Piezoelectric Actuators in Smart Engineering Structures Using Robust Control

In this study, piezoelectric patches are used as actuators to dampen structural oscillations. Damping oscillations is a significant engineering challenge, and the use of piezoelectric patches in smart structures allows for a reduction in oscillations through sophisticated control methods. This analysis involved H-infinity (H∞) robust analysis. H∞ (H-infinity) control formulation is a robust control design method used to ensure system stability and performance under disturbances. When applied to piezoelectric actuators in smart structures, H∞ control aims to design controllers that are robust to variations in system dynamics, external disturbances, and modeling uncertainties, while meeting specified performance criteria. This study outlines the piezoelectric effects and advanced control strategies. A structural model was created using finite elements, and a smart structural model was analyzed. Subsequently, dynamic loads were applied and oscillation damping was successfully achieved by employing advanced control techniques.

Parameter Identification of Model for Piezoelectric Actuators

Piezoelectric actuators are widely used in high-precision positioning systems. The nonlinear characteristics of piezoelectric actuators, such as multi-valued mapping and frequency-dependent hysteresis, severely limit the advancement of the positioning system's accuracy. Therefore, a particle swarm genetic hybrid parameter identification method is proposed by combining the directivity of the particle swarm optimization algorithm and the genetic random characteristics of the genetic algorithm. Thus, the global search and optimization abilities of the parameter identification approach are improved, and the problems, including the genetic algorithm's poor local search capability and the particle swarm optimization algorithm's ease of falling into local optimal solutions, are resolved. The nonlinear hysteretic model of piezoelectric actuators is established based on the hybrid parameter identification algorithm proposed in this paper. The output of the model of the piezoelectric actuator is in accordance with the real output obtained from the experiments, and the root mean square error is only 0.029423 μm. The experimental and simulation results show that the model of piezoelectric actuators established by the proposed identification method can describe the multi-valued mapping and frequency-dependent nonlinear hysteresis characteristics of piezoelectric actuators.

Compensation Method for the Nonlinear Characteristics with Starting Error of a Piezoelectric Actuator in Open-Loop Controls Based on the DSPI Model

Nanopositioning stages with piezoelectric actuators have been widely used in fields such as precision mechanical engineering, but the nonlinear start-up accuracy problem under open-loop control has still not been solved, and more errors will accumulate, especially under open-loop control. This paper first analyzes the causes of the starting errors from both the physical properties of materials and voltages: the starting errors are affected by the material properties of piezoelectric ceramics, and the magnitude of the voltage determines the magnitude of the starting errors. Then, this paper adopts an image-only model of the data separated by a Prandtl-Ishlinskii model (DSPI) based on the classical Prandtl-Ishlinskii model (CPI), which can improve the positioning accuracy of the nanopositioning platform after separating the data based on the start-up error characteristics. This model can improve the positioning accuracy of the nanopositioning platform while solving the problem of nonlinear start-up errors under open-loop control. Finally, the DSPI inverse model is used for the feedforward compensation control of the platform, and the experimental results show that the DSPI model can solve the nonlinear start-up error problem existing under open-loop control. The DSPI model not only has higher modeling accuracy than the CPI model but also has better performance in terms of compensation results. The DSPI model improves the localization accuracy by 99.427% compared to the CPI model. When compared with another improved model, the localization accuracy is improved by 92.763%.

Modeling of Rapid Response Characteristics of Piezoelectric Actuators for Ultra-Precision Machining

Piezoelectric actuators are characterized by high positioning accuracy, high stiffness and a fast response and are widely used in ultra-precision machining technologies such as fast tool servo technology and ultrasonic machining. The rapid response characteristics of piezoelectric actuators often determine the overall quality of machining. However, there has been little research on the fast response characteristics of piezoelectric actuators, and this knowledge gap will lead to low precision and poor quality of the final machining. The fast response characteristics of a piezoelectric actuator were studied in this work. Firstly, the piezoelectric actuator was divided into a no-load state and a load state according to the working state. A fast response analysis and output characteristic analysis were carried out, the corresponding dynamic model was established, and then the model was simulated. Finally, an experimental system was established to verify the dynamic model of the piezoelectric actuator's fast response by conducting an experiment in which the piezoelectric actuator bounces a steel ball. The experimental results verify the correctness of the model and show that the greater the cross-sectional area and height of the piezoelectric actuator, the higher the bouncing height of the ball, and the better the dynamic performance of the piezoelectric actuator. It is believed that this study has guiding significance for the application of the dynamic characteristics of piezoelectric actuators in the machining field.

A Novel Feedforward Model of Piezoelectric Actuator for Precision Rapid Cutting

The piezoelectric actuator has been widely used in modern precision cutting technology due to its fast response speed and high positioning accuracy. In recent years, with the development of precision technology, modern cutting requires higher and higher cutting accuracy and efficiency. Therefore, this paper proposes a feedforward control method based on the modified Bouc-Wen (MBW) model. Firstly, a novel asymmetrical modified Bouc-Wen model with an innovative form of shape control function is developed to model the hysteresis nonlinearity property of piezoelectric actuators. Then, a self-adaptive cooperative particle swarm optimization (PSO) algorithm is developed to identify the parameters of MBW model. The comparative evaluation reveals that the MBW model outperforms the classical Bouc-Wen (CBW) model by 66.4% in modeling accuracy. Compared with traditional PSO algorithm, the self-adaptive cooperative PSO algorithm can obtain minimum fitness in parameter identification. Furthermore, the feedforward control strategy is realized to improve the position tracking accuracy. A position tracking experiment verifies that the feedforward control strategy improves the tracking accuracy of piezoelectric actuators significantly compared with the open-loop control strategy.

Ultraprecise Controller for Piezoelectric Actuators Based on Deep Learning and Model Predictive Control

Piezoelectric actuators (PEA) are high-precision devices used in applications requiring micrometric displacements. However, PEAs present non-linearity phenomena that introduce drawbacks at high precision applications. One of these phenomena is hysteresis, which considerably reduces their performance. The introduction of appropriate control strategies may improve the accuracy of the PEAs. This paper presents a high precision control scheme to be used at PEAs based on the model-based predictive control (MPC) scheme. In this work, the model used to feed the MPC controller has been achieved by means of artificial neural networks (ANN). This approach simplifies the obtaining of the model, since the achievement of a precise mathematical model that reproduces the dynamics of the PEA is a complex task. The presented approach has been embedded over the dSPACE control platform and has been tested over a commercial PEA, supplied by Thorlabs, conducting experiments to demonstrate improvements of the MPC. In addition, the results of the MPC controller have been compared with a proportional-integral-derivative (PID) controller. The experimental results show that the MPC control strategy achieves higher accuracy at high precision PEA applications such as tracking periodic reference signals and sudden reference change.

System Identification and Mathematical Modeling of A Piezoelectric Actuator through A Practical Three-Stage Mechanism

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a full analytical model and a simple system identification (SI) method of a piezoelectric actuator, which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, is described extensively. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results. Some of the most well-known forms of system identification are shown briefly, while a new and simple algorithm is described systematically and verified by the model. The main advantage of this work is to provide a solid background and domain knowledge of modelling and system identification methods for further investigations in the field of piezoelectric actuators. Due to their simplicity, both the model and the system identification method can be easily modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in applying a simple system identification algorithm while using the system-level approach for piezoelectric actuators. Lastly, this review work is concluded and some recommendations for researchers working in this area are presented.

A Modified Prandtl-Ishlinskii Hysteresis Model for Modeling and Compensating Asymmetric Hysteresis of Piezo-Actuated Flexure-Based Systems

Piezo-actuated flexure-based systems are widely used in applications with high accuracy requirements, but the intrinsic hysteresis has a detrimental effect on the performance which should be compensated. Conventional models were presented to model this undesired effect using additional dead-zone operators. This paper presents a new approach using two sets of operators with a distributed compensator to model and compensate for the asymmetric system hysteresis based on inversion calculation with a simplified digitized representation. The experimental results validate the effectiveness of the proposed model in modeling and compensating the asymmetric system hysteresis.

Design and Performance of a Spatial 6-RRRR Compliant Parallel Nanopositioning Stage

Piezoelectric actuators (PEAs) and compliant parallel mechanisms (CPMs) are advantageous for designing nanopositioning stages (NPSs) with multiple degrees of freedom (multi-DOFs). This paper proposes a new NPS that uses PEAs and CPMs with multiple spatial DOFs. First, the design of the mechanism is introduced. Six parallel kinematics revolute-revolute-revolute-revolute (RRRR) branched chains were used to create a 6-RRRR CPM for superior mechanical performance. Three in-plane and three out-of-plane chains were combined using a two-in-one structure to ensure fabrication feasibility. A two-in-one 6-RRRR CPM was employed to build the proposed NPS. Second, the mechanical performance was analyzed. High-efficiency finite-element modeling approaches were derived using the compliance-based matrix method (CMM) and a pseudo-rigid body model (PRBM). The model included both 6-RRRR CPM and NPS. The simulation results validated the static and dynamic performance, and the experimental results verified the kinematics. Based on the newly designed mechanism and verified mechanical performance, the proposed 6-RRRR NPS contributes to the development of spatial multi-DOF NPSs using PEAs and CPMs.

State of the Art and Future Opportunities in MRI-Guided Robot-Assisted Surgery and Interventions

Magnetic resonance imaging (MRI) can provide high-quality 3-D visualization of target anatomy, surrounding tissue, and instrumentation, but there are significant challenges in harnessing it for effectively guiding interventional procedures. Challenges include the strong static magnetic field, rapidly switching magnetic field gradients, high-power radio frequency pulses, sensitivity to electrical noise, and constrained space to operate within the bore of the scanner. MRI has a number of advantages over other medical imaging modalities, including no ionizing radiation, excellent soft-tissue contrast that allows for visualization of tumors and other features that are not readily visible by other modalities, true 3-D imaging capabilities, including the ability to image arbitrary scan plane geometry or perform volumetric imaging, and capability for multimodality sensing, including diffusion, dynamic contrast, blood flow, blood oxygenation, temperature, and tracking of biomarkers. The use of robotic assistants within the MRI bore, alongside the patient during imaging, enables intraoperative MR imaging (iMRI) to guide a surgical intervention in a closed-loop fashion that can include tracking of tissue deformation and target motion, localization of instrumentation, and monitoring of therapy delivery. With the ever-expanding clinical use of MRI, MRI-compatible robotic systems have been heralded as a new approach to assist interventional procedures to allow physicians to treat patients more accurately and effectively. Deploying robotic systems inside the bore synergizes the visual capability of MRI and the manipulation capability of robotic assistance, resulting in a closed-loop surgery architecture. This article details the challenges and history of robotic systems intended to operate in an MRI environment and outlines promising clinical applications and associated state-of-the-art MRI-compatible robotic systems and technology for making this possible.

A Multi-Fidelity Model for Simulations and Sensitivity Analysis of Piezoelectric Inkjet Printheads

The ink drop generation process in piezoelectric droplet-on-demand devices is a complex multiphysics process. A fully resolved simulation of such a system involves a coupled fluid–structure interaction approach employing both computational fluid dynamics (CFD) and computational structural mechanics (CSM) models; thus, it is computationally expensive for engineering design and analysis. In this work, a simplified lumped element model (LEM) is proposed for the simulation of piezoelectric inkjet printheads using the analogy of equivalent electrical circuits. The model’s parameters are computed from three-dimensional fluid and structural simulations, taking into account the detailed geometrical features of the inkjet printhead. Inherently, this multifidelity LEM approach is much faster in simulations of the whole inkjet printhead, while it ably captures fundamental electro-mechanical coupling effects. The approach is validated with experimental data for an existing commercial inkjet printhead with good agreement in droplet speed prediction and frequency responses. The sensitivity analysis of droplet generation conducted for the variation of ink channel geometrical parameters shows the importance of different design variables on the performance of inkjet printheads. It further illustrates the effectiveness of the proposed approach in practical engineering usage.

Designing Ordered Structure with Piezoceramic Actuation Units (OSPAU) for Generating Continual Nanostep Motion

Continual precision actuations with nanoscale resolution over large ranges have extensive requirements in advanced intelligent manufacturing and precise surgical robots. To produce continual nanostep motion, conventionally, multiple pairs of piezo-actuators are employed to operate in inchworm principle under complex three- or four-phase timing signal drive. Inspired by the idea of ordered structures with functional units, a much simpler nanostep piezoelectric actuator consisting of (2 × 2) arrayed, cofired multilayer piezoceramic actuation units is developed, which operates in an artificially generated quasi shear mode (AGQSM) that is missing in natural piezoelectric ceramics. Under only one-phase square-wave voltage drive, the actuator can produce a stable, continual nanostep motion in two ways at nonresonant frequencies, and the obtained minimum step displacement is as low as 7 nm in open control, indicating its potential application as a precise finger or knife actuator in surgical robots. This work is of great guiding significance for future actuator designs using the methodology of ordered structure with piezoceramic actuation units and AGQSM.

A Microfluidic Rotational Motor Driven by Circular Vibrations

Constructing micro-sized machines always involves the problem of how to bring the energy (electric, magnetic, light, electro wetting, vibrational, etc.) source to the device to produce mechanical movements. The paper presents a rotational micro-sized motor (the diameter of the rotor is 350 µm) driven by low frequency (200–700 Hz) circular vibrations, made by two piezoelectric actuators, through the medium of a water droplet with diameter of 1 mm (volume 3.6 µL). The theoretical model presents how to produce the circular streaming (rotation) of the liquid around an infinitely long pillar with micro-sized diameter. The practical application has been focused to make a time-stable circular stream of the medium around the finite long vibrated pillar with diameter of 80 µm in the presence of disturbances produced by the vibrated plate where the pillar is placed. Only the time-stable circular stream in the water droplet around the pillar produces enough energy to rotate the micro-sized rotor. The rotational speed of the rotor is controlled in both directions from −20 rad/s to +26 rad/s. 3D printed mechanical amplifiers of vibrations, driven by piezoelectric actuators, amplify the amplitude of the piezoelectric actuator up to 20 µm in the frequency region of 200 to 700 Hz.

Characterization of Tunable Micro-Lenses with a Versatile Optical Measuring System

In this work, we present the results of the opto⁻electro⁻mechanical characterization of tunable micro-lenses, Tlens®, performed with a single-spot optical measuring system. Tested devices are composed of a transparent soft polymer layer that is deposited on a supporting glass substrate and is covered by a glass membrane with a thin-film piezoelectric actuator on top. Near-infrared optical low-coherence reflectometry is exploited for both static and low-frequency dynamic analyses in the time domain. Optical thickness of the layers and of the overall structure, actuation efficiency, and hysteretic behavior of the piezo-actuator as a function of driving voltage are obtained by processing the back-reflected signal in different ways. The use of optical sources with relatively short coherence lengths allows performing interferometric measurements without spurious resonance effects due to multiple parallel interfaces, furthermore, selecting the plane/layer to be monitored. We finally report results of direct measurements of Tlens® optical power as a function of driving voltage, performed by redirecting a He-Ne laser beam on the lens and monitoring the focused spot at various distances with a digital camera.

Single Cylinder-Type Piezoelectric Actuator with Two Active Kinematic Pairs

There is an ever-increasing demand for small-size, low-cost, and high-precision positioning systems. Therefore, investigation in this field is performed to search for various solutions that can meet technical requirements of precise multi-degree-of-freedom (DOF) positioning systems. This paper presents a new design of a piezoelectric cylindrical actuator with two active kinematic pairs. This means that a single actuator is used to create vibrations that are transformed into the rotation of the sphere located on the top of the cylinder and at the same time ensure movement of the piezoelectric cylinder on the plane. Numerical and experimental investigations of the piezoelectric cylinder have been performed. A mathematical model of contacting force control was developed to solve the problem of positioning of the rotor when it needs to be rotated or moved according to a specific motion trajectory. The numerical simulation included harmonic response analysis of the actuator to analyze the trajectories of the contact points motion. A prototype actuator has been manufactured and tested. Obtained results confirmed that such a device is suitable for both positioning and movement of the actuator in the plane.

Micro Motion Amplifiers for Compact Out-of-Plane Actuation

Small-scale, out-of-plane actuators can enable tactile interfaces; however, achieving sufficient actuator force and displacement can require larger actuators. In this work, 2-mm² out-of-plane microactuators were created, and were demonstrated to output up to 6.3 µm of displacement and 16 mN of blocking force at 170 V. The actuators converted in-plane force and displacement from a piezoelectric extensional actuator into out-of-plane force and displacement using robust, microelectromechanical systems (MEMS)-enabled, half-scissor amplifiers. The microscissors employed two layers of lithographically patterned SU-8 epoxy microstructures, laminated with a thin film of structural polyimide and adhesive to form compact flexural hinges that enabled the actuators’ small area. The self-aligned manufacture minimized assembly error and fabrication complexity. The scissor design dominated the actuators’ performance, and the effects of varying scissor angle, flexure thickness, and adhesive type were characterized to optimize the actuators’ output. Reducing the microscissor angle yielded the highest actuator performance, as it maximized the amplification of the half-scissor’s displacement and minimized scissor deformation under externally applied loads. The actuators’ simultaneously large displacements and blocking forces for their size were quantified by a high displacement-blocking force product per unit area of up to 50 mN·µm/mm². For a linear force–displacement relationship, this corresponds to a work done per unit area of 25 mN·µm/mm².

Compensation of Hysteresis on Piezoelectric Actuators Based on Tripartite PI Model

Piezoelectric ceramic actuators have been widely used in nanopositioning applications owing to their fast response, high stiffness, and ability to generate large forces. However, the existence of nonlinearities such as hysteresis can greatly deteriorate the accuracy of the manipulation, even causing instability of the whole system. In this article, we have explained the causes of hysteresis based on the micropolarization theory and proposed a piezoelectric ceramic deformation speed law. For this, we analyzed the piezoelectric ceramic actuator deformation speed law based on the domain wall theory. Based on this analysis, a three-stage Prandtl–Ishlinskii (PI) model (hereafter referred to as tripartite PI model) was designed and implemented. According to the piezoelectric ceramic deformation speed law, this model makes separate local PI models in different parts of piezoelectric ceramics’ hysteresis curve. The weighting values and threshold values of the tripartite PI model were obtained through a quadratic programming optimization algorithm. Compared to the classical PI model, the tripartite PI model can describe the asymmetry of hysteresis curves more accurately. A tripartite PI inverse controller, PI inverse controller, and Preisach inverse controller were used to compensate for the piezoelectric ceramic actuator in the experiment. The experimental results show that the inclusion of the PI inverse controller and the Preisach inverse controller improved the tracking performance of the tripartite PI inverse model by more than 80%.

Piezoelectric Actuated Phase Shifter Based on External Laser Interferometer: Design, Control and Experimental Validation

To improve the phase-shifting accuracy, this paper presents a novel integrated framework for design, control and experimental validation of the piezoelectric actuated phase shifter with a trade-off between accuracy and cost. The piezoelectric actuators with built-in sensors are adopted to drive the double parallel four-bar linkage flexure hinge-based mechanisms. Three mechanisms form the tripod structure of the assembled phase shifter. Then, a semi-closed loop controller with inner feedback and outer feedforward loops via the external laser interferometer is developed for accurate positioning of the phase shifter. Finally, experiments related with travel range, step response, linearity and repeatability are carried out. The linearity error is 0.21% and the repeatability error of 10 μm displacement is 3 nm. The results clearly demonstrate the good performance of the developed phase shifter and the feasibility of the proposed integrated framework.

Manufacturing an active X-ray mirror prototype in thin glass

Adjustable mirrors equipped with piezo actuators are commonly used at synchrotron and free-electron laser (FEL) beamlines, in order to optimize their focusing properties and sometimes to shape the intensity distribution of the focal spot with the desired profile. Unlike them, X-ray mirrors for astronomy are much thinner in order to enable nesting and reduce the areal mass, and the application of piezo actuators acting normally to the surface appears much more difficult. There remains the possibility to correct the deformations using thin patches that exert a tangential strain on the rear side of the mirror: some research groups are already at work on this approach. The technique reported here relies on actively integrating thin glass foils with commercial piezoceramic patches, fed by voltages driven by the feedback provided by X-rays, while the tension signals are carried by electrodes on the back of the mirror, obtained by photolithography. Finally, the shape detection and the consequent voltage signal to be provided to the piezoelectric array will be determined by X-ray illumination in an intra-focal setup at the XACT facility. In this work, the manufacturing steps for obtaining a first active mirror prototype are described.

Nonlinear mode-coupling in nanomechanical systems

Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler-Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement.

Quantitative modeling of coupled piezo-elastodynamic behavior of piezoelectric actuators bonded to an elastic medium for structural health monitoring: a review

Elastic waves, especially guided waves, generated by a piezoelectric actuator/sensor network, have shown great potential for on-line health monitoring of advanced aerospace, nuclear, and automotive structures in recent decades. Piezoelectric materials can function as both actuators and sensors in these applications due to wide bandwidth, quick response and low costs. One of the most fundamental issues surrounding the effective use of piezoelectric actuators is the quantitative evaluation of the resulting elastic wave propagation by considering the coupled piezo-elastodynamic behavior between the actuator and the host medium. Accurate characterization of the local interfacial stress distribution between the actuator and the host medium is the key issue for the problem. This paper presents a review of the development of analytical, numerical and hybrid approaches for modeling of the coupled piezo-elastodynamic behavior. The resulting elastic wave propagation for structural health monitoring is also summarized.