From model-driven to data-driven : a review of hysteresis modeling in structural and mechanical systems

Hysteresis is a natural phenomenon that widely exists in structural and mechanical systems. The characteristics of structural hysteretic behaviors are complicated. Therefore, numerous methods have been developed to describe hysteresis. In this paper, a review of the available hysteretic modeling methods is carried out. Such methods are divided into: a) model-driven and b) datadriven methods. The model-driven method uses parameter identification to determine parameters. Three types of parametric models are introduced including polynomial models, differential based models, and operator based models. Four algorithms as least mean square error algorithm, Kalman filter algorithm, metaheuristic algorithms, and Bayesian estimation are presented to realize parameter identification. The data-driven method utilizes universal mathematical models to describe hysteretic behavior. Regression model, artificial neural network, least square support vector machine, and deep learning are introduced in turn as the classical data-driven methods. Model-data driven hybrid methods are also discussed to make up for the shortcomings of the two methods. Based on a multi-dimensional evaluation, the existing problems and open challenges of different hysteresis modeling methods are discussed. Some possible research directions about hysteresis description are given in the final section

Parameters Identification for a Composite Piezoelectric Actuator Dynamics

This work presents an approach for identifying the model of a composite piezoelectric (PZT) bimorph actuator dynamics, with the objective of creating a robust model that can be used under various operating conditions. This actuator exhibits nonlinear behavior that can be described using backlash and hysteresis. A linear dynamic model with a damping matrix that incorporates the Bouc–Wen hysteresis model and the backlash operators is developed. This work proposes identifying the actuator’s model parameters using the hybrid master-slave genetic algorithm neural network (HGANN). In this algorithm, the neural network exploits the ability of the genetic algorithm to search globally to optimize its structure, weights, biases and transfer functions to perform time series analysis efficiently. A total of nine datasets (cases) representing three different voltage amplitudes excited at three different frequencies are used to train and validate the model. Four cases are considered for training the NN architecture, connection weights, bias weights and learning rules. The remaining five cases are used to validate the model, which produced results that closely match the experimental ones. The analysis shows that damping parameters are inversely proportional to the excitation frequency. This indicates that the suggested hysteresis model is too general for the PZT model in this work. It also suggests that backlash appears only when dynamic forces become dominant

Study and Development of Mechatronic Devices and Machine Learning Schemes for Industrial Applications

Obiettivo del presente progetto di dottorato è lo studio e sviluppo di sistemi meccatronici e di modelli machine learning per macchine operatrici e celle robotizzate al fine di incrementarne le prestazioni operative e gestionali. Le pressanti esigenze del mercato hanno imposto lavorazioni con livelli di accuratezza sempre più elevati, tempi di risposta e di produzione ridotti e a costi contenuti. In questo contesto nasce il progetto di dottorato, focalizzato su applicazioni di lavorazioni meccaniche (e.g. fresatura), che includono sistemi complessi quali, ad esempio, macchine a 5 assi e, tipicamente, robot industriali, il cui utilizzo varia a seconda dell’impiego. Oltre alle specifiche problematiche delle lavorazioni, si deve anche considerare l’interazione macchina-robot per permettere un’efficiente capacità e gestione dell’intero impianto. La complessità di questo scenario può evidenziare sia specifiche problematiche inerenti alle lavorazioni (e.g. vibrazioni) sia inefficienze più generali che riguardano l’impianto produttivo (e.g. asservimento delle macchine con robot, consumo energetico). Vista la vastità della tematica, il progetto si è suddiviso in due parti, lo studio e sviluppo di due specifici dispositivi meccatronici, basati sull’impiego di attuatori piezoelettrici, che puntano principalmente alla compensazione di vibrazioni indotte dal processo di lavorazione, e l’integrazione di robot per l’asservimento di macchine utensili in celle robotizzate, impiegando modelli di machine learning per definire le traiettorie ed i punti di raggiungibilità del robot, al fine di migliorarne l’accuratezza del posizionamento del pezzo in diverse condizioni. In conclusione, la presente tesi vuole proporre soluzioni meccatroniche e di machine learning per incrementare le prestazioni di macchine e sistemi robotizzati convenzionali. I sistemi studiati possono essere integrati in celle robotizzate, focalizzandosi sia su problematiche specifiche delle lavorazioni in macchine operatrici sia su problematiche a livello di impianto robot-macchina. Le ricerche hanno riguardato un’approfondita valutazione dello stato dell’arte, la definizione dei modelli teorici, la progettazione funzionale e l’identificazione delle criticità del design dei prototipi, la realizzazione delle simulazioni e delle prove sperimentali e l’analisi dei risultati.The aim of this Ph.D. project is the study and development of mechatronic systems and machine learning models for machine tools and robotic applications to improve their performances. The industrial demands have imposed an ever-increasing accuracy and efficiency requirement whilst constraining the cost. In this context, this project focuses on machining processes (e.g. milling) that include complex systems such as 5-axes machine tool and industrial robots, employed for various applications. Beside the issues related to the machining process itself, the interaction between the machining centre and the robot must be considered for the complete industrial plant’s improvement. This scenario´s complexity depicts both specific machining problematics (e.g. vibrations) and more general issues related to the complete plant, such as machine tending with an industrial robot and energy consumption. Regarding the immensity of this area, this project is divided in two parts, the study and development of two mechatronic devices, based on piezoelectric stack actuators, for the active vibration control during the machining process, and the robot machine tending within the robotic cell, employing machine learning schemes for the trajectory definition and robot reachability to improve the corresponding positioning accuracy. In conclusion, this thesis aims to provide a set of solutions, based on mechatronic devices and machine learning schemes, to improve the conventional machining centre and the robotic systems performances. The studied systems can be integrated within a robotic cell, focusing on issues related to the specific machining process and to the interaction between robot-machining centre. This research required a thorough study of the state-of-the-art, the formulation of theoretical models, the functional design development, the identification of the critical aspects in the prototype designs, the simulation and experimental campaigns, and the analysis of the obtained results

Precision Control of Piezo Electric Actuator

芝浦工業大学201

Modeling and Compensation of Hysteresis In Piezoelectric Actuators: A Physical Approach

A study in the polarization domain is conducted by probing the impedance of the piezoelectric actuator as it moves along its trajectory. A sensing signal is overlaid over a driving signal that is used to vary the position of the device. The electric polarisation is extracted from the capacitance measurement calculated from the impedance. These polarisation curves are then modelled using the Jiles-Atherton model and compensated for using the inverse model. These measurements give insight into the ferroelectric processes within the piezoelectric actuator, which operate on the polarisation state. In addition, research has been conducted on the topic of parameter estimation of hysteresis models. This dissertation proposes a Monte Carlo study on a novel normalised Jiles-Atherton model to generate a statistical set of model solutions to compare area and remnant displacement characteristics for different parameter selections. Two parameters were found to be the most responsible for changes in these characteristics, and solutions near the desired values of the measured hysteresis curves were found to be densely distributed in certain areas of the parameter space. Different parameter estimation techniques are proposed for the Prandtl-Ishlinskii model. For this model, the parameters have geometrical significance in the slope of certain points of the hysteresis curve. A novel rescaling procedure is developed to scale a Prandtl-Ishlinskii model hysteresis curve area to a new value without requiring a refitting of the coefficients and a frequency-dependent Prandtl-Ishlinskii model is developed. Finally, a temperature-dependent, asymmetric Prandtl-Ishlinskii (TAPI) model is developed to account for the changes in hysteresis due to the external temperature. These effects are modelled in the charge domain as an extra bound charge that appears as a result of domain reorientation effects. The temperature effectively changes the amount of energy required to break pinning sites in the actuator which changes the shape of the curve. The TAPI model is then implemented on a Fabry-Perot interferometer system consisting of three piezoelectric actuators controlling the placement of a mirror forming the etalon. A decoupled inverse TAPI model is shown to effectively linearise the output of this system at different temperatures

Modeling and Compensation of Hysteresis In Piezoelectric Actuators: A Physical Approach

A study in the polarization domain is conducted by probing the impedance of the piezoelectric actuator as it moves along its trajectory. A sensing signal is overlaid over a driving signal that is used to vary the position of the device. The electric polarisation is extracted from the capacitance measurement calculated from the impedance. These polarisation curves are then modelled using the Jiles-Atherton model and compensated for using the inverse model. These measurements give insight into the ferroelectric processes within the piezoelectric actuator, which operate on the polarisation state. In addition, research has been conducted on the topic of parameter estimation of hysteresis models. This dissertation proposes a Monte Carlo study on a novel normalised Jiles-Atherton model to generate a statistical set of model solutions to compare area and remnant displacement characteristics for different parameter selections. Two parameters were found to be the most responsible for changes in these characteristics, and solutions near the desired values of the measured hysteresis curves were found to be densely distributed in certain areas of the parameter space. Different parameter estimation techniques are proposed for the Prandtl-Ishlinskii model. For this model, the parameters have geometrical significance in the slope of certain points of the hysteresis curve. A novel rescaling procedure is developed to scale a Prandtl-Ishlinskii model hysteresis curve area to a new value without requiring a refitting of the coefficients and a frequency-dependent Prandtl-Ishlinskii model is developed. Finally, a temperature-dependent, asymmetric Prandtl-Ishlinskii (TAPI) model is developed to account for the changes in hysteresis due to the external temperature. These effects are modelled in the charge domain as an extra bound charge that appears as a result of domain reorientation effects. The temperature effectively changes the amount of energy required to break pinning sites in the actuator which changes the shape of the curve. The TAPI model is then implemented on a Fabry-Perot interferometer system consisting of three piezoelectric actuators controlling the placement of a mirror forming the etalon. A decoupled inverse TAPI model is shown to effectively linearise the output of this system at different temperatures

Motion Control of Smart Material Based Actuators: Modeling, Controller Design and Experimental Evaluation

Smart material based actuators, such as piezoelectric, magnetostrictive, and shape memory alloy actuators, are known to exhibit hysteresis effects. When the smart actuators are preceded with plants, such non-smooth nonlinearities usually lead to poor tracking performance, undesired oscillation, or even potential instability in the control systems. The development of control strategies to control the plants preceded with hysteresis actuators has become to an important research topic and imposed a great challenge in the control society. In order to mitigate the hysteresis effects, the most popular approach is to construct the inverse to compensate such effects. In such a case, the mathematical descriptions are generally required. In the literature, several mathematical hysteresis models have been proposed. The most popular hysteresis models perhaps are Preisach model, Prandtl-Ishlinskii model, and Bouc-Wen model. Among the above mentioned models, the Prandtl-Ishlinskii model has an unique property, i.e., the inverse Prandtl-Ishlinskii model can be analytically obtained, which can be used as a feedforward compensator to mitigate the hysteresis effect in the control systems. However, the shortcoming of the Prandtl-Ishlinskii model is also obvious because it can only describe a certain class of hysteresis shapes. Comparing to the Prandtl-Ishlinskii model, a generalized Prandtl-Ishlinskii model has been reported in the literature to describe a more general class of hysteresis shapes in the smart actuators. However, the inverse for the generalized Prandtl-Ishlinskii model has only been given without the strict proof due to the difficulty of the initial loading curve construction though the analytic inverse of the Prandtl-Ishlinskii model is well documented in the literature. Therefore, as a further development, the generalized Prandtl-Ishlinskii model is re-defined and a modified generalized Prandtl-Ishlinskii model is proposed in this dissertation which can still describe similar general class of hysteresis shapes. The benefit is that the concept of initial loading curve can be utilized and a strict analytical inverse model can be derived for the purpose of compensation. The effectiveness of the obtained inverse modified generalized Prandtl-Ishlinskii model has been validated in the both simulations and in experiments on a piezoelectric micropositioning stage. It is also affirmed that the proposed modified generalized Prandtl-Ishlinskii model fulfills two crucial properties for the operator based hysteresis models, the wiping out property and the congruency property. Usually the hysteresis nonlinearities in smart actuators are unknown, the direct open-loop feedforward inverse compensation will introduce notably inverse compensation error with an estimated inverse construction. A closed-loop adaptive controller is therefore required. The challenge in fusing the inverse compensation and the robust adaptive control is that the strict stability proof of the closed loop control system is difficult to obtain due to the fact that an error expression of the inverse compensation has not been established when the hysteresis is unknown. In this dissertation research, by developing the error expression of the inverse compensation for modified generalized Prandtl-Ishlinskii model, two types of inverse based robust adaptive controllers are designed for a class of uncertain systems preceded by a smart material based actuator with hysteresis nonlinearities. When the system states are available, an inverse based adaptive variable structure control approach is designed. The strict stability proof is established thereafter. Comparing with other works in the literature, the benefit for such a design is that the proposed inverse based scheme can achieve the tracking without necessarily adapting the uncertain parameters (the number could be large) in the hysteresis model, which leads to the computational efficiency. Furthermore, an inverse based adaptive output-feedback control scheme is developed when the exactly knowledge of most of the states is unavailable and the only accessible state is the output of the system. An observer is therefore constructed to estimate the unavailable states from the measurements of a single output. By taking consideration of the analytical expression of the inverse compensation error, the global stability of the close-loop control system as well as the required tracking accuracy are achieved. The effectiveness of the proposed output-feedback controller is validated in both simulations and experiments

Advanced Control of Piezoelectric Actuators.

168 p.A lo largo de las últimas décadas, la ingeniería de precisión ha tenido un papel importante como tecnología puntera donde la tendencia a la reducción de tamaño de las herramientas industriales ha sido clave. Los procesos industriales comenzaron a demandar precisión en el rango de nanómetros a micrómetros. Pese a que los actuadores convencionales no pueden reducirse lo suficiente ni lograr tal exactitud, los actuadores piezoeléctricos son una tecnología innovadora en este campo y su rendimiento aún está en estudio en la comunidad científica. Los actuadores piezoeléctricos se usan comúnmente en micro y nanomecatrónica para aplicaciones de posicionamiento debido a su alta resolución y fuerza de actuación (pueden llegar a soportar fuerzas de hasta 100 Newtons) en comparación con su tamaño. Todas estas características también se pueden combinar con una actuación rápida y rigidez, según los requisitos de la aplicación. Por lo tanto, con estas características, los actuadores piezoeléctricos pueden ser utilizados en una amplia variedad de aplicaciones industriales. Los efectos negativos, como la fluencia, vibraciones y la histéresis, se estudian comúnmente para mejorar el rendimiento cuando se requiere una alta precisión. Uno de los efectos que más reduce el rendimiento de los PEA es la histéresis. Esto se produce especialmente cuando el actuador está en una aplicación de guiado, por lo que la histéresis puede inducir errores que pueden alcanzar un valor de hasta 22%. Este fenómeno no lineal se puede definir como un efecto generado por la combinación de acciones mecánicas y eléctricas que depende de estados previos. La histéresis se puede reducir principalmente mediante dos estrategias: rediseño de materiales o algoritmos de control tipo feedback. El rediseño de material comprende varias desventajas por lo que el motivo principal de esta tesis está enfocado al diseño de algoritmos de control para reducir la histéresis. El objetivo principal de esta tesis es el desarrollo de estrategias de control avanzadas que puedan mejorar la precisión de seguimiento de los actuadores piezoeléctricos comerciale

Modeling and Control of Piezoelectric Actuators

Piezoelectric actuators (PEAs) utilize the inverse piezoelectric effect to generate fine displacement with a resolution down to sub-nanometers and as such, they have been widely used in various micro- and nanopositioning applications. However, the modeling and control of PEAs have proven to be challenging tasks. The main difficulties lie in the existence of various nonlinear or difficult-to-model effects in PEAs, such as hysteresis, creep, and distributive vibration dynamics. Such effects can seriously degrade the PEA tracking control performances or even lead to instability. This raises a great need to model and control PEAs for improved performance. This research is aimed at developing novel models for PEAs and on this basis, developing model-based control schemes for the PEA tracking control taking into account the aforementioned nonlinear effects. In the first part of this research, a model of a PEA for the effects of hysteresis, creep, and vibration dynamics was developed. Notably, the widely-used Preisach hysteresis model cannot represent the one-sided hysteresis of PEAs. To overcome this shortcoming, a rate-independent hysteresis model based on a novel hysteresis operator modified from the Preisach hysteresis operator was developed, which was then integrated with the models of creep and vibration dynamics to form a comprehensive model for PEAs. For its validation, experiments were carried out on a commercially-available PEA and the results obtained agreed with those from model simulations. By taking into account the linear dynamics and hysteretic behavior of the PEA as well as the presliding friction between the moveable platform and the end-effector, a model of the piezoelectric-driven stick-slip (PDSS) actuator was also developed in the first part of the research. The effectiveness of the developed model was illustrated by the experiments on the PDSS actuator prototyped in the author's lab. In the second part of the research, control schemes were developed based on the aforementioned PEA models for tracking control of PEAs. Firstly, a novel PID-based sliding mode (PIDSM) controller was developed. The rational behind the use of a sliding mode (SM) control is that the SM control can effectively suppress the effects of matched uncertainties, while the PEA hysteresis, creep, and external load can be represented by a lumped matched uncertainty based on the developed model. To solve the chattering and steady-state problems, associated with the ideal SM control and the SM control with boundary layer (SMCBL), the novel PIDSM control developed in the present study replaces the switching control term in the ideal SM control schemes with a PID regulator. Experiments were carried out on a commercially-available PEA and the results obtained illustrate the effectiveness of the PIDSM controller, and its superiorities over other schemes of PID control, ideal SM control, and the SMCBL in terms of steady state error elimination, chattering suppression, and tracking error suppression. Secondly, a PIDSM observer was also developed based on the model of PEAs to provide the PIDSM controller with state estimates of the PEA. And the PIDSM controller and the PIDSM observer were combined to form an integrated control scheme (PIDSM observer-controller or PIDSMOC) for PEAs. The effectiveness of the PIDSM observer and the PIDSMOC were also validated experimentally. The superiority of the PIDSMOC over the PIDSM controller with σ-β filter control scheme was also analyzed and demonstrated experimentally. The significance of this research lies in the development of novel models for PEAs and PDSS actuators, which can be of great help in the design and control of such actuators. Also, the development of the PIDSM controller, the PIDSM observer, and their integrated form, i.e., PIDSMOC, enables the improved performance of tracking control of PEAs with the presence of various nonlinear or difficult-to-model effects

Discrete Modeling and Sliding Mode Control of Piezoelectric Actuators

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs