Stack Actuator Research Articles

Direct identification of generalized Prandtl–Ishlinskii model inversion for asymmetric hysteresis compensation

In this study, we present an identification-based direct construction of the inverse generalized Prandtl–Ishlinskii (P–I) model to facilitate inverse model-based feedforward compensation of asymmetric hysteresis nonlinearities. Compared with the derivation of the inverse model analytically from a generalized P–I model, this direct modeling approach has the following advantages. First, direct inverse model identification is formulated as a nonlinear optimization problem, which is not subject to the constraint condition on the generalized P–I model's threshold and density functions, where this is indispensable for the analytical model inversion procedure. Second, this approach may be a simple and attractive alternative when the identification precision of a generalized P–I model is limited by the constraint condition, which necessarily results in insufficient hysteresis compensation functionality for the analytically derived inverse model. Finally, direct inverse model identification can overcome the drawbacks of the analytical inversion method, including the accumulation of parameter estimation errors in an analytical inverse model because these parameters are computed from the generalized P–I model's parameters in a recursive manner. Our experimental results demonstrated that the implementation of open-loop control with the directly identified inverse generalized P–I model as a feedforward compensator achieved precise compensation for the asymmetric hysteresis nonlinearities of a piezoelectric stack actuator.

Modeling and design of a pre-stressed piezoelectric stack actuator

To provide a method for designing a pre-stressed PSA with high-performance, it is very meaningful to model the dynamic characteristics of the pre-stressed PSA accurately. A novel model, which considers both the electric side and the mechanical side of the PSA as distributed systems, is put forward to describe the dynamics characteristics of the PSA and the pre-stressed PSA. The role of the pre-stressed mechanism is derived and analyzed by extended transfer matrix method, and then the principle of design of the pre-stressed mechanism is obtained. The theoretical analysis is in accordance with the experimental results.

Fuzzy sliding mode control of flexible spinning beam using a wireless piezoelectric stack actuator

Spinning structures play an outstanding role in aerospace engineering. The vibration caused by eccentric forces or external excitations would damage the structures. Vibration suppression of such spinning structures is necessary, but challenging because of the arrangement of actuators. A new wireless piezoelectric stack actuator spinning in a varying magnetic field is introduced in this paper to avoid the wires winding with large control force. The control voltage on the actuator is generated by the motion of the wires in magnetic field. Besides, fuzzy sliding mode control with universal fuzzy sets based on the wireless actuator is investigated. Numerical simulation demonstrates that the tip displacement response of the spinning beam reduces over 98% compared with that open loop, while the magnitude of the peak in frequency domain decreases from 0.0976dB to 0.0383dB. It proved that the proposed actuator is feasible and the fuzzy sliding mode controller could suppress the vibration of spinning beam effectively with a strong robustness to noise.

A new self-tuning fuzzy controller for vibration of a flexible structure subjected to multi-frequency excitations

This work proposes a new self-tuning fuzzy controller for vibration control of a flexible structure subjected to both single-frequency and multi-frequency excitations. A piezoelectric stack actuator is used to generate control force to attenuate vibrations in the resonant and non-resonant frequency ranges. As a first step, modal frequencies and modal shapes of the flexible beam structure are obtained via the finite element method, and these are verified through comparison with the measured values. Second, in order to attenuate multi-frequency vibration of the beam, a new fuzzy controller with self-tuning factors is proposed. This controller is independent of the structure model and very adaptive to variable excitations. Then, vibration control performances of the self-tuning fuzzy controller are experimentally investigated under two different excitation conditions: single-frequency and multi-frequency excitations. It is shown that vibration control capability of the proposed controller outperforms convent...

Compensated positive position feedback for active control of piezoelectric structures

This article presents a compensated positive position feedback strategy for active control of flexible structures with piezoelectric actuators. In the proposed compensated positive position feedback method, a negative feedback compensator is involved to remedy the deficiency of traditional positive position feedback and to introduce roll-off characteristic at low frequencies. Thus, compensated positive position feedback controllers can be developed with minimal influences on lower order modes and cause no steady-state error to the controlled system. For demonstration purpose, the design processes and the effectiveness of the compensated positive position feedback method are illustrated by active control of a cable net structure with integrated piezoelectric stacked actuators. The numerical simulations demonstrate that compared to the conventional positive position feedback method, the proposed compensated positive position feedback approach overcomes the fundamental defects of frequency shift and spillover into lower order modes and achieves the goal of step-tracking with zero steady-state error. These comparative results confirm the efficacy and superiority of the proposed compensated positive position feedback methodology in active control of flexible structures.

Traveling wave control of stringed musical instruments

Traveling wave control is a technique in which the energy propagating around a structure in the form of waves can be manipulated directly in order to change the overall dynamic behaviour of the structure. In this research, traveling wave control is applied to a musical instrument string with a view to affecting the timbre of the sounds produced by the string when vibrating. A highly linear custom optical sensor is built which is capable of detecting a wave traveling on a string in a single direction, and a piezo stack actuator is situated under the termination point of the string allowing the reflection of the wave to be manipulated directly. Various controllers are analyzed theoretically in terms of their performance, stability, and musical usefulness. They are then implemented and evaluated in terms of their relevance to the design of new musical instruments.

Optimal design of a smart post-buckled beam actuator using bat algorithm: simulations and experiments

The optimized design of a smart post-buckled beam actuator (PBA) is performed in this study. A smart material based piezoceramic stack actuator is used as a prime-mover to drive the buckled beam actuator. Piezoceramic actuators are high force, small displacement devices; they possess high energy density and have high bandwidth. In this study, bench top experiments are conducted to investigate the angular tip deflections due to the PBA. A new design of a linear-to-linear motion amplification device (LX-4) is developed to circumvent the small displacement handicap of piezoceramic stack actuators. LX-4 enhances the piezoceramic actuator mechanical leverage by a factor of four. The PBA model is based on dynamic elastic stability and is analyzed using the Mathieu–Hill equation. A formal optimization is carried out using a newly developed meta-heuristic nature inspired algorithm, named as the bat algorithm (BA). The BA utilizes the echolocation capability of bats. An optimized PBA in conjunction with LX-4 generates end rotations of the order of 15° at the output end. The optimized PBA design incurs less weight and induces large end rotations, which will be useful in development of various mechanical and aerospace devices, such as helicopter trailing edge flaps, micro and nano aerial vehicles and other robotic systems.

Active vibration isolation with a dielectric elastomer stack actuator

This work presents the development, simulation and experimental investigation of a demonstrator for active vibration isolation with dielectric elastomers (DEs). The electromechanical behavior of the developed DE stack actuator is first characterized experimentally and a suitable simulation model is parametrized accordingly. The potential of the actuator for active vibration isolation is shown in a specially designed single axis test rig. The influence of different control strategies on the transmission behavior from the excited base to the mass is studied. A special aspect of the control strategy is the compensation of the specific nonlinearities. The analysis proves the potential of DE actuators for active vibration isolation purposes. The presented broadband active isolation could enable the use of DEs in various technical fields of application.

An efficient piezoelectric energy harvester with frequency self-tuning

A beam energy harvester made of an aluminum substrate surface bonded with piezoelectric patches and a stack actuator is developed to achieve an efficient energy harvesting technology with a new developed frequency self-tuning process. To accomplish the self-tuning process, an adjustable axial force applied to the energy harvester is generated by the piezoelectric stack actuator. The stack actuator is controlled by a charged voltage on a small tuning capacitor, which is connected to and charged by the harvester. The function of the stack actuator is to automatically tune the natural frequency of the harvester to match the major exciting frequency of the ambient vibration through the tuning capacitor. To describe the energy harvesting and the self-tuning process, an iteration numerical method is developed to solve the dynamic response of the harvester and the generated electric charge. Effects of the piezoelectric patch sizes on the energy harvester's power generation are conducted and discussed. Research findings show that the self-tuning process significantly increases the power output from the harvester by more than 26 times compared to the one without the developed tuning process. Furthermore, the finite element method (FEM) is employed to verify the effectiveness of the proposed self-tuning method.

Decentralized adaptive fuzzy vibration control of smart gossamer space structure

Gossamer space structures technology have gained widely applications in space missions. However, the vibration problem is a great challenge which makes the technology complicated. The overall motivation of this work is to develop a vibration control system for gossamer space structures. In this study, a space membrane structure with piezoelectric stack actuators bracketed on its support frame is considered. First, the description of the smart space membrane structure and its dynamic model are presented. Then, a decentralized adaptive fuzzy control method is developed to control the structure vibration. Finally, experimental system is built up, and two vibration control experiment cases are carried out to verify the proposed control method. Experimental results demonstrate that the proposed control method is more effective than the fuzzy control method.

Investigation of fracture properties of a piezoelectric stack actuator using the digital image correlation technique

In this study, the fracture properties of a piezoelectric stack actuator made of a single crystal (PMN-29PT) were investigated using a three point bending test along with the digital image correlation (DIC) technique. To simplify the model of the piezoelectric stack and minimize the cost, two layers of PMN-29PT and one thin copper electrode were glued together using silver conductive adhesive instead of a real piezoelectric stack with 40PMN-29PT layers. The PMN-29PT layers were then strongly attached with a two square section acrylic beam forming a beam with the same geometry as the piezoelectric stack. The three point bending test results showed that the force at the crack onset was around 85% of the fracture force. The maximum stress and fracture energy from force-displacement data were measured to be 1.41MPa and 3.83J/m2, respectively. Furthermore, the fracture surface indicated that the fracture energy was affected by the surface of the copper electrode, and that the rough surface of the electrode can increase the fracture energy. The fracture energy was determined using a simple beam theory. The fracture energy according to the simple beam theory was slightly smaller than that from force-displacement data. Understanding the measured fracture properties of the piezoelectric stack will help us prevent the fracture of the stack when the piezoelectric stack actuator is handled.

Vibration isolation for parameter-varying rotor systems using piezoelectric actuators and gain-scheduled control

This paper deals with the active vibration isolation for a rotor subject to gyroscopic oscillations, where gain-scheduled [Formula: see text]-control is used to steer an active, piezoelectric bearing. Rotating machines are often exposed to gyroscopic effects, which occur due to bending deformations of rotors and subsequent tilting of eccentric mass elements. Gyroscopic moments observed at rotors are proportional to the rotational speed and couple radial degrees of freedom. This relationship with the operating conditions renders the system dynamics well-suited for the use of linear parameter-varying models and controllers, relying on the rotational speed as an uncertain parameter. In this paper, we design linear gain-scheduled [Formula: see text]-controllers guaranteeing both robust stability and performance within a given range of operating conditions. The paper is based on a rotor test rig with two unbalance-induced resonance frequencies in its operating range. The rotor has two protruding discs, one of which is centered between one active and one passive bearing support. The active support consists of two piezoelectric stack actuators and two collocated piezoelectric load washers. Closed-loop performance is assessed via isolation of unbalance-induced vibrations using both simulation and supporting experimental data.

Modeling of a three degrees of freedom piezo-actuated mechanism

This paper presents the modeling and experimentation of a three degrees of freedom (3-DOF) piezo-actuated mechanism. The displacements of the piezoelectric stack actuators are amplified with lever mechanisms to achieve large displacement output. In order to accurately model the mechanism, a comprehensive model, which uses the transfer matrix method to describe the dynamics characteristics and the modified Bouc–Wen hysteresis operator to represent the hysteresis, is presented. Ultimately, the proposed comprehensive model of the mechanism is experimentally investigated for its performance. Experimental results show that the proposed comprehensive model can accurately portray the hysteresis and dynamics characteristics of the 3-DOF piezo-actuated mechanism.

Resonant frequency and hysteresis of a stack actuator made of single crystal (PMN-29PT) layers

In this study, we have presented the dynamic behavior of a piezoelectric stack actuator made of forty layers of single-crystal (PMN-29PT) with an area of 10 × 10 mm2 and thickness of 1 mm. To conduct a dynamic test of the actuator, we built a test apparatus with dummy weights that was placed over the top of the actuator to measure the actuation displacement. The resonant frequencies of the actuator with and without the dummy weight were determined as the excitation frequencies where a significant increase in the actuation displacement could be observed. We also proposed an analytical multi-degree-of-freedom (MDOF) model of the actuator to analytically predict the resonant frequency. Finite element analyses were conducted to validate the analytically predicted and measured resonant frequencies. With no dummy weight, the resonant frequency of the actuator was measured at 730.00 Hz, which was 0.70% higher than the one calculated by the MDOF model and 0.10% smaller than that of the finite element model. With a dummy weight, the measured resonant frequency was lower than 730.00 Hz and close enough to those computed by the MDOF model and the finite element model. The hysteresis curves of the actuator at various frequencies indicated that the actuator might incur a small energy loss.

A novel microgripper hybrid driven by a piezoelectric stack actuator and piezoelectric cantilever actuators.

For the piezo-driven microgripper, one issue is to enlarge the grasping stroke and realize parallel grasping movement in the compact design. Piezoelectric stack actuator (PSA) and piezoelectric cantilever actuator (PCA) are two kinds of typical piezoelectric actuators. In this study, a novel microgripper hybrid driven by a PSA and two PCAs is proposed, which can be a better solution for the issue, compared with the previous microgripper using PSA-driven multi-stages displacement amplification mechanism (DAM) or using longer and narrower PCAs. A compact one-stage orthogonal DAM is proposed for the PSA in the microgripper, which can enlarge the grasping stroke and realize parallel grasping movement. The proposed orthogonal DAM is a triangulation amplification-based mechanism with undetermined structural parameters. Bidirectional symmetric input forces/displacements are not required in the proposed design. The number of the undetermined parameters and the solution principle are analyzed. Finite element analysis is used to verify the proposed DAM. The gripper arms are designed as two PCAs, for which the grasping and parasitic movements of the free end are modeled. Piezoelectric-static coupling finite element analysis is used to verify the models. The PCAs-driven grasping with considerable parasitic movement can be used in the coarse positioning. The integration of the hybrid-driven microgripper is presented, and its performances are presented and verified by experiments.

Preloading Piezoelectric Stack Actuators in High-Speed Nanopositioning Systems

Recent development in high-speed nanotechnology applications such as scanning probe microscopy and nanofabrication has increased interest on the advancement of high-bandwidth flexure-guided nanopositioning systems. These systems are capable of providing motions with sub-nanometer resolution over a positioning bandwidth of a few kilohertz or more. High-speed nanopositioning devices are commonly driven by compact and stiff piezoelectric stack actuators. However, these actuators are highly sensitive to tensile and lateral forces. During high-speed operations, excessive inertia force due to the effective mass of nanopositioning system could potentially damage the actuator. To protect the piezoelectric actuator, preload is often applied to compensate for these inertial forces. This article surveys key challenges in existing preload techniques in the context of high-speed nanopositioning designs, and explores how these challenges can be overcome.

Blocking force of a piezoelectric stack actuator made of single crystal layers (PMN-29PT)

In this study, we fabricated and characterized a stack actuator made of forty layers of 1 mm thick PMN-29PT with a cross-sectional area of 10 × 10 mm2. From the measurement of actuation displacement, we confirmed that the piezoelectric strain constant in the direction of thickness of the material is 2000 pm V−1, as suggested by the manufacturer. The blocking forces of the actuator are measured to be 230 N, 369 N, and 478 N for 100 V, 200 V, and 300 V, respectively. The measured blocking forces showed large discrepancies from the estimated blocking forces calculated using linear models, especially for a high voltage application. An empirical equation acquired by fitting the measured blocking forces indicates that the blocking force has a nonlinear relationship with the applied voltage. The measured hysteresis showed a slight nonlinear voltage-stroke relationship and small energy loss.

Compact piezoelectric tripod manipulator based on a reverse bridge-type amplification mechanism

We report a hierarchical piezoelectric tripod manipulator based on a reverse bridge-type displacement amplifier. The reverse bridge-type amplification mechanism is pre-strained by each piezo-stack actuator up to 60 μm and is cross-stacked in a series arrangement to make a compact and high-stroke manipulator having load-bearing characteristics. The designed manipulator with three degrees of freedom is compact with a height of 56.0 mm, a diameter of 48.6 mm and total weight of 115 g. It achieves a translational stroke of up to 880 μm in heaving motion and a tilting angle of up to 2.0° in rotational motion within the operating voltage and power range of the piezoelectric stack actuator. A key feature of the present design is built-in and pre-strained displacement amplification mechanisms integrated with piezoelectric stacked actuators, resulting in a compact tripod manipulator having exceptionally high stroke and load-bearing capacity.

The effective frequency range of an active suspended handle based on the saturation effects of a piezo stack actuator

This paper presents a novel approach to the design of an active suspended handle by identifying the effective frequency range, based on the saturation effects of the piezo stack actuator, in terms of the force-displacement-voltage relationship as a function of the excitation frequency. The effective range allows for proper matching between the operating speed of the machine and the suspended handle. A model of the active suspended handle was developed, which took into account the non-linear saturation effect of the piezo stack actuator. A proportional-integral-derivative controller generated the counter voltage for the piezo stack actuator, using a proportional feedback gain (P) step up method, in order to attenuate the vibration transmitted to the handle. By including the saturation effect, the Pearson’s correlation coefficient (R2) of the model improved to 0.97, within the frequency range of 50 ∼ 500 Hz. Using this approach, we identified that the effective frequency range of isolation with transmissibility less than unity is between 250 ∼ 450 Hz. The active suspended handle was attached to a die grinder with a nominal operating speed of 25000 rpm and the vibration transmitted from the die grinder to the handle was reduced by 91%.

High speed single- and dual-stage vertical positioners.

This article presents a high-speed single- and dual-stage vertical positioners for applications in optical systems. Each positioner employs a unique end-constraint method with orthogonal flexures to preload a piezoelectric stack actuator. This end-constraint method also significantly increases the first mechanical resonance frequency. The single-stage positioner has a displacement range of 7.6 μm and a first resonance frequency of 46.8 kHz. The dual-stage design consists of a long-range slow-stage and a short-range fast-stage. An inertial counterbalance technique was implemented on the fast-stage to cancel inertial forces resulting from high-speed motion. The dual-stage positioner has a combined travel range of approximately 10 μm and a first evident resonance frequency of 130 kHz.