An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> The development and application of a new dynamic measuring method of capacitance variation of piezoelectric materials, especially of lead zirconate titanate (PZT) ceramics, with an alternating electric field are presented. This method makes it possible to separate the capacitance variation due to nonlinear effect from that due to temperature change, to obtain the adiabatic nonlinear coefficients, to fix the sign of the nonlinear coefficient, and to determine each order of coefficients, separating the orders of the capacitance variation as a function of the applied electric field. <s> BIB001 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> A nonlinear lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and, in particular, for microrobotic applications requiring accurate position and/or force control. In formulating this model, the authors propose a generalized Maxwell resistive capacitor as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data. Validation is followed by a discussion of model implications for purposes of actuator control. <s> BIB002 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Piezoelectric transducers are known to exhibit less hysterisis when driven with current or charge rather than voltage. Despite this advantage, such methods have found little practical application due to the poor low-frequency response of present current and charge driver designs. This paper introduces the compliance feedback current driver containing a secondary voltage feedback loop to prevent DC charging of capacitive loads and to compensate for any voltage or current offsets within the circuit. Low-frequency bandwidths in the milli-Hertz range can be achieved. One application for such a device is the synthesis of piezoelectric shunt damping circuits. A number of block diagram transformations are presented to simplify the realization of analog or digital admittance transfer functions from a schematic circuit diagram. <s> BIB003 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Nanotechnology is the science of understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing nanoscale science, engineering, and technology, nanotechnology involves imaging, measuring, modeling, and manipulation of matter at this level of precision. An important aspect of research in nanotechnology involves precision control and manipulation of devices and materials at a nanoscale, i.e., nanopositioning. Nanopositioners are precision mechatronic systems designed to move objects over a small range with a resolution down to a fraction of an atomic diameter. The desired attributes of a nanopositioner are extremely high resolution, accuracy, stability, and fast response. The key to successful nanopositioning is accurate position sensing and feedback control of the motion. This paper presents an overview of nanopositioning technologies and devices emphasizing the key role of advanced control techniques in improving precision, accuracy, and speed of operation of these systems. <s> BIB004 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Piezoelectric meso- and microactuator systems required for manipulation or assembly of microscale objects demand reliable force and/or displacement information. Available sensors are prone to dimension restrictions or precision limitation. Self-sensing method, based on the electric charge measurement, may represent a solution in terms of cost-effectiveness and integration, the actuator performing simultaneously as its own sensor. This paper presents a self-sensing method dedicated to free uni- and bimorph piezocantilevers but can also be adapted to other piezoactuator types. The integrated electric current, used to convert the charge, can be compensated against piezoelectric material nonlinearities to provide accurate displacement information. The advantages relative to existing self-sensing methods consist in the ability to keep this displacement information for long-term periods (more than a thousand seconds) and in the reduction in signal noise. After introductive issues related to the method the base ... <s> BIB005 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Piezoelectric actuators are typically modeled as capacitive elements for control purposes. An important model parameter, clamped capacitance, is traditionally considered constant and obtained through offline measurements. However, the capacitance value changes with operating conditions such as electric fields, environmental temperatures, and aging. In addition, traditional capacitance measurements are not hysteresis free. In this research, a hysteresis independent real time capacitance measurement technique is proposed. This is achieved by superimposing a high frequency ripple over the normal control voltage signal and comparing the resulting current signal to the voltage ripple. Since the mechanical bandwidth of the actuator is much lower than the ripple voltage, no measurable movement is induced by the measurement technique, and a clamped capacitance is determined. It is demonstrated that the measurement is largely independent of hysteresis and it shows good agreement with an LCR meter. The on-line capacitance measurement is very useful for characterising piezoelectric actuators and for implementing more robust control schemes. <s> BIB006 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Piezoelectric stack actuators are commonly used in a number of different position control applications due to their compactness, high resolution, speed and dynamic properties. For accurate position control, position feedback has traditionally been employed since the parameters of the constitutive equations change with temperature and age. In addition, the identification of constitutive parameters is complicated by the presence of hysteresis voltage that is not accounted for in the linear constitutive equations. Recently, there has been a push towards sensor less control. This approach requires an accurate identification technique of the constitutive parameters. For this purpose, the constitutive equations used to identify the piezoelectric parameters are usually considered linear under a low electric field. However, at larger driving voltages hysteresis effect become significant and the parameters identified at lower excitation levels are no longer valid. This is traditionally addressed by providing constitutive parameters as a function of applied voltage. However, this is usually done for the ascending hysteresis branch only. The changes due to the descending hysteresis branch are commonly ignored. As a result, it is often difficult to match the constitutive equations to experimental data. We propose a new identification procedure that is based on online capacitance measurements of the piezo actuators. These measurements indicate, that the piezo capacitance is not constant, but a linear function of linearized piezo voltage. Using this result, we are able to construct values for the remaining constitutive parameters that are largely independent of piezo voltage. The resulting constitutive equations match our experimental actuator performance well no matter where they are applied in the hysteresis loop. This new identification technique then provides more accurate piezo models that are very useful for developing sensor less control strategies for piezo actuators.© 2011 ASME <s> BIB007 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Soft piezoelectric actuators are extensively used in micro- and nanopositioning applications. Traditional sensorless position control approaches use a hysteresis mapping between voltage and position in a voltage feedforward control scheme in order to compensate for hysteresis errors. However, several factors such as frequency, temperature, and aging influence this mapping. Recently, charge control for positioning is also attracting interest among researchers due to the linear relationship between position and charge. However, a sophisticated hardware design is required to minimize charge drift. In this study, a new sensorless position control technique is proposed which requires neither an accurate inverse mapping nor a sophisticated charge amplifier in order to compensate for hysteresis. A constitutive relationship is employed to infer position from charge measurement through current integration. To eliminate drift from the charge-based measurement, an observer is presented in this study which uses a second self-sensing position estimate that is based on the variation of effective piezoelectric capacitance with stroke. The proposed observer is tested as a position feedback sensor inside a simple integrating control loop and applied to step profiles of variable stroke and sinusoidal profiles of constant and mixed frequencies. The responses are compared with a laser interferometer and the maximum observer error between the laser and the observer is 0.89 μm ( 3% of the maximum stroke) over a frequency range of 10 to 100 Hz. <s> BIB008 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Abstract Piezoelectric displacement contains hysteresis and creep properties. Therefore, a displacement sensor is indispensable in precise positioning devices; however, the additional space and cost are problems. On the other hand, self-sensing methods that utilize the piezoelectric actuator itself as the displacement sensor have been proposed. With these self-sensing methods, precise positioning becomes possible without an additional displacement sensor. We developed a self-sensing method utilizing the non-hysteresis relationship between the permittivity change and the piezoelectric displacement. Furthermore, a differential current measurement method using two piezoelectric elements with a bimorph actuator could improve the positioning accuracy. In this study, we examine the control of a positioning stage using two multilayered piezoelectric actuators by applying the differential current measurement method for self-sensing control. The results indicate that the differential current measurement method is effective for precise positioning control. The positioning errors due to hysteresis decreased from 0.8 μm to 0.1 μm for a 10 μm displacement range. In addition, permittivity feedback control could compensate for the creep property. <s> BIB009 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Real-Time PEA's Electric Properties Measurement <s> Abstract This article extends the conventional permittivity change based displacement self-sensing technique for piezoelectric actuators to an impedance change based displacement–force self-sensing technique. The presented methodology evaluates changes in capacitance and resistance at an electrical resonance frequency and uses a third order polynomial fit to estimate displacement and force. Experimental validations show a mean error of 1.8%, and an error standard deviation of 1.9% for displacement and a mean error of 1.7%, and an error standard deviation of 1.8% for force. <s> BIB010
SSA based on the PEA's change of electrical properties relates to piezoelectric devices used for simultaneous control and displacement sensing based on the impedance variation thereof. Since the impedance variation of the PEA is a consequence of its deformation, the SSA discussed here uses a real-time measurement of the PEA's impedance to reconstruct its deformation. This is made possible thanks to a lowamplitude/high-frequency excitation signal v d that is added to a control signal v c , which actuates the PEA (see Fig. 10 ). The excitation signal, also called detection signal, does not generate any deformation and only serves to evaluate the PEA's impedance variation. The control input signal v c is solely responsible for the PEA's deformation and is generated according to the desired trajectory. To successfully estimate the displacement of the PEA from the measurement of the variation of its impedance, two elements are necessary: 1) a proper separation of the control and impedance detection signals enabling on to control the PEA and derive precise PEA's deformation information; 2) the design of the estimator that uses the detection signal to estimate the PEA's generated displacement. Huang et al.  patented a bridge circuit for both signals' separation (control and impedance detection signals) and the estimation of the PEA's generated displacement. The proposed bridge circuit is connected to a piezoelectric element and to a voltage-controlled element. The voltage-controlled element (capacitor and resistor in series) is supposed to mimic the electrical response parameters of the piezoelectric element and match at all times the current flowing out of the PEA Fig. 10 . Block diagram: simultaneous control and displacement measurement of a PEA using SSA based on the PEA's change of electrical properties. F ext is the applied external force, θ is the temperature variation, and g i (·)| i=1,2,3 represent the estimator used to reconstruct the PEA's displacementδ, perceived forceF ext , and surrounding temperature variation θ from the real-time calculation of its impedance magnitude change |Z | and the applied input voltage v c . Fig. 11 . Block diagram of the self-sensing bridge circuit for controlling and sensing the response of PEAs  . 50-driving input stage, 80-v c , 78-v d , 14-PEA, 70-reference arm of the bridge, 62-actuator arm of the bridge circuit, and 84-current flowing out of the PEA. (identified as 84 in Fig. 11 ). The current flowing out of the PEA reflects the dynamic impedance thereof. The difference between the actuator arm and the reference arm is used to adjust the voltage-controlled element and to indicate the deformation of the PEA. In addition, the system has a compensating circuit connected to the bridge circuit and the driving stage for deriving a compensation signal. The compensation signal is added to v c and v d in order to provide a damping correction, a stiffening correction, and an inertial conditioning correction based on the signal received from the low-frequency difference amplifier. Whereas SSA is supposed to allow a reduction in cost and space occupation, the proposed method by Huang et al.  is more likely to be bulkier than the position sensor it is supposed to replace due to the important number of elements used for its implementation. Furthermore, the control and detection voltage, v c and v d , respectively, to be applied to the system are chosen so that they do not cause saturation or nonlinear behavior of the PEA. This limits the control voltage to a few tens of volts and does not exploit the full range of the piezoelectric element actuation. Instead of a single electrical circuit to obtain the impedance detection signal and estimate the PEA's generated displacement, Saigusa and Morita BIB009 opted for a two-stage approach. First, a differential current measurement associated with a lock-in amplifier captures the PEA's impedance variation of a bimorph actuator. Thence, the estimator, a thirdorder polynomial of the measured current amplitude, is used to estimate the PEA's generated displacement. Whereas this method is supposed not to be restricted as to the input voltage to be applied for actuation and detection, considering the relative permittivity of the PEA as the unique parameter to estimate the generated displacement thereof is only accurate for small deformation of the piezoelectric element and a limited range of the detection signal frequency. Indeed, the authors made two hypotheses for their approach to hold true: 1) the piezoelectric element is modeled as a capacitor and 2) the permittivity is proportional to the current amplitude because the dimensions of the PEA, such as the thickness and electrode size, can be considered to be constant. For the first hypothesis, the equivalent electric model of a piezoelectric element is frequency-dependent, ranging from a capacitor to an inductor. Therefore, modeling the PEA as a capacitor is only accurate for a fixed frequency range of the detection signal. For the second hypothesis, only small deformations of the PEA in the x-direction may have to neglect the deformation in the other directions. Nevertheless, a more valid approach would suggest linking the current amplitude to the capacitance variation of the piezoelectric element. Thence, the capacitance variation would be used to estimate the PEA's generated displacement BIB006 , BIB001 , BIB007 . Furthermore, a lock-in amplifier is an expensive and cumbersome instrument that hindrances the cost and space reduction that SSA is supposed to bring. Seethaler  patented an apparatus and method for in situ impedance measurement of a PEA located in a fuel injector of a combustion chamber of an internal combustion. They suggested the use of a voltage sensor, a current sensor, and a computer for a real-time computation of the PEA's impedance variation. The proposed method uses a discrete Fourier transform (DFT) to extract the voltage and current coefficient from the discrete frequency domain and compute the PEA's impedance as a ratio of the voltage and current at the detection frequency f d , that is where v d and I d represent the digitized detection voltage and current, respectively. Referring to (7) , the impedance Z modeling the PEA includes a resistor R in series with the PEA's capacitance C pea . The conducted experiment to derive this model indicated a phase shift of 60 • between v d and I d . Although other configurations can be used to produce the same phase shift, the authors opted for a resistor and capacitor in series. The proposed in situ impedance measurement was used by Mansour and Seethaler BIB010 in a third-order polynomial fit to estimate the PEA's generated displacement and the force applied thereto. To the best of our knowledge, the apparatus and method suggested in  constitute the most packageable implementation for SSA based on PEA's change of electrical properties. SSA based on piezoelectric direct effect uses charge measurement to infer the PEA's generated displacement. This technique faces a challenge with charge drift due to offset currents. To eliminate the charge drift and allow static and quasi-static applications, Ivan et al. BIB005 presented a simplified current integrator circuit (modified charge amplifier). However, this requires additional circuitry. For SSA based on the PEA's change of electrical properties, such as the one introduced in BIB007 , the PEA's generated displacement is obtained from a real-time measurement of the effective capacitance of the PEA. However, this technique suffers from considerable noise and hence can only be used for slow operations. Islam and Seethaler BIB008 developed a hybrid position observer (HPO) that fused the capacitance-based SSA estimate with the charge-based SSA estimate into a single high-quality position estimate (see Fig. 12 ). The first position estimate uses the well-documented linear relationship between charge and position BIB004 , BIB005 , BIB002 , BIB003 , which provides a highly dynamic position signal that unfortunately suffers from drift due to the charge leakage. The second position estimate is obtained from the relationship between effective actuator capacitance and position BIB006 , BIB007 . Due to high-frequency noise, this second relationship can only provide low-frequency position estimates. However, since drift in the first estimate is a low-frequency phenomenon, it can be eliminated with the Fig. 12 . Flowchart of the hybrid SSA position observer BIB008 .C p is the PEA effective capacitance andx is the PEA's position estimate using the hybrid SSA observer. U ≡ v c and U r ≡ v d . second estimate using the HPO. Once a reliable position signal is achieved, it can be used in a traditional feedback controller replacing the dedicated position sensor.