An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <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> B. Charge-Based SSA <s> The proper equivalent interface circuit of a piezoelectric material below ultrasonic frequency range is developed and analyzed incorporating a voltage source and a capacitor theoretically and experimentally. The emphasis is placed on the physical connection between a capacitor and a voltage source. The first model considered is of a capacitor connected in series with a voltage source. The second model consists of a capacitor connected in parallel with a voltage source. This paper presents the analyses of these two different circuit models for a piezoceramic by discussing the electric impedance and phase angle of a piezoceramic theoretically and experimentally and determines the best-fit model of a PZT to use for structural vibration applications. <s> BIB002 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <s> This paper is aimed to explore the equivalent circuit models of piezoelectric ceramics with the consideration of energy dissipation. Based on the electrical impedance, the equivalent circuit models of piezoelectric ceramics are investigated under unloaded and loaded conditions. The characteristics and physical meanings of the circuit models are discussed by considering the frequency range of interest. The circuit models and discussions in this paper can provide a good understanding on the electrical behaviors of the piezoelectric ceramics when designing and analyzing the piezo-based systems. <s> BIB003 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <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> BIB004 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <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> BIB005 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <s> The motorized spindle is the core component of CNC machine tools, and the vibration of it reduces the machining precision and service life of the machine tools. Owing to the fast response, large output force, and displacement of the piezoelectric stack, it is often used as the actuator in the active vibration control of the spindle. A piezoelectric self-sensing actuator (SSA) can reduce the cost of the active vibration control system and simplify the structure by eliminating the use of a sensor, because a SSA can have both actuating and sensing functions at the same time. The signal separation method of a SSA based on a bridge circuit is widely applied because of its simple principle and easy implementation. However, it is difficult to maintain dynamic balance of the circuit. Prior research has used adaptive algorithm to balance of the bridge circuit on the flexible beam dynamically, but those algorithms need no correlation between sensing and control voltage, which limit the applications of SSA in the vibration control of the rotor-bearing system. Here, the electromechanical coupling model of the piezoelectric stack is established, followed by establishment of the dynamic model of the spindle system. Next, a new adaptive signal separation method based on the bridge circuit is proposed, which can separate relative small sensing voltage from related mixed voltage adaptively. The experimental results show that when the self-sensing signal obtained from the proposed method is used as a displacement signal, the vibration of the motorized spindle can be suppressed effectively through a linear quadratic Gaussian (LQG) algorithm. <s> BIB006 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <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 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> B. Charge-Based SSA <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> BIB008
Charge-based SSA approach relies on the linear charge-deformation relationship of PEAs BIB005 , BIB004 . It is known that the application of v c on a PEA creates charges due to its dielectric characteristics Q d plus charges due to the PEA's strain Q δ [see Fig. 2(c) ]. For the linear relationship between the PEA's generated displacement δ and Q δ to be exploited, Q δ must be separated from Q d . To this end, Hagood and Anderson BIB001 introduced an antiparallel circuit for the offsetting of the dielectric feedthrough Q d to directly measure the strain-induced charges of the PEA through direct charge amplification (see Fig. 4 ). Once this separation is done, δ can be estimated through the relationship where α Q is denoted as the PEA charge-displacement coefficient. The coefficients α Q and α v are identified empirically BIB006 , BIB004 . Like for the voltage-based SSA, only an exact match of the PEA's electrical characteristics in the antiparallel branch allows for perfect discrimination of Q δ from Q d . Therefore, all the abovementioned drawbacks of the voltage-based SSA are to be considered for the charge-based SSA, whereas for the self-sensing strain bridge, the three capacitors must be considered to balance the bridge; in the case of the antiparallel circuit, only the capacitor of the antiparallel branch is considered. This makes the creation of an antiparallel branch that accounts for all the PEA's defects (e.g., relaxation time, nonlinearities, and so on) feasible. In this case, a thorough analysis of the PEA's electrical characteristics and its dependences to mechanical and electrical excitations (frequency and amplitude) is required to guarantee the complete offset of Q d and retrievement of Q δ . Numerous works have been carried out on the design of equivalent circuit models of piezoelectric materials. Park BIB002 found that the circuit model with a capacitor and internal resistor in series could represent the behavior of piezoelectric ceramics much better than the model with capacitor and resistor in parallel when considering the energy dissipation. Guan and Liao BIB003 combined the behavior of the parallel model at low frequency and that of the series model at high frequency and showed that this representation well fit with the experimental tests. Liseli et al. BIB007 captured the influence of the control voltage v c (amplitude and frequency) on PEAs with an impedance map (see Fig. 5 ). Mansour and Seethaler BIB008 highlighted the effect of an external force on the PEA's impedance. To summarize, to discriminate Q δ from Q d , one needs an electrical component in the antiparallel branch that accounts for humidity, ambient temperature, control voltage (amplitude and frequency), and external force applied upon the PEA. Unfortunately, no analog electrical component fits the piezoelectric material impedance dependences. Nevertheless, a numerical equivalent electronic circuit can be designed to integrate all these dependences for a thorough separation of Q δ from Q d . Considering that a digital impedance is designed for robust discrimination of Q δ from Q d , two problems still need to be addressed, which are given in the following. 1) A PEA or sensor is an electromechanically coupled system, that is, the design for actuation use should be done in consideration of the impact on the sensor aspect and vice versa. Accordingly, one requires a PEA design optimization for both actuation and observation for the applicability of either voltage-or charge-based SSA. 2) The transitional behavior of the PEA's strain-induced charges to allow for static or quasi-static PEA's displacement estimation. Indeed, after an instantaneous deformation of a PEA due to the application of an electric field, if the electric field is maintained, the PEA will keep deforming due to the creep effect. This deformation, even though small, will keep producing strain-induced charges Q δ , the difference between C pea and C r will keep increasing, and α Q may no longer apply to reconstruct the PEA's displacementδ from Q δ . Fig. 6 shows a simplified block diagram for a simultaneous control and displacement measurement of a PEA using either the voltage-or the charge-based SSA. Fig. 6 allows apprehending the similarities and subtleties in the implementation of these two SSA schemes based on the piezoelectric direct effect.