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

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

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

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

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

Sliding Mode-Based Robust Control for Piezoelectric Actuators with Inverse Dynamics Estimation

This paper presents an improved control approach to be used for piezoelectric actuators. The proposed approach is based on sliding mode control with estimation perturbation (SMCPE) techniques. Also, a proportional-integral-derivative (PID)-type sliding surface is proposed for position tracking. The proposed approach has been studied and implemented in a commercial actuator. A model for the system is introduced, which includes the Bouc-Wen (BW) model to represent the hysteresis, and it is identified by means of the System Identification Toolbox in Matlab/Simulink. Experimental data show that the proposed controller has a better performance when compared to a proportional-integral (PI) controller or a conventional SMCPE in motion tracking. Furthermore, a sub-micrometer accuracy tracking can be obtained while compensating for the hysteresis effect.This research was partially funded by the Basque Government through the project ETORTEK KK-2017/00033, and by the UPV/EHU through the projects PPGA18/04 and UFI 11/07

Modeling and Control of Piezoactive Micro and Nano Systems

Piezoelectrically-driven (piezoactive) systems such as nanopositioning platforms, scanning probe microscopes, and nanomechanical cantilever probes are advantageous devices enabling molecular-level imaging, manipulation, and characterization in disciplines ranging from materials science to physics and biology. Such emerging applications require precise modeling, control and manipulation of objects, components and subsystems ranging in sizes from few nanometers to micrometers. This dissertation presents a comprehensive modeling and control framework for piezoactive micro and nano systems utilized in various applications. The development of a precise memory-based hysteresis model for feedforward tracking as well as a Lyapunov-based robust-adaptive controller for feedback tracking control of nanopositioning stages are presented first. Although hysteresis is the most degrading factor in feedforward control, it can be effectively compensated through a robust feedback control design. Moreover, an adaptive controller can enhance the performance of closed-loop system that suffers from parametric uncertainties at high-frequency operations. Comparisons with the widely-used PID controller demonstrate the effectiveness of the proposed controller in tracking of high-frequency trajectories. The proposed controller is then implemented in a laser-free Atomic Force Microscopy (AFM) setup for high-speed and low-cost imaging of surfaces with micrometer and nanometer scale variations. It is demonstrated that the developed AFM is able to produce high-quality images at scanning frequencies up to 30 Hz, where a PID controller is unable to present acceptable results. To improve the control performance of piezoactive nanopositioning stages in tracking of time-varying trajectories with frequent stepped discontinuities, which is a common problem in SPM systems, a supervisory switching controller is designed and integrated with the proposed robust adaptive controller. The controller switches between two control modes, one mode tuned for stepped trajectory tracking and the other one tuned for continuous trajectory tracking. Switching conditions and compatibility conditions of the control inputs in switching instances are derived and analyzed. Experimental implementation of the proposed switching controller indicates significant improvements of control performance in tracking of time-varying discontinuous trajectories for which single-mode controllers yield undesirable results. Distributed-parameters modeling and control of rod-type solid-state actuators are then studied to enable accurate tracking control of piezoactive positioning systems in a wide frequency range including several resonant frequencies of system. Using the extended Hamilton\u27s principle, system partial differential equation of motion and its boundary conditions are derived. Standard vibration analysis techniques are utilized to formulate the truncated finite-mode state-space representation of the system. A new state-space controller is then proposed for asymptotic output tracking control of system. Integration of an optimal state-observer and a Lyapunov-based robust controller are presented and discussed to improve the practicability of the proposed framework. Simulation results demonstrate that distributed-parameters modeling and control is inevitable if ultra-high bandwidth tracking is desired. The last part of the dissertation, discusses new developments in modeling and system identification of piezoelectrically-driven Active Probes as advantageous nanomechanical cantilevers in various applications including tapping mode AFM and biomass sensors. Due to the discontinuous cross-section of Active Probes, a general framework is developed and presented for multiple-mode vibration analysis of system. Application in the precise pico-gram scale mass detection is then presented using frequency-shift method. This approach can benefit the characterization of DNA solutions or other biological species for medical applications

HIGH-BANDWIDTH IDENTIFICATION AND COMPENSATION OF HYSTERETIC DYNAMICS

Ph.DDOCTOR OF PHILOSOPH