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 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

Modeling and robust control strategy for a control-optimized piezoelectric microgripper.

International audienceIn this paper, modeling and robust control strategy for a new control-optimized piezoelectric microgripper are presented. The device to be controlled is a piezoelectric flexible mechanism dedicated to micromanipulation. It has been previously designed with an emphasis to control strategy, using a new topological optimization method, by considering innovative frequency-based criteria. A complete non-linear model relating the voltage and the resulting deflection is established taking into account hysteresis as a plurilinear model subjected to uncertainties. The approach used for controlling the actuator tip is based on a mixed High Authority Control (HAC) / Low Authority Control (LAC) strategy for designing a wide-band regulator. It consists of a Positive Position Feedback (PPF) damping controller approach combined with a low-frequency integral controller which is shown to have robustness performances as good as a RST-based robust pole placement approach for the microgripper. The rejection of the vibrations, naturally induced by the flexible structure, and the control of the tip displacement have been successfully performed. Because we had taken into account frequency-based criteria from the first designing step of our device, we demonstrate that the tuning of the HAC/LAC can be easily performed and leads to low regulator order

Design and optimal control of a multistable, cooperative microactuator

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty

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

A Review of Modeling and Control of Piezoelectric Stick-Slip Actuators

Piezoelectric stick-slip actuators with high precision, large actuating force, and high displacement resolution are currently widely used in the field of high-precision micro-nano processing and manufacturing. However, the non-negligible, non-linear factors and complexity of their characteristics make its modeling and control quite difficult and affect the positioning accuracy and stability of the system. To obtain higher positioning accuracy and efficiency, modeling and control of piezoelectric stick-slip actuators are meaningful and necessary. Firstly, according to the working principle of stick-slip drive, this paper introduces the sub-models with different characteristics, such as hysteresis, dynamics, and friction, and presents the comprehensive modeling representative piezoelectric stick-slip actuators. Next, the control approaches suggested by different scholars are also summarized. Appropriate control strategies are adopted to reduce its tracking error and position error in response to the influence of various factors. Lastly, future research and application prospects in modeling and control are pointed out

Precision Control of Piezo Electric Actuator

芝浦工業大学201

Improvement in the Imaging Performance of Atomic Force Microscopy: A Survey

Nanotechnology is the branch of science which deals with the manipulation of matters at an extremely high resolution down to the atomic level. In recent years, atomic force microscopy (AFM) has proven to be extremely versatile as an investigative tool in this field. The imaging performance of AFMs is hindered by: 1) the complex behavior of piezo materials, such as vibrations due to the lightly damped low-frequency resonant modes, inherent hysteresis, and creep nonlinearities; 2) the cross-coupling effect caused by the piezoelectric tube scanner (PTS); 3) the limited bandwidth of the probe; 4) the limitations of the conventional raster scanning method using a triangular reference signal; 5) the limited bandwidth of the proportional-integral controllers used in AFMs; 6) the offset, noise, and limited sensitivity of position sensors and photodetectors; and 7) the limited sampling rate of the AFM's measurement unit. Due to these limitations, an AFM has a high spatial but low temporal resolution, i.e., its imaging is slow, e.g., an image frame of a living cell takes up to 120 s, which means that rapid biological processes that occur in seconds cannot be studied using commercially available AFMs. There is a need to perform fast scans using an AFM with nanoscale accuracy. This paper presents a survey of the literature, presents an overview of a few emerging innovative solutions in AFM imaging, and proposes future research directions.This work was supported in part by the Australian Research Council (ARC) under Grant FL11010002 and Grant DP160101121 and the UNSW Canberra under a Rector's Visiting Fellowshi