Stack Actuator Research Articles

Measurement Range Enhancement of a Scanning Probe by the Real Time Adjustment of the Interferometer Reference Mirror

Scanning probes on the micro/nano-coordinate measuring machines (micro/nano-CMMs) can produce on/off signals and achieve 3D measurement ability within a specific range. The authors have developed several scanning probes based on a 2D angle sensor and a miniature Michelson interferometer that can work within ± $10~\mu \text{m}$ . When the probe’s lateral displacement is greater than $10~\mu \text{m}$ , the interferometer signal is easy to break, limiting the measurement range of these probes. A 2D angle fine-tuning stage using piezoelectric stack actuators is designed to adjust the reference mirror in real-time to solve signal separation between the reference beam and the measuring beam of the miniature Michelson interferometer. The coupling of the 2D angle fine-tuning stage in the x and y directions is analyzed, and the coupling model is established for a relatively precise compensation. Experimental results show that through the proposed 2D angle fine-tuning stage, the measurement range of the probe can be extended to ± $30~\mu \text{m}$ , and the interference signal can still remain stable and uninterrupted.

Tracking control of a 3-dimensional piezo-driven micro-positioning system using a dynamic Prandtl–Ishlinskii model

A controller composed of a feed-forward loop based on a novel dynamic Prandtl–Ishlinskii (P-I) model and a PID feedback control loop is developed to support a 3-dimensional piezo-driven micro-positioning system for high-bandwidth tracking control. By considering the dynamic characteristics of the power amplifier, the dynamic P-I model can accurately describe the rate-dependent hysteresis of piezoelectric stack actuators (PSAs). To ensure that the hysteresis model is independent of system load, the P-I hysteresis operator in that model characterizes the relationship between the output force and the input voltage of PSAs. The dynamics equation of the mechanical is established by using the cutoff modal method. The feedforward control is designed based on the dynamic hysteresis model to reduce the rate-dependent hysteresis. The PID control is incorporated with the feedforward control to increase the tracking accuracy. Experimental results indicate that the controller can overcome the hysteresis efficiently and preserve good positioning accuracy in 1–100 Hz bandwidth. Just by introducing the dynamic characteristics of the power amplifier, which can be expressed as a first-order differential equation, the P-I model can accurately describe the rate-dependent hysteresis of the PSA, which provides a simple method to describe and control piezoelectric actuators and piezo-driven systems in a wide frequency.

The Effect of Spool Displacement Control to the Flow Rate in the Piezoelectric Stack-Based Valve System Subjected to High Operating Temperature

This work investigates the effect of spool displacement control of the piezoelectric stack actuator (PSA) based valve system on the flow motion of the pressure drop and flow rate. As a first step, the governing equations of the structural parts of the displacement amplifier and spool are derived, followed by the governing equation of the fluid part considering control volume and steady flow force. Then, an appropriate size of the valve is designed and manufactured. An experimental apparatus to control the spool displacement is set up in the heat chamber and tracking control for the spool displacement is evaluated at 20 °C and 100 °C by implementing a proportional-integral-derivative (PID) feedback controller. The tracking controls of the spool displacement associated with the sinusoidal and triangular trajectories are realized at 20 °C and 100 °C. It is demonstrated that the tracking controls for the sinusoidal and triangular trajectories have been well carried out showing the tracking error less than 3 μm at both temperatures. In addition, the flow motions for the pressure drop and the flow rate of the proposed valve system are experimentally investigated. It is identified from this investigation that both pressure drop and flow rate evaluated 20 °C have been decreased up to 18% at 100 °C. This result directly indicates that the temperature effect to control performance of the structural part and fluid part in the proposed PSA based valve system is different and hence careful attention is required to achieve the successful development of advanced valve systems subjected to a wide range of the operating temperature.

A Digitized Representation of the Modified Prandtl-Ishlinskii Hysteresis Model for Modeling and Compensating Piezoelectric Actuator Hysteresis.

Piezoelectric actuators are widely used in micromanipulation and miniature robots due to their rapid response and high repeatability. The piezoelectric actuators often have undesired hysteresis. The Prandtl–Ishlinskii (PI) hysteresis model is one of the most popular models for modeling and compensating the hysteresis behaviour. This paper presents an alternative digitized representation of the modified Prandtl–Ishlinskii with the dead-zone operators (MPI) hysteresis model to describe the asymmetric hysteresis behavior of piezoelectric actuators. Using a binary number with n digits to represent the classical Prandtl–Ishlinskii hysteresis model with n elementary operators, the inverse model can be easily constructed. A similar representation of the dead-zone operators is also described. With the proposed digitized representation, the model is more intuitive and the inversion calculation is avoided. An experiment with a piezoelectric stacked linear actuator is conducted to validate the proposed digitized MPI hysteresis model and it is shown that it has almost the same performance as compared to the classical representation.

Integral terminal sliding-mode robust vibration control of large space intelligent truss structures using a disturbance observer

This study aims to develop an advanced integral terminal sliding-mode robust control method using a disturbance observer (DO) to suppress the forced vibration of a large space intelligent truss structure (LSITS). First, the dynamics of the electromechanical coupling of the piezoelectric stack actuator and the LSITS, based on finite element and Lagrangian methods, are established. Subsequently, to constrict the vibration of the structure, a novel integral terminal sliding-mode control (ITSMC) law for the DO is used to estimate the parameter perturbation of the LSITS based on a continuous external disturbance. Simulation results show that, under a forced vibration and compared with the ITSMC system without a DO, the displacement amplitude of the ITSMC system with the DO is effectively reduced. In the case where the model parameters of the LSITS deviate by ±50%, and an unknown continuous external disturbance exists, the control system with the DO can adequately attenuate the structural vibration and realize robust control. Concurrently, the voltage of the employed piezoelectric stack actuator is reduced, and voltage jitter is alleviated.

Hybrid feedback PID-FxLMS algorithm for active vibration control of cantilever beam with piezoelectric stack actuator

FxLMS (Filtered-x Least Mean Square) algorithm and PID (Proportional Integral Derivative) controller have been widely used for AVC (Active Vibration Control). Yet, the convergence rate and vibration suppression performance are restricted by each other for both the classical FxLMS algorithm and the traditional PID controller. A hybrid PID-FxLMS algorithm which combines the feedback FxLMS algorithm and PID controller is proposed, and applied to improve the vibration control efficiency of piezoelectric cantilever beam. In order to conveniently install the piezoelectric stack on the beam structures, a new piezoelectric stack actuator is designed and installed at the root of cantilever beam. Meanwhile, a coupled finite element model of the piezoelectric stack actuator and cantilever beam is established in ABAQUS, and the state-space model of the coupled system is obtained. Subsequently, based on the obtained state-space model, an AVC simulation and experimental system is built to verify the effectiveness of the proposed algorithm. Numerical and experimental results show that convergence rate and vibration suppression performance of the hybrid PID-FxLMS algorithm are much better than that of the classical FxLMS algorithm or traditional PID controller alone, while the hybrid controller also has strong adaptability and anti-noise ability.

Development and Test of a Two-Dimensional Stacked Terfenol-D Actuator With High Bandwidth and Large Stroke

Smart material actuators (SMAs) can provide motion with high resolution and high bandwidth, but the output stroke is relatively small. Therefore, motion amplification mechanisms for SMAs have drawn considerable attentions in recent years. However, most of existing mechanisms realize the motion amplification at the expense of working bandwidth. To achieve large stroke and high bandwidth simultaneously, a novel two-dimensional stacked magnetostrictive actuator (TSMA) was developed and tested by adopting the magnetostrictive material, i.e., the Terfenol-D in this article. The U-shaped sleeves were employed to support the axial and radial two-dimensional stacking of three Terfenol-D rods. Then, an analytical model was established based on working principle of the TSMA, and a design of experiment analysis was carried out for the sensitivity study of the TSMA's key structural parameters. Next, the involved parameters of the established analytical model were obtained via system identification. Furthermore, several experimental tests of a fabricated prototype for the TSMA were carried out. The results show that the stroke of the proposed TSMA can reach 65 μ m. The displacement amplification ratio is achieved as 2.8 and the working bandwidth is kept as 500 Hz. This proves that the proposed structure can significantly increase the displacement with a little loss of bandwidth. Finally, a set of preliminary closed-loop tests using a traditional incremental proportion-integration-differentiation (PID) control were carried out to improve the motion precision. The closed-loop tracking results of 10-100 Hz sinusoid references show that the root-mean-square errors are less than 4$\%$ using a simple PID control alone.

Investigations on piezo actuated micro XY stage for vibration-assisted micro milling

Vibration assisted machining is an advanced non-conventional precision machining technique aiming at improving the machining performance by superimposing a small amplitude, high-frequency vibration either on the tool or on the workpiece. This article presents the mechanical design, electromechanical simulation, and experimentation on the developed prototype of the flexural hinged micro XY stage for the vibration-assisted micro-milling system. The micro XY stage comprises three layers of flexural hinge structure surrounding the central parallel kinematic structure. The finite element analysis method is adopted to evaluate the static structural stiffness and harmonic behaviour. Two multilayer piezoelectric stack actuators drive the micro XY stage in X and Y directions. The experimental results show that the micro XY stage has a vibrating work area of 17.06 µm × 17.11 µm with a hysteresis nonlinearity and cross-coupling displacements on both axes. Therefore, an electromechanical model is essential to compensate for the hysteresis behaviour and cross-coupling displacements. Open-loop tracking control experiments determine the accuracy of the developed electromechanical model. Implementing a combined hysteresis and cross-coupling displacement compensation approach into the electromechanical model resulted in an open-loop tracking error of 7% for the synchronised circular path and a maximum deviation of 0.6 µm from the linear path.

Linear and nonlinear analysis of traditional and non-traditional piezoelectric vibration absorber with time delay feedback for simultaneous resonance conditions

In the present work, vibration suppression of a single degree of freedom nonlinear spring-mass primary (main) system subjected to simultaneous external harmonic and parametric excitation by using traditional and non-traditional active nonlinear vibration absorber (ANVA) is carried out. The traditional and non-traditional ANVA consists of a PZT (lead zirconate titanate) stack actuator in series with a nonlinear spring and a damper. In the traditional ANVA, the damper is connected to the main system whereas, in non-traditional ANVA, the damper is connected to the base of the main system. The governing nonlinear equations of motion for the system have been derived using weighted modal matrix approach considering novel actuation force by time delay in displacement, velocity and acceleration feedback of the main system by the PZT stack actuator and the nonlinear spring in series combination. The method of multiple scales (MMS) is used to obtain the reduced equations which are solved using Newton’s method. The responses of the system for the primary, principal parametric and simultaneous primary and principal parametric resonance conditions have been studied. The results are compared with those obtained by using the harmonic balance method (HBM), numerical method and with previous literature. From these results, two resonating peaks in the frequency response of the main system are shown by using the reduced equation of the MMS which was not reported in earlier literature. It is shown that for the active case the vibration of the undamped main system is completely reduced at the specified operating frequency for both the linear and nonlinear systems. Also, for a wider range of operating frequencies, the vibration of the main system is reduced by actively tuning the absorber for various mass ratios. Further, the efficacy of the active force is observed in reducing the instability regions and improving the critical value of excitations in the trivial state.

High-bandwidth modeling for rate-dependent hysteresis nonlinearity using a standard Prandtl–Ishlinskii model

Rate-dependent hysteresis of piezoelectric stack actuators (PSAs) is known to cause oscillations and instabilities. This paper introduces a novel electro-mechanical coupling model that can accurately characterize the high-bandwidth rate-dependent hysteresis of a PSA. The proposed model contains three components to fully represent the output response of the system, namely, an electric model that is used to describe the electric dynamic behaviors of the PSA and its power amplifier, a hysteresis model that is applied to represent the inverse piezoelectric effect, and a mechanical model that is able to characterize the mechanical dynamic behavior of the PSA. It should be noted that, in the mechanical model, the force generated by the inverse piezoelectric effect of piezoelectric wafers is considered a distributed force and the dynamic model of the PSA is regarded as a longitudinal vibration straight bar with a uniform cross section. Through this proposed model, high modeling accuracy is achieved well with high-bandwidth varying frequencies (1–1000 Hz) as well as varying amplitudes. This paper provides a simple and effective novel method for the high-bandwidth modeling of smart material-based actuators with rate-dependent hysteresis nonlinearity.

Development of a novel two-DOF piezo-driven fast steering mirror with high stiffness and good decoupling characteristic

A novel two-DOF piezo-driven fast steering mirror (PFSM) with high stiffness and good decoupling characteristic was proposed. This PFSM could realize rotary motions around X-axis and Y-axis by differential push–pull structure with four piezoelectric stack actuators (PSAs) arranged in cross and orthogonal state, and its lateral stiffness was high enough to overcome the problem that PSA was easy to be destroyed by large lateral force. The PFSM was designed and its working principle was described in detail. The static model was established to analyze the stiffness characteristic of the structure and precisely predict the output angles. The finite element method (FEM) was performed to verify the effectiveness of the proposed structure and static model. A prototype of the PFSM was fabricated, and an experimental setup was established. The experiments showed that the proposed PFSM could achieve rotary motion ranges of 2.33 mrad around X-axis and 2.25 mrad around Y-axis under the voltage of 120 V, respectively. And the resolution was measured as high as 0.28 μrad with the voltage increment of 0.2 V. Furthermore, the first order resonance frequency was measured as 4578 Hz and a good decoupling characteristic was obtained, the coupling errors of both two axes were below 0.75%. The two-DOF PFSM could be applied to the laser communication and the adaptive optics system based on its merits of high stiffness, high resolution and good decoupling characteristic.

The Application of Classical Control in the Design and Analysis of Power Amplifiers for Driving Piezoelectric Stack Actuators

This study proposes a new method to design an analog circuit based on the control model of the circuit, and the method is applied in the design of the power amplifiers for driving piezoelectric stack actuators. Focusing on the stability of the circuit, two power amplifiers for driving piezoelectric stack actuators are analyzed deeply. The power amplifier using high-voltage operational amplifiers has a simple circuit structure, and the bandwidth and the ripple of the power amplifier are about 43 kHz and 16 mV, respectively. As for the power amplifier using general operational amplifiers, it possesses the qualities of low cost and simple circuit structure, and the bandwidth and the ripple are 53 kHz and less than 2 mV, respectively. Moreover, the proposed power amplifiers can well drive the mechanism stage during the moving range of the piezoelectric stack actuator, and the travelling ranges are both about 13 μm. Viewing the circuit design as control system design, applying control system design method in circuit design and working with PSpice simulation of the circuit: these are the main contents of the proposed method, and the method offers an answer to designing a power amplifier systematically.

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

Piezoelectric actuators (PEA) are frequently employed in applications where nano-Micr-odisplacement is required because of their high-precision performance. However, the positioning is affected substantially by the hysteresis which resembles in an nonlinear effect. In addition, hysteresis mathematical models own deficiencies that can influence on the reference following performance. The objective of this study was to enhance the tracking accuracy of a commercial PEA stack actuator with the implementation of a novel approach which consists in the use of a Super-Twisting Algorithm (STA) combined with artificial neural networks (ANN). A Lyapunov stability proof is bestowed to explain the theoretical solution. Experimental results of the proposed method were compared with a proportional-integral-derivative (PID) controller. The outcomes in a real PEA reported that the novel structure is stable as it was proved theoretically, and the experiments provided a significant error reduction in contrast with the PID.

Development of a low capacitance two-axis piezoelectric tilting mirror used for optical assisted micromanipulation

A novel two-axis piezoelectric tilting mirror (PETM) was proposed for optical assisted micromanipulation, which avoided the shortcomings of high capacitance, relatively high cost and complex structure of general multi-axis steering mirrors using piezoelectric ceramic stack actuator. The developed PETM realized two-axis tilting motions via a simple bonded-type piezoelectric composite beam. The parametric sensitivity analyses of the tilting range and the fundamental frequency to the structural parameters were performed via FEM simulation, which facilitated serialization of the PETM. A tentative prototype was fabricated, and an experimental setup was built to carry out verification experiments. The preliminary characteristic tests including coupling motion, hysteresis and tilting motion resolution were accomplished to investigate its performances; the feasibility of closed-loop application of the PETM was confirmed by positioning and tracking experiments, which revealed its features of fast response, high positioning accuracy and feasible motion tracking capacity. Furthermore, the potential application of the PETM to manipulate laser beam in micromanipulation system was demonstrated preliminarily. In brief, the developed PETM realized low capacitance of 13.61 nF per axis to reduce the requirement for power amplifier. It can be a suitable device for optical assisted micromanipulation system by virtue of fast response, simple structure and extensible characteristics.

Active Vibration Control of Helicopter Maneuvering Flight Using Feedforward‐Robust Hybrid Control Based on Reference Signal Reconstruction

Current control laws for active control of helicopter structural vibration are designed for steady‐state flight conditions, while the vibration response of maneuvering flight has not been taken into consideration yet. In order to obtain full‐time vibration suppression capability, the authors propose a filtered least mean square‐mixed sensitivity robust control method based on reference signal reconstruction (LMS‐MSRC), driving piezoelectric stack actuators to suppress helicopter structural vibration response in maneuvering flight. When feedback controller designed by H∞ theory is implemented, active damping is added on the secondary path to weaken the adverse effects of its sudden changes in maneuvering flight state. Furthermore, a reference signal reconstruction scheme is given concerning equivalent secondary path. In addition, the reconstruction accuracy, the convergence speed, stability, and global validity of the hybrid controller are analysed. Compared with multichannel Fx‐LMS, numerical simulations of LMS‐MSRC for vibration suppression are undertaken with a helicopter simplified finite element model under several typical flight conditions. Further experiments of real‐time free‐free beam vibration control are performed, driven by a stacked piezoelectric actuator. The instantaneous overshoot of measured response is 42% less than the peak value and its attenuation reaches 85% within 2.5 s. Numerical and experimental results reveal that the proposed algorithm is practical for suppressing transient disturbance and multifrequency helicopter vibration response during maneuvering flight with faster convergence speed and better robustness.

Design and Analysis of a Novel Compliant Tensile Testing Module Based on Buckled Fixed-Guided Beam

The need to accurately measure the mechanical properties of freestanding thin films such as carbon nanotube reinforced nanocomposite thin films and various buckypaper is increasingly urgent. This paper presents the design and control of a novel compliant tensile testing module based on buckled fixed-guided beams aimed at accurately measuring the mechanical properties of freestanding thin films. The piezoelectric stack actuator that can provide high resolution for the output displacement is chosen to actuate the tensile testing module. The advantages of the module are its compactness, no friction, no wear, low cost and good repeatability. The performance is further evaluated by the established analytical model using the elliptic integral approach and the nonlinear finite-element analysis (FEA). A metal prototype of the tensile testing design has been fabricated and the performance of the fabricated prototype is investigated through open-loop displacement response experiments. Experimental results demonstrate the effectiveness of the proposed ideas for the mechanism. The design holds great potential applications in measuring mechanical properties of freestanding thin-film materials such as carbon nanotube reinforced nanocomposite thin films and various buckypaper as well as other freestanding thin-film materials.

Towards wearable tremor suppression using dielectric elastomer stack actuators

Active wearable tremor suppression devices apply actuators to the human body to produce joint torques that reduce tremor motion. This potential alternative to medications and surgery has the advantage of providing robust tremor treatment that is non-invasive, but the bulkiness of typical engineering actuators currently prohibits clinical implementations. Dielectric elastomer stack actuators (DESAs) offer a potential pathway towards achieving soft, low-profile tremor suppression devices: DESAs have similar mechanical properties as human muscles and can conform to the human limb. However, low actuation levels and a lack of commercial availability limit the development of DESA-based orthoses. Employing a control approach that only suppresses tremor while allowing the actuators to follow voluntary motion passively significantly decreases actuation requirements to improve potential for clinical devices. Still, DESAs that may offer the necessary actuation characteristics require specialized equipment and techniques. This research advances DESA-based tremor suppression by experimentally demonstrating DESA-based suppression of tremor-like signals on a scaled system using easily manufactured DESAs. Further discussion quantifies the DESA parameters that will enable physical implementations of human-scale tremor suppression and identifies pathways towards achieving those parameters.

A High-Voltage and Low-Noise Power Amplifier for Driving Piezoelectric Stack Actuators.

In this paper, based on the principles of general operational amplifiers, a high-voltage operational amplifier is developed. Considering the influences of piezoelectric stack actuators on the circuit, a novel structure using the high-voltage operational amplifier as a noninverting amplifier is proposed. Because of the simple circuit principles and the voltage feedback control structure, the proposed power amplifier has the advantages of low noise and small size, and it can be realized by discrete electric elements easily. In the application of precision positioning, a power amplifier using the proposed circuit principles for driving piezoelectric stack actuators is designed, simulated, and tested. The simulated results show that the proposed power amplifier could conform to the theory of the circuit. The experimental results show that the designed power amplifier conforms to the simulation, the bandwidth of the power amplifier is about 57 kHz, and the ripple of the power amplifier is less than 2 mV. Furthermore, the output of the proposed power amplifier maintains the same type of wave within in a large range of frequency, while the input is the sinusoidal or square wave, and the resolution of the mechanism which the power amplifier is applied in is about 4.5 nm. By selecting the critical electronic elements and using feedback control, the proposed circuit structure is able to realize a low-cost and high-performance power amplifier to drive piezoelectric stack actuators flexibly, which is the novel work of the paper.

Error Signal Differential Term Feedback Enhanced Variable Step Size FxLMS Algorithm for Piezoelectric Active Vibration Control

FxLMS (Filtered-x Least Mean Square) algorithm is widely used in the field of AVC (active vibration control) for its good convergence and strong adaptability. However, the convergence rate and steady-state error are mutually restricted for the fixed step FxLMS algorithm. Increasing step size μ to accelerate the convergence rate will result in larger steady-state error and even cause control divergence. In this paper, a new DVSFxLMS (error signal Differential term feedback Variable Step size FxLMS) algorithm is proposed by establishing nonlinear function between μ and error signal, while using differential term of the error signal as the feedback control function. Subsequently, a DVSFxLMS controller is designed to carry out the AVC simulation and experiments on cantilever beam with PSA (piezoelectric stack actuator). Simulation and experimental results show that the proposed DVSFxLMS algorithm has faster convergence rate and smaller steady-state error than the traditional FxLMS algorithm, which also has strong antinoise ability and adaptive control ability to quickly track the variable external disturbance.

Development and characterization of novel piezoceramic material based stack actuator

The present research investigated the performance characteristics of multilayer stack actuator fabricated using the novel lead-free BaZr0.05Ti0.95O3 (BZT) piezoceramic material in the high field amplitude and low frequency dynamic regime. A systematic approach was undertaken, firstly, to experimentally study the electromechanical strain and degree of hysteresis of a single layer, and evaluate the dependency on the field amplitude and frequency. Based on the obtained characteristics of the single layer, a careful choice of the combination of field amplitude and frequency was implemented to study the free stroke of a multilayer stack actuator. The novel material based stack actuator fabricated at the laboratory scale yielded encouraging results for high precision actuatoric applications.