An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> II. SSA BASED ON THE PIEZOELECTRIC DIRECT EFFECT <s> A lumped-parameter model of a piezoeletric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the 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. <s> BIB001 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> II. SSA BASED ON THE PIEZOELECTRIC DIRECT EFFECT <s> A self-sensing actuator is a new concept for intelligent material, where a single piece of piezoelectric element simultaneously performs as both a sensor and an actuator. This idea should be advantageous especially for control of flexible structures. The key of this device is an electric bridge circuit that includes a piezoelectric element as a component. This circuit could give significant information about strain in the element if it were well-balanced. Our aim is to design controllers which enable practical self-sensing actuation in the presence of uncertainty that loses the balance of the circuit. In this paper, we proposed two approaches to realize self-sensing actuation which deal with this uncertainty differently. Experimental results proved the effectiveness of self-sensing actuation in both vibration suppression and tracking control of a cantilever. <s> BIB002 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> II. SSA BASED ON THE PIEZOELECTRIC DIRECT EFFECT <s> Lead zirconate titanate (PZT) offers high resolution down to the sub-nanometer range, high stiffness, and fast response times. Unfortunately, PZT suffers from creep or drifting in open loop control, namely an undesirable drift in displacement and increase in error with time, therefore there is a strong need for a model to compensate for drift in PZT actuators for high precision and accuracy tracking and control applications. In this paper the drift of a PZT stack actuator is experimentally investigated. The authors present an explanation of the findings and develop a drift operator that is incorporated into a comprehensive dynamic electromechanical model for PZT. The presented model compensates for drift and hysteresis inherent to PZT and describes both the electrical and mechanical properties of PZT, along with the electromechanical coupling between the two domains, to achieve absolute positioning for minutes in duration. The model is experimentally tested over extended periods of time for a variety of static and dynamic input conditions, namely with step inputs, square wave inputs, an on/off switch-like waveform, and sinusoidal input excitations, to yield a maximum average error of 68.2 nm. The model has the potential of expanding the bandwidth of PZT applications to very low frequencies for use in switches and load cells and can achieve higher accuracies in both open loop positioning and closed loop tracking systems. <s> BIB003 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> II. SSA BASED ON THE PIEZOELECTRIC DIRECT EFFECT <s> This paper presents a position control approach considering vibration suppression using self-sensing techniques in piezoelectric actuators. In order to achieve the high precision positioning using piezoelectric actuators, mechanical vibrations as well as nonlinear properties should be compensated. In this paper, a robust vibration suppression control system against resonant frequency variations is designed, where a minor loop aided by a self-sensing technique is added on the position control system. In the minor loop design, the reduction of sensitivity characteristic at around the vibration frequencies is considered to suppress the residual vibration for the reference and disturbance. Major loop for augmented plant including self-sensing minor loop, on the other hand, is designed by considering system stability and servo characteristic. The proposed approach has been evaluated by experiments using a piezo-driven stage. <s> BIB004 </s> An Overview of Piezoelectric Self-Sensing Actuation for Nanopositioning Applications: Electrical Circuits, Displacement, and Force Estimation <s> II. SSA BASED ON THE PIEZOELECTRIC DIRECT EFFECT <s> Using standard microelectromechanical system (MEMS) processes to coat a microcantilever with a piezoelectric layer results in a versatile transducer with inherent self-sensing capabilities. For applications in multifrequency atomic force microscopy (MF-AFM), we illustrate that a single piezoelectric layer can be simultaneously used for multimode excitation and detection of the cantilever deflection. This is achieved by a charge sensor with a bandwidth of 10 MHz and dual feedthrough cancellation to recover the resonant modes that are heavily buried in feedthrough originating from the piezoelectric capacitance. The setup enables the omission of the commonly used piezoelectric stack actuator and optical beam deflection sensor, alleviating limitations due to distorted frequency responses and instrumentation cost, respectively. The proposed method benefits from a more than two orders of magnitude increase in deflection to strain sensitivity on the fifth eigenmode leading to a remarkable signal-to-noise ratio. Experimental results using bimodal AFM imaging on a two component polymer sample validate that the self-sensing scheme can therefore be used to provide both the feedback signal, for topography imaging on the fundamental mode, and phase imaging on the higher eigenmode. <s> BIB005
A key characteristic of piezoelectric materials is the use of the piezoelectric reverse effect to actuate structures in addition to the piezoelectric direct effect to sense structural deformations. An external force F ext applied to a piezoelectric material will provoke its deformation δ and the deformation will cause the apparition of electrical charges Q δ on the material's surface, which defines the piezoelectric direct effect. A voltage v c applied to the piezoelectric material will generate an electric field E responsible for the transduced force F t that will provoke the deformation δ of the material, which defines the piezoelectric reverse effect. The piezoelectric reverse and direct effects are not exclusive. The electrodes used to supply the PEAs can also be used to get the appearing charges Q δ that result from its deformation δ. Fig. 1 shows an early representation of the electromechanical behavior of piezoelectric transducers. When examining PEA physical models BIB001 - BIB003 , it is noted that two forces can be the causes of the PEA's deformation. These forces are an external mechanical force F ext and a transduced force F t due to the application of v c . Therefore, whether it is F ext or v c , we observe a deformation δ of the PEA. According to the piezoelectric direct effect, the deformation of a piezoelectric material induces charges Q δ . Furthermore, for a range of frequency, PEAs are known to behave as capacitors, i.e., the application of an input voltage v c will generate charges Q d due to its dielectric characteristics. The SSA based on the piezoelectric direct effect aims to separate the charges due to the PEA's deformation Q δ from those due to the dielectric effect Q d and reconstruct the PEA's displacement δ from Q δ without the need of an external position sensor. This is made possible due to a dual dielectric feedthrough cancellation that helps recover the signal arising from the PEA's deformation. The dual feedthrough cancellation offsets the PEA dielectric behavior 1 so that only the signal generated by the PEA's deformation can be measured. This operation is all the more important, given that Q d Q δ , i.e., the dielectric signal magnitude is several orders of magnitude higher than that generated by the deformation of the PEA. For the remainder of this section, we will only focus on the electrical domain (see Fig. 2 ) for the review of the different dielectric feedthrough cancellation circuits used in the literature. The dielectric feedthrough cancellation circuit to be utilized depends on the adopted strain-electrical signal behavior of the PEA. Two equivalent electrical schematics are used to describe PEAs' behavior: 1) A capacitor C pea and a strain-dependent voltage source v δ in series with C pea BIB005 , BIB004 . For static and quasistatic applications, a leaking resistance R L parallel to C pea , commonly negligible but significant at lower frequency to account for current leak, is added to the schematic BIB002 [see Fig. 2 (b)]. 2) A strain-dependent charge source Q δ in parallel with the nominal piezoelectric capacitance C pea and a leaking resistance R L to account for the leaking current [see Fig. 2 (c)]. For both schematics, a hysteresis operator H(·) is used to characterize the hysteresis nonlinearity that typifies PEAs. Nevertheless, for SSA based on the piezoelectric direct effect, the deformation is said to be proportional to the electrical signal it generates. Therefore, although present, the hysteresis is neglected during the determination of the PEA's displacement estimate. One can either use the voltage-based SSA that employs the equivalent voltage source representation or the charge-based SSA that employs the equivalent charge source representation to estimate the strain or perceived force of the PEA.