A flexure-based kinematically decoupled micropositioning stage with a centimeter range dedicated to micro/nano manufacturing

Precision positioning stages with large strokes and high positioning accuracy are attractive for high-performance micro/nano manufacturing. This paper presents the dynamic design and characteristic investigation of a novel XY micropositioning stage. Firstly, the mechanism of the stage was introduced. The XY stage was directly driven by two linear motors, and the X- and Y- axes kinematic decoupling was realized through a novel flexible decoupling mechanism based on flexure hinges and preloaded spring. The dynamic model of the XY stage was established, and the influences of the rotational stiffness of the flexure hinge and the initial positions of the working table on the dynamic rotation of the positioning stage were investigated. The stiffness and geometric parameters of the flexure hinges were determined at the condition that the angular displacements of the working table were within ±0.5° with a motion stroke of ±25 mm. Finally the stage performance was investigated through simulation and experiments, the X- and Y-axes step responses, the rotation angular and positioning accuracy of the stage were obtained. The results show that the stage exhibits good performance and can be used for micro/nano manufacturing

PKM mechatronic clamping adaptive device

This study proposes a novel adaptive fixturing device based on active clamping systems for smart micropositioning of thin-walled precision parts. The modular architecture and the structure flexibility make the system suitable for various industrial applications. The proposed device is realized as a Parallel Kinematic Machine (PKM), opportunely sensorized and controlled, able to perform automatic error-free workpiece clamping procedures, drastically reducing the overall fixturing set-up time. The paper describes the kinematics and dynamics of this mechatronic system. A first campaign of experimental trails has been carried out on the prototype, obtaining promising results

Hybrid PSO-tuned PID and hysteresis-observer based control for piezoelectric micropositioning stages

Piezo-actuated micropositioning stages consist of a piezoelectric actuator that operates a positioning system. Hysteresis nonlinearity is one of the significant variables limiting the positioning precision of these stages. This paper introduces a technique of developing a hybrid controller for a precise positioning tracking of a piezoelectric micropositioning system. Bouc-Wen nonlinear hysteresis model is utilized to denote the hysteresis nonlinear phenomenon of the piezo-actuated system. A hysteresis observer-based feedforward controller is designed based on Luenberger observer. This feedforward controller is then coupled with a particle swarm optimization (PSO)-based proportional-integral-derivative (PID) feedback controller to form a hybrid controller. A new fitness function is used to compute the optimal PID gains. This fitness function is intended to reduce the overshoot, steady-state error, and the rise and settling times. The findings of this work indicate that using the developed controller structure can significantly decrease the hysteresis effect. In addition, the proposed structure shows the ability to reduce the error is to 0.046% of the maximum displacement range. Such performance demonstrates that the proposed hybrid control structure is efficient for precise micropositioning applications.Piezo-actuated micropositioning stages consist of a piezoelectric actuator that operates a positioning system. Hysteresis nonlinearity is one of the significant variables limiting the positioning precision of these stages. This paper introduces a technique of developing a hybrid controller for a precise positioning tracking of a piezoelectric micropositioning system. Bouc-Wen nonlinear hysteresis model is utilized to denote the hysteresis nonlinear phenomenon of the piezo-actuated system. A hysteresis observer-based feedforward controller is designed based on Luenberger observer. This feedforward controller is then coupled with a particle swarm optimization (PSO)-based proportional-integral-derivative (PID) feedback controller to form a hybrid controller. A new fitness function is used to compute the optimal PID gains. This fitness function is intended to reduce the overshoot, steady-state error, and the rise and settling times. The findings of this work indicate that using the developed controller structure can significantly decrease the hysteresis effect. In addition, the proposed structure shows the ability to reduce the error is to 0.046% of the maximum displacement range. Such performance demonstrates that the proposed hybrid control structure is efficient for precise micropositioning applications

Modeling and tracking control of a novel XYθz stage

A XYθz stage is designed and experimentally tested. This developed stage is driven by three piezoelectric actuators (PZTs) and guided by a flexure hinge based mechanism with three symmetric T-shape hinges. It was manufactured monolithically by using wire electrical discharge machining technology. In addition, considering the both electrical and mechanical characteristics, a third-order dynamic model of the 3-DOF system has been established to investigate the relationship between the input voltage and the output displacement of the entire system. The parameters of the third-order dynamic model were estimated by using the system identification toolbox. Furthermore, decoupling control is also proposed to solve the existed coupling motion of the stage. In order to compensate the hysteresis of PZT, the inverse Bouc-Wen model was utilized as a feedforward hysteresis compensator. Finally, extensive experiments were performed to verify the good decoupling and tracking performances of the developed stage

Comparison of hysteresis of high accuracy positioning system with piezoelectric actuators

In the paper, high accuracy positioning systems with flexible elements are investigated. In the analyzed systems, piezoelectric actuators are used for the transmission of motion and the hystereric phenomenon in them is investigated. Effect of the hysteretic phenomena to the precision of the high accuracy positioning systems is of special importance. For the investigations, a special experimental setup was designed and produced as well as the method of the experimental procedure was proposed. The experimental setup includes a computer, a piezocontroller, an inductive displacement sensor and a dynamic data collector. The dynamic data collector is used for the collection of data and for the transfer of data to the software for further processing. Numerical modelling of the hysteretic was performed by using the Matlab/Simulink software. In the process of investigations, it was determined that the maximum dispersion error of the hysteretic model is less than 5 % when compared with the experimental results. Thus, it is concluded that the proposed method of hysteretic phenomenon modelling is suitable for modelling of high accuracy positioning systems with flexible elements, which are controlled by piezoelectric actuators

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

Enhanced Positioning Bandwidth in Nanopositioners via Strategic Pole Placement of the Tracking Controller

Funding: This research received no external funding.Peer reviewedPublisher PD

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

Development of a piezo-driven 3-DOF stage with T-shape flexible hinge mechanism

This paper presents a 3-DOF (Degree of freedom) stage with T-shape flexible hinge mechanism for the applications in the precision measurement equipments and micro/nano manipulation systems. The stage is driven by three piezoelectric actuators (PEAs) and guided by a flexible hinge based mechanism with three symmetric T-shape hinges. The proposed T-shape flexible hinge mechanism can provide excellent planar motion capability with high stability, and thus guarantee the outstanding dynamics characteristics. The theoretical modeling of the stage was carried out and the stiffness and the dynamic resonance frequency have been obtained. The kinematic model of the 3-DOF stage was established and the workspace has been analyzed. The characteristics of the stage were investigated using finite element analysis (FEA). Experiments were conducted to examine the performance of the stage, through this stage, X-axis translational motion stroke of 6.9 µm, Y-axis translational motion stroke of 8.5 µm and rotational motion stroke along Z-axis of 289 µrad can be achieved. A hybrid feedforward/feedback control methodology has been proposed to eliminate the nonlinear hysteresis, the trajectory tracking performances and to reduce external disturbance of the 3-DOF stage