An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <s> The possibility of using a single piezoelectric element simultaneously as both a structural actuator and collocated sensor is investigated. The coupled actuator and sensor equations for an arbitrary elastic structure with piezoelectric elements are developed using an assumed modes energy method. Examination of these equations suggests a simple implementation of collocated strain or strain rate sensing using a voltage driven piezoelectric element. The properties of such a collocated strain or strain rate sensor are presented. The general equations are applied to the case of a cantilevered beam with surface mounted piezoceramics. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with a single piezoelectric element used for collocated strain rate feedback. <s> BIB001 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <s> In this paper, self-sensing control of a micro-actuator for the hard disk drive is presented. The micro-actuator is a suspension driving type. The micro-actuator uses a PZT actuator pair, installed on the assembly of the suspension. The self-sensing micro actuator can be used to form a combined actuation and sensing mechanism. Direct velocity feedback control and positive position feedback control of a self-sensing microactuator for an HDD is presented. The experimental results show that the direct velocity feedback controller and the positive position feedback controller are effective in suppressing the vibration modes. Experiments successfully demonstrate that the self-sensing actuator can be used for active feedback control of the HDD suspension assembly vibration. <s> BIB002 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <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> BIB003 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <s> This contribution is concerned with self-sensing actuation (SSA) for the adaptive vibration control of smart structures with piezoelectric actuators. The electro-mechanical model of a Kirchhoff plate equipped with two piezoelectric patches is rewritten in the form of an infinite dimensional port controlled Hamiltonian system with dissipation (PCHD) where collocation of input and output is achieved by SSA. In the case of piezoelectric actuators, self sensing requires a robust separation of electric current due to the direct piezoelectric effect from the measured electric current. Because of the unfavorable ratio of these two signals, the design of an approximate observer for the electric current due to the direct piezoelectric effect is proposed. The control design goal is the asymptotic suppression of a harmonic disturbance with unknown frequency, amplitude and phase. The control law is derived for the plant augmented by an appropriate exosystem, which models the properties of the disturbance. The novelty of this contribution is the extension of the control design methods from the finite dimensional case to the infinite dimensional one. The stability analysis for the infinite dimensional system is based on the concept of L"2-stability and the small gain theorem. Vibration attenuation around a dominant eigenfrequency is demonstrated by simulation and experiment. <s> BIB004 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <s> Self-sensing technique consists of using an actuator as a sensor at the same time. This is possible for most actuators with physically reversible principle such as piezoelectric materials. The main advantages of self-sensing are: 1) the embeddability of the measurement technique, and 2) its low cost as no additional sensor is required. This paper presents a self-sensing technique for piezoelectric actuators used in precise positioning applications like micromanipulation and microassembly. The main novelty is that both displacement and force signals can be simultaneously estimated. This allows a feedback control using one of these two signals with a display of the other signal. To demonstrate this advantage, a robust $H_\infty$ feedback control on displacement with real-time display of the force is used as an application of the proposed self-sensing technique. In this paper, experimental results obtained with a piezoelectric cantilever actuator validate and demonstrate the efficiency of the proposed self-sensing. <s> BIB005 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <s> This paper proposes a self-sensing measurement technique to perform the precise estimation of the displacements along two axes in a two-degrees-of-freedom (2-DOF) piezoelectric actuator. For that, a new electrical circuit scheme that permits charge amplification is first proposed to match the different electrodes combination of the 2-DOF actuator. Then, a new bivariable observer that precisely estimates the displacements is calculated and implemented experimentally in a cascade with the electrical circuit to complete the self-sensing. The experimental tests and results verification with external sensors revealed that the measured displacements given by the developed self-sensing measurement technique derive better than a micron of precision which well fits to micromanipulation applications. Discussion about the features and the performances improvement perspectives of the suggested approach are presented at the end of the paper. <s> BIB006 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> D. Quasi-Static SSA Based on the Piezoelectric Direct Effect <s> This letter presents a displacement self-sensing method for piezoelectric actuators that takes into account the effect of the deformation of these latter on their electrical impedance. A self-updating digital electrical impedance equivalent to that of the piezoelement is suggested in order to overcome the mismatch problem met when considering a static analog electrical impedance as classically used. Then, the design of an observer that performs a thorough separation of the electric current due to the direct piezoelectric effect from the measured electric current is proposed in order to estimate the piezoelectric actuator displacement. The experimental results validate the proposed approach and demonstrate the efficiency of the developed self-sensing circuit and its observer to estimate the displacement of the piezoceramics actuator for long duration measurement of constant step signal. <s> BIB007
The charge-based SSA implementation relies on the linear charge-deformation relationship of PEAs, and it can be enhanced through the optimization of the PEA's geometry and constituent materials choice. However, when implementing the charge-based SSA, the charges are not directly measured but rather derived from current measurement (or voltage measurement for voltage-based SSA), that is, the rate of change of strain is measured rather than the strain itself. As a result, charge-and voltage-based SSAs have been essentially used for vibration control BIB002 , BIB001 , BIB004 . Ivan et al. BIB003 adopted the already existing antiparallel compensation scheme by Hagood and Anderson BIB001 and added an integrator amplifier to enable static and quasi-static SSA (see Fig. 8 ). In this approach, the antiparallel compensation allows the discrimination of the strain-induced currentQ δ fromQ d , the current due to the dielectric effect of the PEA. The integrator amplifier makes it possible to reconstruct Q δ fromQ δ . Moreover, a leakage resistor R L is included to account for the leakage current. The reconstructed strain-induced charges Q δ is then used for a static or quasi-static estimation of the PEA's deformation. This approach has been implemented and has demonstrated good potential for static and quasi-static charge-based SSA BIB005 , BIB006 ,  . As for previous cases of charge-based SSA, the main disadvantage of this approach is the difficulty in completely offsettingQ d . Indeed, even for this approach, the reference capacitor C r must match the PEA's capacitance C pea at all times for the charge-based SSA implementation to succeed. First, C r and C pea need to have the same relaxation time, that is, τ r = τ pea . Second, since C pea value changes as a function of the control voltage, external force, temperature, and so on, one cannot afford to use an offsetting capacitor C r with a constant value. The dynamic behavior of the PEA electric impedance implies that considering only a static equivalent model in an SSA circuit will unquestionably produce errors in the measurements of the charges generated by the piezoelement deformation and, consequently, errors in the estimation of the displacement (strain) and/or the applied force. Unfortunately, no analog electrical component fits the piezoelectric dynamic impedance (see Fig. 5 ). Notwithstanding, a numerical equivalent electrical circuit can easily be shaped to tackle this issue. The advantage of numerical processing is that it allows the use of more complex electrical impedance models of PEAs. Liseli et al. BIB007 proposed a way to reduce errors in the estimation of the displacement at the tip of cantilever PEAs through their equivalent numerical impedance Fig. 8 . Electrical circuit for quasi-static charge-based SSA BIB003 . The dashed (− − −) part is to be considered only for lower frequency nearby dc (R r = R L ). Fig. 9 . Simplified block diagram of the charge-based SSA considering the dynamic impedance of a PEA. G(s) is the equivalent mechanical system that reliably reproduces the mechanical behavior of the PEA when subjected to v c , and F t = f (v c , v out ) is the transduced force resulting from the application of v c . F t expresses the normal force responsible for the PEA expansion or contraction in the absence of any external mechanical stress. h(v c ) expresses the relationship between the input voltage v c and the impedance magnitude change |Z |. ADC stands for analog-to-digital converter. (see Fig. 9 ). The suggested equivalent numerical impedance considers the impact of the mechanical deformation of the piezoelectric element on its electrical impedance. It permitted a more rigorous cancellation ofQ d and, consequently, a more accurate measurement ofQ δ , the current that reflects the PEA's deformation. Experiments are conducted to validate the proposed approach and demonstrate the efficiency thereof to estimate the displacement of the PEA for long-duration measurement of constant step signal.