Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

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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 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

Robust fractional-order fast terminal sliding mode control with fixed-time reaching law for high-performance nanopositioning

Open Access via the Wiley Agreement ACKNOWLEDGEMENTS This work is supported by the China Scholarship Council under Grant No. 201908410107 and by the National Natural Science Foundation of China under Grant No. 51505133. The authors also thank the anonymous reviewers for their insightful and constructive comments.Peer reviewedPublisher PD

Design and experimental validation of a piezoelectric actuator tracking control based on fuzzy logic and neural compensation

This work proposes two control feedback-feedforward algorithms, based on fuzzy logic in combination with neural networks, aimed at reducing the tracking error and improving the actuation signal of piezoelectric actuators. These are frequently used devices in a wide range of applications due to their high precision in micro- and nanopositioning combined with their mechanical stiffness. Nevertheless, the hysteresis is one the main phenomenon that degrades the performance of these actuators in tracking operations. The proposed control schemes were tested experimentally in a commercial piezoelectric actuator. They were implemented with a dSPACE 1104 device, which was used for signal generation and acquisition purposes. The performance of the proposed control schemes was compared to conventional structures based on proportional-integral-derivative and fuzzy logic in feedback configuration. Experimental results show the advantages of the proposed controllers, since they are capable of reducing the error to significant magnitude orders.The authors wish to express their gratitude to the Basque Government, through the project EKOHEGAZ (ELKARTEK KK-2021/00092), to the Diputación Foral de Álava (DFA), through the project CONAVANTER, and to the UPV/EHU, through the project GIU20/063, for supporting this work

Control of a 3D piezo-actuating table by using an adaptive sliding-mode controller for a drilling process

AbstractRecently, the micropositioner has become an important developing target for achieving the requirements of precision machinery. The piezo-actuating device plays a very important role in this application area. In this paper, a model-free adaptive sliding-mode controller is proposed for a 3D piezo-actuating system because of the system’s hysteresis nonlinearity and time-varying characteristics. This control strategy employs the functional approximation technique to establish the unknown function for releasing the model based requirements of the sliding-mode control. The update laws for the coefficients of the Fourier series function parameters are derived from a Lyapunov function to guarantee the control system stability. To verify the effectiveness of the proposed controller, drilling process control using the designed controller is investigated in this paper

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

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

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

Robust Adaptive Control of a Micro Telemanipulation System Using Sliding Mode-Based Force Estimation

Abstract-Piezoelectric actuators are widely used in micro manipulation applications. However, hysteresis nonlinearity limits the accuracy of these actuators. This paper presents a novel approach for utilizing a piezoelectric nano-stage as the slave manipulator of a teleoperation system based on a sliding mode controller. The Prandtl-Ishlinskii (PI) model is used to model actuator hysteresis in feedforward scheme to cancel out this nonlinearity. The presented approach requires full state and force measurements at both the master and slave sides. Such a system is costly and also difficult to implement. Therefore, sliding mode unknown input observer (UIO) is proposed for full state and force estimations. Furthermore, the effects of uncertainties in the constant parameters on the estimated external forces should be eliminated. So, a robust adaptive controller is proposed and its stability is guaranteed through the Lyapunov criterion. Performance of the proposed control architecture is verified through experiments