stu-dents’ pre- and post-module responses is shown in Table IV. Asubset of the total data (pre: and post: ; seeTable III for PSD Spring 2008) was considered because 37 pre-and post-questionnaires were linkable through an identifier.

A. Questionnaire Results

The pre- and post-module questionnaires (Table III) includeda series of five open-ended questions that asked specificallyabout nanotechnology and piezoactuators: 1) What is nanotech-nology? 2) What is a piezoactuator, why is it important? 3) Whatis the piezoelectric effect? 4) Identify a nano and/or biotech-nology that utilize a piezoactuator; and 5) What are the majorissues with high precision control of piezoactuators?1 The post-module questionnaires also included the following three Likert-type items: 1) How important are piezoactuators? 2) How ex-cited are you about nanotechnology? and 3) Rate your under-standing of modeling of piezoactuators. Students were asked torate their responses on a scale of either 0 to 10 or 0 to 5,2 withhigher numbers indicating higher levels of importance, excite-ment, or perceived understanding.

As shown in Table III, the standard deviations suggest thatthere was a high degree of variability in students’ knowledge of

1Question 2 was administered to students in PSD only, while question 5 wasonly administered to students in Mechatronics.

2In PSD—Spring 2008, the wording of the items and response scales wererevised slightly to provide better anchors for students’ responses.



TABLE IVRESULTS OF t-TESTS COMPARING POST-MODULE TO PRE-MODULE RESPONSES ON QUESTIONNAIRE ITEMS FOR PSD SPRING 2008

nanotechnology (question 1) prior to the module implementa-tion across the three classes. However, overall, students earnedan average score of 2.90 out of 5.0 points on thisitem, suggesting that prior to the modules students had a reason-able general knowledge of the topic. It is interesting to note thatthe Fall 2007 PSD class demonstrated a much stronger under-standing in their responses on this item, earning an average scoreof 4.29 when compared to students in Spring 2008class ( , ). A possible explanation is the in-structor’s expectation of students’ understanding increases withthe number of implementations, which impacts the scoring ofthe questionnaires.

Students in the PSD classes were asked to explain the piezo-electric effect as part of the pre- and post-module questionnaires(question 2 in Table III). Across the two classes, students earnedan average of 2.27 out of 5 points for their re-sponses to this item before implementing the module. After-ward, the average increased to 3.33 (SD=1.58). Similarly, whilestudents may be able to define nanotechnology generally, theyhave less knowledge of specific content related to piezoactua-tors at the premodule stage.

For questions 3 and 4, asking students to describe a piezoac-tuator and its importance and identifying applications that usepiezoactuators, respectively, results across the three coursesshowed a notable increase in the average at post-module, from2.17 to 2.94 for question 3 and 1.70 to 2.80 for question 4.Disaggregating the data by class shows no discernible patternwith regard to the three classes.

Finally, students in the Mechatronics class were asked aboutthe major issues with high precision control of piezoactuators.Out of a possible 5 points, students earned an average of 1.77

points at premodule, then 3.45 atpost-module. At premodule, this suggested that while studentsmay be familiar with nanotechnology and piezoactuators, theyhad only limited knowledge of specific issues related to their useor control.

Following implementation of the modules, students wereasked to rate the importance of piezoactuators and nanotech-

nology, their excitement about nanotechnology, their ownunderstanding of the subject matter, and the usefulness ofprojects and homework to gaining an understanding of thematerial. The response to the Likert-type questionnaires indi-cated that students rated the importance of piezoactuators asrelatively high, with 81.9% of students selecting 7 out of 10 orhigher for this item. These same students reported moderateaverage levels of excitement, 6.18, . Studentswere somewhat more conservative in their ratings of their ownunderstanding of the subject matter, the highest rating was 8 outof 10, with only 27.0% responding 7 or higher. Finally, studentswere asked if the project and homework assignments helpedthem to develop a better understanding of piezoactuators. Forthis item, approximately 31.8% of students strongly agreed orfelt that the assignments were very helpful (a response of 7 orhigher out of 10), with an average rating of 5.50, .

The results between pre- and post-module questionnaires inTable III show differences in students’ responses to the open-ended questionnaire items. However, in the first two implemen-tations of the modules (PSD Spring 2007 and Mechatronics Fall2007), there was no mechanism for linking students’ pre- andpost-module responses, so there was no way to determine if thesame students answered both the pre- and post-module ques-tionnaires. This made it difficult to determine if the higher scoreson the post-module questionnaire items were due to changes instudents’ knowledge or simply because a different subset of stu-dents with greater knowledge responded.

However, in the Spring 2008 PSD course, the assessmentplan was modified to allow for linking of students’ pre- andpost-module responses, in order to determine if there had beenchanges in students’ knowledge. As can be seen in Table III,the post-module means on all but the first question were higherthan the premodule means. A subset of the datafrom students who had complete the pre- and post-module re-sponses were analyzed using t-tests to examine if the differencesin scores from pre- to post-module were statistically significant.The results can be found in Table III. With the exception of ques-



tion 1 “What is nanotechnology?” there were statistically sig-nificant differences between scores on the pre- and post-moduleresponses to the questionnaire items. Students scored signifi-cantly higher after the implementation of the module on theitems asking students to explain what a piezoactuator is and whyit is important ( , ), the piezoelectric effect( , ), and identify a nano and/or biotech-nology that utilizes a piezoactuator ( , ).For each of these items, the post-module mean was over 0.80with a standard deviation higher than the premodule mean.

There was also a statistically significant difference betweenpre- and post-module responses for the item asking students torate their own understanding of nanotechnology on a five-pointscale ( , ). Interestingly, the averagerating was higher before module implementation than it wasafter module implementation (4.32 versus 3.27, respectively).The mean difference represents an approximate 0.89 SD declinein students’ rating of their understanding of nanotechnology.While this may seem counter-intuitive, this result is often seenin projects of this type. Once individuals have the opportunityto engage with content that is unfamiliar, they often revise theirperceptions of their understanding based on new information,which results in lower ratings post-intervention.

The pre- to post-module comparisons suggest that studentsdid, in fact, experience a positive change in their knowledgeand understanding of nanotechnology and piezoactuators. Stu-dents demonstrated a stronger understanding of piezoactuators,the piezoelectric effect, and had greater ability to identify anano- or biotechnology that used piezoactuators after the mod-ules had been implemented. A control group was not consideredin this study, and the comparisons were thus limited to a singleclass. Therefore, it is impossible to attribute the positive changesin students’ scores directly to the implementation of the mod-ules. For example, after being introduced to the content, studentsmight have chosen to seek out additional information indepen-dently, which could also explain the significant results. How-ever, the fact that there were positive changes suggests that theuse of these modules to deliver nanotechnology and piezoactu-ator-related content to ME students might have some merit andwarrants further investigation through broader implementationand evaluation.

B. Focus Groups

Ten students participated in voluntary focus groups andprovided their perceptions about the developed lecture andlaboratory components. With the exception of one student, allstudents expressed that this was their first formal experiencewith this material and that, prior to this, they had encounteredtopics related to nano- and biotechnologies primarily throughtheir own independent reading or investigation. Echoing stu-dents’ responses on the questionnaires, students commentedthat they found the material “very interesting” and are “excited”to learn more and broaden their understanding of applicationsrelated to piezoactuators. In terms of the lecture and labora-tory materials themselves, students suggested that having theopportunity to “spend more time” and get “more information”in “greater depth” would be extremely useful. Participantsindicate that having additional opportunities to “play with the

technology” and “have visuals to see how it works” in combi-nation with substantive feedback on their assignments wouldgreatly enhance their learning. Students also expressed an in-terest in being provided with additional information regardingthe materials themselves, such as what they cost and where theycan be purchased or accessed. Finally, students suggested thatgiven how new and rapidly expanding this area is both in termsof application and research, providing an introduction earlier inthe program would increase student interest, as would seminarson advanced topics devoted to this material.

C. Additional Considerations

One of the main challenges of implementing the moduleswas time. For example, the modeling modules involved severalhour-long lectures that can be time-consuming. Without carefulpreparation, time can be taken away from covering other impor-tant course material. Also, students’ limited exposure to non-linear systems posed a challenge when discussing the hysteresisbehavior. The instructor found it difficult to keep students mo-tivated in their learning and considers that this may be becausestudents could not directly relate to hysteresis. As for the exper-iments, for a large class, a large number of experimental setupswere required, which can be costly to both produce and main-tain.

VIII. CONCLUSION

The development of lecture and laboratory teaching modulesthat focus on modeling and control of piezoactuators for the MEundergraduate curriculum was described. The modules were de-signed for dynamics and control courses as well as for mecha-tronics courses. The entire suite of modules can be used as awhole, or in part, to teach concepts such as dynamics modeling,electromechanical coupling, and feedback and feedforward con-trol using the piezoactuator as an example system. An exper-imental piezoactuator platform was designed to give studentshands-on experience in modeling and controlling piezoactua-tors for high-precision positioning applications. The teachingmodules were implemented in one junior-level and two senior-level classes in system dynamics, control, and mechatronics.The t-test was used to test the hypothesis, and through linkedpre- to post-module comparisons, assessment results indicatedthat students experienced a positive change in their knowledgeand understanding of the material.

REFERENCES

[1] M. C. Roco and W. S. Bainbridge, “Societal implications ofnanoscience and nanotechnology,” National Science Foundation,Tech. rep., 2001.

[2] S. O. R. Moheimani and A. J. Fleming, Piezoelectric Transducers forVibration Control and Damping (Advances in Industrial Control).New York: Springer, 2006.

[3] R. Wiesendanger, Scanning Probe Microscopy and Spectroscopy.Cambridge, U.K.: Cambridge Univ. Press, 1994.

[4] B. Edinger, M. Frecker, and J. Gardner, “Dynamic modeling of an inno-vative piezoelectric actuator for minimally invasive surgery,” J. Intell.Mater. Syst. Structures, vol. 11, no. 10, pp. 765–770, 2000.

[5] D. G. Alciatore and M. B. Histand, Introduction to Mechatronics andMeasurement Systems, 2nd ed. Boston, MA: McGraw-Hill, 2003.

[6] W. J. Palm, III, System Dynamics. Boston, MA: McGraw-Hill, 2005.[7] “Engineering Accreditation Commission: 2005–2006 Criteria for Ac-

crediting Engineering Programs,” ABET, 2004.



[8] S. Ashley, “Getting a hold of mechatronics,” Mech. Eng. Mag., vol.119, no. 5, pp. 60–63, 1997.

[9] S. Meek, S. Field, and S. Devasia, “Mechatronics education in theDepartment of Mechanical Engineering at the University of Utah,”Mechatronics, vol. 13, pp. 1–11, 2003.

[10] V. Giurgiutiu, J. Lyons, D. Rocheleau, and W. Liu, “Mechatronics/microcontroller education for mechanical engineering students at theUniversity of South Carolina,” Mechatronics, vol. 15, pp. 1025–1036,2005.

[11] B. Furman and E. Moen, “Evaluation of alternative microcontrollers formechatronics education,” Comput. Educ. J., vol. 15, no. 3, pp. 22–33,2005.

[12] L. Breger, “Creative design class on piezo- and pyroelectricity,” inProc. Frontiers in Educ. Conf., 1989, pp. 167–170.

[13] L. Penrod, D. Talley, J. Froyd, R. Caso, D. Lagoudas, and T. Kohutek,“Integrating smart materials into a first-year engineering curriculum:A case study,” in Proc. Frontiers in Educ. Conf., 2002, vol. 2, pp.F3B-21–F3B-26.

[14] T. Chang, P. Jaroonsiriphan, and X. Sun, “Integrating nanotechnologyinto undergraduate experience: A Web-based approach,” Int. J. Eng.Educ., vol. 18, no. 5, pp. 557–565, 2002.

[15] S. Roundy, P. K. Wright, and J. M. Rabaey, Energy Scavenging forWireless Sensor Networks. Norwell, MA: Kluwer, 2004.

[16] “Piezoelectric ceramics: Principles and applications,” APC Interna-tional, Ltd, Mackeyville, PA, 2002.

[17] D. Croft, G. Shed, and S. Devasia, “Creep, hysteresis, and vibrationcompensation for piezoactuators: Atomic force microscopy applica-tion,” J. Dyn. Syst., Meas., Control, vol. 123, pp. 35–43, 2001.

[18] W. P. Mason, “Quartz crystal applications,” in Quartz Crystals forElectrical Circuits, R. A. Heising, Ed. New York: Van Nostrand,1946, pp. 11–56.

[19] W. D. Callister, Materials Science and Engineering: An Introduc-tion. New York: Wiley, 1994.

[20] K. K. Leang, Q. Zou, and S. Devasia, “Feedforward control of piezoac-tuators in atomic force microscope systems: Inversion-based compen-sation for dynamics and hysteresis,” IEEE Control Syst. Mag., vol. 29,no. 1, pp. 70–82, Feb. 2009.

[21] K. Ogata, System Dynamics, fourth ed. Englewood Cliffs, NJ: Pren-tice-Hall, 2004.

[22] L. E. Malvern, Introduction to the Mechanics of a ContinuousMedium. Englewood Cliffs, NJ: Prentice-Hall, 1969.

[23] K. K. Leang and S. Devasia, “Design of hysteresis-compensating itera-tive learning control for piezo positioners: Application to atomic forcemicroscopes,” Mechatronics, vol. 16, no. 3–4, pp. 141–158, 2006.

[24] D. Hughes and J. T. Wen, “Preisach modeling of piezoceramic andshape memory alloy hysteresis,” Smart Mater. Struct., vol. 6, pp.287–300, 1997.

[25] P. Ge and M. Jouaneh, “Generalized Preisach model for hysteresisnonlinearity of piezoceramic actuators,” Precision Eng., vol. 20, pp.99–111, 1997.

[26] D. C. Jiles and D. L. Atherton, “Theory of ferromagnetic hysteresis,”J. Magn. Magn. Mater., vol. 61, pp. 48–60, 1986.

[27] I. D. Mayergoyz, Mathematical Models of Hysteresis. New York:Springer-Verlag, 1991.

[28] S. Salapaka, A. Sebastin, J. P. Cleveland, and M. V. Salapaka, “Highbandwidth nano-positioner: A robust control approach,” Rev. Sci.Instr., vol. 73, no. 9, pp. 3232–3241, 2002.

[29] R. C. Barrett and C. F. Quate, “Optical scan-correction system ap-plied to atomic force microscopy,” Rev. Sci. Instr., vol. 62, no. 6, pp.1393–1399, 1991.

[30] K. Dirscherl, J. Garnaes, L. Nielsen, J. F. Jogensen, and M. P. Sorensen,“Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci.Technol. B, vol. 18, no. 2, pp. 621–625, 2000.

[31] S. Devasia, E. Eleftheriou, and S. O. R. Moheimani, “A survey of con-trol issues in nanopositioning,” IEEE Trans. Control Syst. Technol., vol.15, no. 5, pp. 802–823, Sep. 2007.

[32] Y. Wu and Q. Zou, “Iterative control approach to compensate for boththe hysteresis and the dynamics effects of piezo actuators,” IEEE Con-trol Syst. Technol., vol. 15, no. 5, pp. 936–944, Sep. 2007.

[33] H. Y.-F. Lam, Analog and Digital Filters: Design and Realization.New York: Prentice-Hall, 1979.

[34] I. D. Mayergoyz and A. A. Adly, “Numerical implementation of thefeedback Preisach model,” IEEE Trans. Magn., vol. 28, no. 5, pp.2605–2607, Sep. 1992.

[35] H.-J. Lee and D. A. Saravanos, “The effect of temperature dependentmaterial properties on the response of piezoelectric composite mate-rials,” J. Intell. Mater. Syst. Structures, vol. 9, pp. 503–508, 1998.

[36] F. Lowrie, M. Cain, M. Stewart, and M. Gee, “Time dependentbehaviour of piezo-electric materials,” National Physical Laboratory,Tech. rep., 1999.

[37] Y. Shan, J. E. Speich, and K. K. Leang, “Low-cost reflective infraredsensors for sub-micro-level position measurement and control,” IEEE/ASME Trans. Mechatronics, vol. 13, no. 6, pp. 700–709, Dec. 2008.

[38] J. F. Jorgensen, K. Carneiro, L. L. Madsen, and K. Conradsen, “Hys-teresis correction of scanning tunneling microscope images,” J. Vac.Sci. Technol. B, vol. 12, no. 3, pp. 1702–1704, 1994.

[39] P. Ge and M. Jouaneh, “Tracking control of a piezoceramic actuator,”IEEE Trans. Control Syst. Technol., vol. 4, no. 3, pp. 209–216, Jul.1996.

Kam K. Leang (M’08) received the B.S. and M.S. degrees in mechanical en-gineering from the University of Utah, Salt Lake City, in 1997 and 1999, re-spectively, and the Ph.D. degree from the University of Washington, Seattle, inDecember 2004.

He joined the Department of Mechanical Engineering, University of Nevada-Reno, in 2008. From 2005 to 2008, he taught in the Mechanical EngineeringDepartment at Virginia Commonwealth University, Richmond. His research in-terests include modeling and control of piezoactuators for scanning probe mi-croscopy applications, fabrication and control of electroactive polymers, mecha-tronics, and design of microelectromechanical systems (MEMS) for nanotech-nology.

Dr. Leang is a Member of ASME and SPIE.

Qingze Zou received the B.S. degree in automatic control from the Universityof Electronic Science and Technology of China (UESTC), Chengdu, China, in1994, the M.S. degree in mechanical engineering from Tsinghua University,Beijing, China, in 1997, and the Ph.D. degree in mechanical engineering fromthe University of Washington, Seattle, in 2003.

He joined the Department of Mechanical Engineering, Iowa State Univer-sity, Ames, as an Assistant Professor in 2004. His primary research interests arein inversion-based output tracking theory, high-speed imaging and broadbandcharacterization of soft materials using scanning probe microscope (SPM), andhigh-throughput nanomanufacturing.

Dr. Zou is a recipient of the NSF CAREER Award in 2009. He is a Memberof ASME.

Gina Pannozzo received the B.A. degree in psychology from Binghamton Uni-versity, State University of New York (SUNY), Binghamton, in 1991, and theM.A. and Ph.D. degrees in educational psychology from the University at Buf-falo, SUNY, Buffalo, in 1994 and 2005, respectively.

She joined the Foundations of Education Department, Virginia Common-wealth University, Richmond, in August 2005. Her research interests includestudent encouragement in school, classroom and school climate, culture andsense of community, and impact of small class size on students and teachers.


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