Piezoelectric Actuator System Research Articles

Trajectory compensation based adaptive control (TCAC) for high-precision piezoelectric actuators

Piezoelectric actuator (PEA) has been widely used in micro-systems, due to the advantages of nano-scale precision, rapid response speed, high stiffness, etc. Nevertheless, the intrinsic nonlinearities of PEA, particularly hysteresis, severely deteriorate its positioning and tracking control accuracy. In most existing control algorithms of PEA, the approximate inverse model of hysteresis is developed to compensate for motion error, which requires high modeling accuracy. To avoid the influence of complex modeling procedures and modeling errors on tracking precision, a trajectory compensation-based adaptive control method has been proposed in this paper. Firstly, a simple linear controller is used to establish the closed-loop feedback system and to guarantee the basic tracking performance of the PEA system. And then, the trajectory compensation is designed according to the frequency analysis of the closed-loop control system. Finally, nonlinear adaptive compensation is used to eliminate the residual errors of the above linear frequency domain model. Different from conventional controllers, the proposed method can achieve excellent tracking control performance without any hysteresis model of PEA. The stability and convergence of the proposed method have been theoretically proved. In addition to theoretical guarantees, the proposed method is validated experimentally and demonstrated to achieve the root-mean-square and maximum value of tracking errors to less than 8 nm and 25 nm, respectively, which has a clear accuracy advantage over other methods.

Data-driven robust iterative learning control of linear systems

We propose a data-driven robust iterative learning control (ILC) technique to multi-input-multi-output (MIMO) linear systems. Control of MIMO linear systems, particularly with strong cross-axis coupling, is challenging as modeling of a MIMO system can be complicated, time-consuming, and often requires a trade-off between robustness and performance. As such, limitations exist in current ILC techniques. The aim of this paper is to develop an efficient and easy-to-use data-driven ILC technique to output tracking of MIMO linear systems under random disturbance. Through the proposed technique, the complicated modeling process and the robustness-accuracy trade-off are avoided, and the up-to-now system dynamics is captured by constructing and updating the iteration gain using the input and output data in the last iteration. It is shown that monotonic convergence of the ILC algorithm is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual tracking error. The proposed technique is illustrated through experiments on a three-input three-output piezoelectric actuator system, with comparison to the adaptive multi-axis inversion-based iterative control (A-MAIIC) technique. The experimental results show rapid convergence and improved formance of the proposed technique when the cross-axis coupling is strong.

Hysteresis Segmentation Modeling and Experiment of Piezoelectric Ceramic Actuator

Piezoelectric ceramics have been widely used in ultraprecision displacement drive systems because of their excellent performance such as fast response and high positioning accuracy. However, its tracking control accuracy is limited by its inherent hysteresis nonlinearity. To date, the parameter identification of the hysteresis model that has been developed is complex. This situation has resulted in the difficulty for the model to be used in the real-time control system of piezoelectric ceramic actuators. This article proposed a new mathematical model that can accurately describe hysteresis nonlinearity. The hysteresis main loop in the model is approximated using high-order rational fractions. The hysteresis segmentation model is completed through the recursive algorithm. Simulation and experimental results show that the hysteresis characteristics between the input voltages and output displacements have been clearly modeled. This segmentation modeling process is simple. In addition, the computation is low and accuracy is high. The model proposed in this article can complete the modeling of complex hysteresis phenomena of the multidegree-of-freedom micromotion stage with force–voltage coupling. Through a series of experiments to verify the effectiveness of the model in this article, thereby laying the model foundation for the subsequent control of the piezoelectric ceramic actuator. This result also provides a strong scientific basis for future research on the application of piezoelectric ceramic actuators in ultraprecision motion systems and further improves the positioning accuracy of the system.

Modelling of piezoelectric actuating systems subjected to variable loads and frequencies and applications to prescribed performance control

Piezoelectric actuators can offer micro/nano-level precision actuating ability and have been employed in different applications. For the piezoelectric actuating systems, the output actuating performance is affected not only by the internal non-smooth hysteresis but also by the operating load and the excitation frequency. To improve the actuating precision, predicting the nonlinear behaviour of the piezoelectric actuating system is essential for effective designs of control approaches. In this paper, a modified rate-dependent Prandtl–Ishlinskii model is presented to explore the coupling effects analytically between the internal hysteresis and the operating frequency with the external loads and predict the output behaviour of the piezoelectric actuating system accurately. The proposed modelling method is testified on a piezoelectric actuating platform under broad ranges of excitation frequencies (1–80 Hz) and external loads (0–0.5 kg), and the comparison results using the rate-dependent Prandtl–Ishlinskii (RDPI) model are also provided to prove the precision of the proposed method. Combining with the modified RDPI model, a guaranteeing preselected tracking controller is developed to ensure the output performance, and a set of tracking experiments under different frequencies with load is performed. The experimental results compared with PID control performance validate the effectiveness of the proposed prescribed performance control method and its high actuating performance against the adverse effects from the external hysteresis nonlinearities and external loads.

In-vessel piezoelectric actuation system for DTT ECRH launchers: Conceptual design

The Electron Cyclotron Resonance Heating (ECRH) system of Divertor Tokamak Test (DTT) facility will feature up to 35.2 MW installed power. At the time of its completion, it will be the most powerful ECRH system ever realized. In full power configuration, 4 sectors of the tokamak will be equipped with equatorial and upper antennas with respectively 6 and 2 launchers each, for a total of 32 launchers, fed by 16 1-MW, 170-GHz gyrotrons and 16 1.2-MW, 170-GHz gyrotrons. The last mirror of each ECRH launcher should be independently steerable about two axes to provide the required operational flexibility. Due to the high number of independent launchers in a relatively small space, a compact driving mechanism is required. In state-of-the-art ECRH systems, out-of-vessel drives are connected to the steering mirror through long shafts or bellows. In this paper, we present the conceptual design of an innovative driving mechanism, which relies on in-vessel piezoelectric actuators and compliant hinges to meet compactness requirements, minimize system’s inertia, friction and backlash, while maximizing positioning accuracy. The work includes a general overview of the system, the model of the semi-compliant transmission, the identification of candidate materials and the sizing of the driving mechanism.

A Fractional-Order Normalized Bouc–Wen Model for Piezoelectric Hysteresis Nonlinearity

This article presents a new fractional-order normalized Bouc–Wen (BW) (FONBW) model to describe the asymmetric and rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW) model is only efficient for the symmetric and rate-independent hysteresis description, the FONBW model is devoted to characterizing the asymmetric and rate-dependent behaviors of the hysteresis in PEAs by adopting an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> th-order polynomial input function and two fractional operators, respectively. Different from the traditional modified BW models, the proposed FONBW model also eliminates the redundancy of parameters in the CBW model via the normalization processing. By this way, the developed FONBW model has a relatively simple mathematic expression with fewer parameters to simultaneously characterize the asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters are identified by the self-adaptive differential evolution algorithm. To validate the effectiveness of the proposed model, a series of model verification and inverse-multiplicative-structure-based feedforward control experiments are carried out on a PEA system. Results show that the proposed model is superior to the CBW model and traditional modified BW model in modeling accuracy and hysteresis compensation.

Adaptive sliding mode control with hysteresis compensation-based neuroevolution for motion tracking of piezoelectric actuator

In this paper, an adaptive sliding mode control with hysteresis compensation-based neuroevolution (ACNE) is proposed for precise motion tracking of the piezoelectric actuator (PEA) in the presence of uncertainties, disturbances, and nonlinearity hysteresis characteristics. Firstly, a new memetic differential evolution (MeDE) algorithm is proposed to optimize the weights of a 3-layer neural network (called neuroevolution or NE). In MeDE, a differential evolution algorithm is used as a global search scheme and the Jaya algorithm is used as local search exploitation. Secondly, an inverse hysteresis model of PEA is identified by the neuroevolution model to provide a feed-forward NE control signal to compensate for the hysteresis behavior of PEA system. Thirdly, an adaptive neural sliding mode control plus feedforward NE (ACNE) control is designed to enhance the quality control and guarantee asymptotical stability for PEA system. Based on the Lyapunov method, the stability of the closed-loop system is analyzed and proved. Finally, the experimental Thorlabs piezoelectric actuator (PEA) is set up to verify the robustness and effectiveness of the proposed approach. Results show that the identified MeDE-Neuroevolution model has successfully applied to model the inverse hysteretic of PEA system and the performance of MeDE has better than Jaya, DE, and PSO in terms of best, worst, average, and standard deviation. Furthermore, in motion tracking control, the performance of proposed ACNE control has more accurate than a classical PID control, a feedforward control, a hybrid feedback–feedforward control, and an adaptive neural sliding mode control without a compensator.

Polynomial-based Stability Analysis of Modified IMC-PID Controller for Piezoelectric Actuator System in Time Delay Environment

Piezoelectric actuators are widely used in several industrial applications requiring precision positioning. However, the positioning accuracy of this nonlinear actuator is severely limited by physical phenomenon such as hysteresis, uncertainties. Accordingly, to improve the performance of piezo micro–nano positioning system, appropriate control laws are designed to linearize the hysteresis through closed-loop approaches. A modified internal model controller (MIMC) is useful with regard to efficient computational hardware resource utilization when compared with the conventional approach provided the resulting controller is stable. This paper focuses on one such widely used and computationally inexpensive control framework in the form of PID-based MIMC to mitigate hysteretic nonlinearity in piezoelectric actuators with the aim to investigate the time delay uncertainty handling range of the controller. The system stability pertaining to time delay has been analyzed numerically and the maximum delay that the system can withstand without losing its stability, i.e. the delay margin has been determined using polynomial-based approach. It has been found that upon increasing the delay beyond a specific critical value, the controller performance is limited and the system turns unstable. Simulations carried out in time delay environment validate the theoretically achieved results.

Backstepping Sliding-Mode Control of Piezoelectric Single-Piston Pump-Controlled Actuator

A piston piezoelectric (PZT) pump has many advantages for the use of light actuators. How to deal with the contradiction between the intermittent oil supplying and position control precision is essential when designing the controller. In order to accurately control the output of the actuator, a backstepping sliding-mode control method based on the Lyapunov function is introduced, and the controller is designed on the basis of establishing the mathematical model of the system. The simulation results show that, compared with fuzzy PID and ordinary sliding-mode control, backstepping sliding-mode control has a stronger anti-jamming ability and tracking performance, and improves the control accuracy and stability of the piezoelectric pump-controlled actuator system.

Fractional order sliding mode control based on single parameter adaptive law for nano‐positioning of piezoelectric actuators

A fractional order sliding mode control (FOSMC) based on single parameter adaptive law for nano-positioning of Piezoelectric Actuators (PEAs) is proposed. First, the Bouc–Wen (B–W) model is used to describe the hysteresis of the nano-position platform based on PEAs, which provides a mathematical model for the subsequent controller design. Then, theoretical support is provided to design the FOSMC based on adaptive law of different parameters, which are proposed for the displacement tracking problem of PEAs, and the position error convergence is also proved. Moreover, the core parameters of FOSMC based on single parameter adaptive law are identified by hybrid differential evolution (HDE) and adaptive differential evolution (ADE), which require considering the relationship between the scaling factor and the cross-probability factor. Finally, experiments have been conducted with the displacement signals mixed with multiple frequencies and multiple amplitudes and the results obtained from them show that the proposed control scheme can produce a faster response and smaller tracking errors in PEAs system as compared to traditional control algorithms.

Reducing the systematic error of the average fluid flow rate in axisymmetric computer model of piezoelectric micropump

Mathematical and computer models of an axisymmetric coupled problem of interaction of a fluid and an elastic body for the solving partial differential equations by the finite element method FreeFem ++ software are proposed. In these models, periodic vibrations of annular piezoelectric actuators placed on an elastic tube of circular cross-section lead to radial deformations of the tube. With a synchronous oscillation of the system of piezoelectric actuators, the average fluid flow rate is zero. An asymmetric oscillation pattern (micropump mode) results in a nonzero average flow rate. Two types of boundary conditions are considered in the region of contact between the piezoelectric drive and the tube — Dirichlet and Neumann. The computer model was tested for unsteady fluid flow induced by a pressure gradient applied along the pipe with a circular cross section. With synchronous oscillation of piezoelectric actuators, a nonzero average fluid flow is a systematic error. This value was compared with the asymmetric oscillation pattern of piezoelectric actuators to determine the contribution of the systematic error to the pump-generated fluid flow rate. Based on the fluid flow velocity profile and the results of profiling the program code, the optimal parameters of the computational meshes for the channel (dense uniform) and tube walls (nonuniform, consistent with the velocity profile and reconstructing at each time step) were determined, which reduce the magnitude of the systematic error. The main way to reduce the error is to increase the density of the computational mesh, which leads to an increase in the required computing resources. An alternative method is proposed for reducing the systematic error due to an additional pressure drop applied to the channel. Depending on the type of boundary conditions and the number of piezoelectric actuators, this method can reduce the systematic error by 1 − 2 orders of magnitude without increasing the simulation time.

Characterization of energy consumption of new piezo actuator system used for hydraulic on/off valves

This paper presents a newly developed four-way digital piezo valve system composed of four high-response on/off piezo valves. The main part of the new on/off piezo valves introduces the piezo actuator system, which can be used instead of conventional solenoids. One of the important aspects related to the energy consumption of hydraulic linear drives is the use of energy-efficient hydraulic valves that require low switching energy and low holding power consumption. The first part of the paper presents the theoretical background of piezo technology, which is very important for understanding the properties of piezoelectric actuators. It is followed by a detailed description of the new piezoelectric actuator system used in on/off valves and four-way digital piezo valve system. The main part presents a thorough experimental analysis of the electrical energy consumption of the new piezoelectric actuator system, which can be used both as an actuator of hydraulic high-response on/off valves as well as an energy-efficient micropositioner. To validate the electrical switching energy and the holding power consumption of the new piezoelectric actuator system, several existing on/off valves were used as reference. The experimental analysis shows a huge reduction of electrical energy consumption when using the new piezo actuator system for hydraulic on/off valve actuation. Especially the holding power consumption in the stationary active state is about 6 times lower compared to other hydraulic on/off valves.

Robust adaptive motion tracking of piezoelectric actuated stages using online neural-network-based sliding mode control

Robust and precise motion tracking for micro-electro-mechanical systems in the presence of inherent nonlinearity and external disturbance is of great importance in many applications. Due to high sensitivity to environmental variations, the entire model or some parameters of the system tend to change unexpectedly. Existing offline nonlinearity models are computationally intensive and may be not suitable under system perturbations. In this work, for a class of piezoelectric actuated (PEA) system, a new online neural-network-based sliding mode control (OLNN-SMC) scheme is developed to obtain robust adaptive precision motions. The nonlinearity of the PEA system is identified online and compensated using singularity-free neural networks (NNs). To alleviate the residual NN approximation errors and meanwhile maintain robust stability under external disturbance, a feedback sliding-mode is synthesized into the control law. Considering unknown and varying disturbances, an adaptive mechanism is designed to achieve robust adaptive motion tracking. The controller is implemented and evaluated through experiments on a PEA platform. Results show that the proposed OLNN-SMC is superior to existing proportional-integral-derivative control with disturbance observer (PID+DOB) and adaptive sliding mode control (ASMC) in terms of sinusoidal tracking and disturbance rejection. In particular, the root-mean-square (RMS) errors for sinusoidal tracking at 0.1–10 Hz using the proposed OLNN-SMC are reduced by 83.5% compared with the cases using PID+DOB or ASMC.

Asymmetric indirect-driven self-sensing actuation and its application to piezoelectric systems

Self-sensing actuators use a single piezoelectric element as actuators and sensors simultaneously. This paper proposes the asymmetric indirect-driven self-sensing actuation (AIDSSA) circuit to realize the concept of self-sensing in piezoelectric-actuated systems. Unlike traditional circuits relying on differential amplifiers, the AIDSSA circuit is constructed with only op-amps and uses negative feedback to reject the common-mode interferences from the control command. The new circuit requires simpler conditions of component matching and is able to sense the mechanical responses with a uniform gain and without a phase lag. The actuator is able to achieve full-stroke actuation while sensing is performed, because AIDSSA introduces no undesirable dynamics into the control loop. For the first time, the sensing and actuation transfer functions in self-sensing actuators have become fully decoupled at all frequencies. The investigation takes the form of an industrial application of hard disk drives, and demonstrates the usefulness the circuit in complex positioning systems. Experimental results show that the position error variance, a measure of disturbance rejection capability, has been improved by about 15% in the track-following mode relative to the same servo before modifications.

A Piezoelectric Robotic System for MRI Targeting Assessments of Therapeutics During Dipole Field Navigation

Dipole field navigation (DFN) is a method that has been developed to deliver therapeutics toward tumoral regions by navigating microcarriers in the vascular network. To do so, DFN distorts the high uniform magnetic field of a clinical magnetic resonance imaging (MRI) scanner using precisely located ferromagnetic balls to create magnetic gradients to implement the directional forces required to navigate magnetically saturated therapeutic microcarriers along a planned trajectory in the vasculature. Such local distortions of the magnetic field prevent MRI-based targeting assessments. As such, a system must be put in place to precisely move the ferromagnetic balls back-and-forth to alternate between MRI targeting assessment and DFN. Here, a piezoelectric actuation system is proposed. In vitro experiments conducted inside the bore of a 3T clinical MRI scanner show the feasibility for reliable targeting assessments with magnetic distortions sufficient to achieve a 100% success rate of magnetic microparticles being navigated through a predefined target branch at a bifurcation. Results show a 21.6% decrease in SNR with a maximum value of 2.2% MR-image distortion and a faintly visible image artifact after the piezoelectric system moved the soft ferromagnetic balls in the MRI targeting assessment position.

Adaptive Tracking Control for the Piezoelectric Actuated Stage Using the Krasnosel’skii-Pokrovskii Operator

In this paper, a discrete second order linear equation with the Krasnosel’skii-Pokrovskii (KP) operator is used to describe the piezoelectric actuated stage. The weights of the KP operators are identified by the gradient descent algorithm. To suppress the hysteresis nonlinearity of the piezoelectric actuated stage, this paper proposes an adaptive tracking control with the hysteresis decomposition on the designed error surface. The proposed adaptive tracking controller dispenses with any form of the feed-forward hysteresis compensation and the unknown parameters of the discrete second order linear equation are adaptively adjusted. Some simulations are implemented to verify the effectiveness of the KP operators, then a series of modeling and control experiments are carried out on the piezoelectric actuated stages experimental systems. The comparative experimental results verify the feasibility of the KP operators modeling method and the adaptive tracking control method.

Linearization of Recurrent-Neural-Network- Based Models for Predictive Control of Nano-Positioning Systems Using Data-Driven Koopman Operators

Recent studies have shown that the nonlinear dynamics of nano-positioning systems (e.g., piezo-electric actuators (PEAs)) can be accurately captured by recurrent neural networks (RNNs). One direct application of this technique is PEA system control for precision positioning: linearize the nonlinear RNN model and then apply model predictive control (MPC). However, due to the linearization approach commonly used (e.g., Taylor series), the control bandwidth and the control performance are quite limited as the obtained linear system is only guaranteed to be accurate within small neighborhood of the linearization point. To address this issue, we propose a Koopman operator-based approach for linearization and then use the obtained linear parameter-varying model for predictive control. This linearization scheme can significantly decrease the overall approximation error within the MPC prediction horizon, and thus, lead to improved tracking performance. The proposed approach was validated through two applications-trajectory tracking of PEA, and deformation control of polymers during atomic force microscope nano-indentation.

The Developments of piezoelectric Materials and Shape Memory Alloys in Robotic Actuator Systems

There is a high demand for functional smart materials, especially for new material groups in advanced Technologies. These materials are used in the actuator, sensor, control systems, and robotic systems, in addition, they can be hybridized with traditional material to create a particular function. Piezoelectric materials and shape memory alloys are the most important families among these groups. This review includes an overview of shape memory alloys (SMAs) and piezoelectric material actuator systems in terms of robotic applications. The theoretical background of each SMAs and piezoelectric materials is well explained. Different types of each system are interpreted. Using actuator-based SMAs and piezoelectricity in the robotic area is extensively overviewed. Some weaknesses and challenges facing such systems have discussed through recent studies in the literature.

Current-Cycle Iterative Learning Control for High-Precision Position Tracking of Piezoelectric Actuator System via Active Disturbance Rejection Control for Hysteresis Compensation

As a typical smart structure, the piezoelectric actuator (PEA) is an essential constituent component in piezoelectric-driven positioning stages. Nevertheless, the positioning precision is severely degraded by its innate rate-dependent hysteretic nonlinearity. In this article, an innovative control method which combines active disturbance rejection control (ADRC) and current-cycle iterative learning control (CILC) is proposed by constructing PEA as a second-order disturbance-based structure to handle both the hysteretic nonlinearities and dynamic uncertainties of PEA. The proposed method differs from the prevalent model-inverse solution in hysteresis compensation, where the control performance of the latter relies extremely on the accurateness of the hysteretic model while the former does not require a mathematical model of hysteresis since it is considered as a general disturbance and eliminated. Compared with the existing hysteresis compensation via pure ADRC method, the proposed method has improved robustness by incorporating an additional Iterative learning control (ILC) loop to ADRC. Comparative experimentations are executed on a PEA system and results imply that the proposed approach has better control performance than pure proportional-integral control and ADRC.

Model-free robust finite-time force tracking control for piezoelectric actuators using time-delay estimation with adaptive fuzzy compensator

A robust and practical force control system is crucial to the sensitive piezo-driven micromanipulation applications. This paper presents a new model-free robust finite-time force tracking controller for piezoelectric actuators (PEAs). The proposed controller composes of three intuitive terms: (1) a time-delay estimation (TDE) term that eliminates the requirement of detailed information about the PEA system, realizing model-free control; (2) a fast integral terminal sliding mode-based desired error dynamics injection term that ensures fast convergence and high tracking precision; (3) a correcting term based on adaptive fuzzy logic system that compensates for TDE errors caused by discontinuous nonlinearities and improves the robustness of the system. Force differential signal used in the controller is estimated online by a force state estimator. Stability of the closed-loop system and finite-time convergence are analyzed in theory. Comparative experiments are carried out on a PEA system with two superposed PEAs. Results show that the proposed control strategy has faster convergence, higher tracking accuracy and stronger robustness compared with the traditional TDE-based force controllers.