Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

A new approach to compensate the strong hysteresis nonlinearity in piezoelectric materials is proposed. Based on the inverse multiplicative scheme, the approach avoids models inversion as employed in existing works. The compensator is therefore simple to implement and does not require additional computation as soon as the direct model is available. The proposed compensation technique is valuable for hysteresis that are modeled with the Bouc-Wen set of equations.

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Bouc–Wen Modeling and Inverse Multiplicative Structure to Compensate Hysteresis Nonlinearity in Piezoelectric Actuators

This paper provides a survey of results in linear parameter-varying (LPV) control that have been validated by experiments and/or high-fidelity simulations. The LPV controller synthesis techniques employed in the references of this survey are briefly reviewed and compared. The methods are classified into polytopic, linear fractional transformation, and gridding-based techniques and it is reviewed how in each of these approaches, synthesis can be carried out as a convex optimization problem via a finite number of linear matrix inequalities (LMIs) for both parameter-independent and parameter-dependent Lyapunov functions. The literature is categorized with regard to the application, the complexity induced by the controlled system’s dynamic and scheduling orders, as well as the synthesis method. Exemplary cases dealing with specific control design problems are presented in more detail to point control engineers to possible approaches that have been successfully applied. Furthermore, key publications in LPV control are related to application achievements on a timeline.

A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations

This paper presents a modified Prandtl-Ishlinskii (P-I) (MPI) model for the asymmetric hysteresis description and compensation of piezoelectric actuators. Considering the fact that the classical P-I (CPI) model is only efficient for the symmetric hysteresis description, the MPI model is proposed to describe the asymmetric hysteresis nonlinearity of piezoceramic actuators (PCAs). Different from the commonly used approach for the development of asymmetric P-I models by replacing the classical play operator with complex nonlinear operators, the proposed MPI model still utilizes the classical play operator as the elementary operator, while a generalized input function is introduced to replace the linear input function in the CPI model. By this way, the developed MPI model has a relative simple mathematic format with fewer parameters to characterize the asymmetric hysteresis behavior of PCAs. The benefit for the developed MPI model also lies in the fact that an analytic inverse model of the CPI model can be directly applied for the inverse compensation of the asymmetric hysteresis nonlinearity represented by the developed MPI model in real-time applications. To validate the developed MPI model and the inverse hysteresis compensator, simulation, and experimental results on a piezoceramic actuated platform are presented.

Modeling and Compensation of Asymmetric Hysteresis Nonlinearity for Piezoceramic Actuators With a Modified Prandtl–Ishlinskii Model

In this paper, a general skeleton on modeling, controller design, and applications of the piezoelectric positioning stages is presented. Toward this framework, a general model is first proposed to characterize dynamic behaviors of the stage, including frequency response of the stage, voltage-charge hysteresis and nonlinear electric behavior. To illustrate the validity of the proposed general model, a dynamic backlash-like model is adopted as one of hysteresis models to describe the hysteresis effect, which is confirmed by experimental tests. Thus, the developed model provides a general frame for controller design. As an illustration to this aspect, a robust adaptive controller is developed based on a reduced dynamic model under both unknown hysteresis nonlinearities and parameter uncertainties. The proposed control law ensures the boundedness of the closed-loop signals and desired tracking precision. Finally, experimental tests with different motion trajectories are conducted to verify the proposed general model and the robust control law. Experimental results demonstrate the excellent tracking performance, which validates the feasibility and effectiveness of the proposed approach.

Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design, and Experimental Evaluation

Piezocantilevers are commonly used for the actuation of micromechatronic systems. These systems are generally used to perform micromanipulation tasks which require high positioning accuracy. However, the nonlinearities, i.e., the hysteresis and the creep, of piezoelectric materials and the influence of the environment (vibrations, temperature change, etc.) create difficulties for such a performance to be achieved. Various models have been used to take into account the nonlinearities but they are often complex. In this paper, we study a one degree of freedom piezoelectric cantilever. For that, we propose a simple new model where the hysteresis curve is approximated by a quadrilateral and the creep is considered to be a disturbance. To facilitate the modelling, we first demonstrate that the dynamic hysteresis of the piezocantilever is equivalent to a static hysteresis, i.e., a varying gain, in series with a linear dynamic part. The obtained model is used to synthesize a linear robust controller, making it possible to achieve the performances required in micromanipulation tasks. The experimental results show the relevance of the combination of the developed model and the synthesized robust H infin controller.

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Quadrilateral Modelling and Robust Control of a Nonlinear Piezoelectric Cantilever

The manipulation of very small objects is one of the most important tasks in microrobotics. Micromanipulators are required in all fields where precise manipulation of very small objects must be performed like microsurgery or assembly of MEMS. It is well known that downsizing the tools used in the macroworld is not appropriate to achieve tasks in the microworld. In this paper we present a prototype of a microgripper made up of piezoelectric bending unimorphs. A dynamic model of the piezoelectric unimorphs is developed. Various identification methods have been applied in order to verify the validity of the model. An observer has been built in order to estimate the forces applied at the tip of the fingers. Knowing these forces is very important to avoid destruction of objects during manipulation. The microgripper is able to handle microobjects in a wide range of size by changing the initial distance between the fingers. The resolution of positioning obtained is better than 10 nm for each finger. Every finger can be actuated individually so that dexterous handling can be achieved. This system allows us to perform precise micromanipulation tasks.

A microgripper using smart piezoelectric actuators

The studies presented in this paper are motivated by the high performances required in micromanipulation/microassembly tasks. For that, this paper presents the development, the modeling, and the control of a 2-DOF (in linear and angular motion) micropositioning device. Based on the stick-slip motion principle, the device is characterized by unlimited strokes and submicrometric resolutions. First, experiments were carried out to characterize the performances of the micropositioning device in resolution and speed. After that, a state-space model was developed for the substep functioning. Such functioning is interesting for a highly accurate task like nanopositioning. The model is validated experimentally. Finally, a controller was designed and applied to the micropositioning device. The results show good robustness margins and a response time of the closed-loop system.

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Development, Modeling, and Control of a Micro-/Nanopositioning 2-DOF Stick–Slip Device

Microgrippers with integrated force sensors are very efficient tools for dexterous manipulation of objects in the microworld (size less than 100 μm). In this paper, we first propose a modeling approach of a nonlinear electrostatic microgripper with integrated force sensor while handling calibrated microglass balls of 80- μm diameter. Limit of the linear operating range of the microgripper is investigated and a nonlinear model is proposed and validated experimentally for large displacements. We then propose the design of an optimal force feedback controller to ensure reliable handling operations with appropriate gripping forces. To overcome the limitation caused by the low signal-to-noise ratio provided by the sensor, a Kalman filter is used to estimate the states of the process from noise measurements. The control law is implemented and validated using real-time experiments for 10 μN gripping force reference with a noise level (peak-to-peak magnitude of the noise) reaching 8 μN in the worst case. The effectiveness of the optimal filter is proven by comparison with external interferometric measurements.

https://hal.archives-ouvertes.fr/hal-00874563/document

Modeling and Optimal Force Control of a Nonlinear Electrostatic Microgripper

This paper deals with a historical overview of the activities of the French FEMTO-ST institute in the field of microrobotic manipulation and assembly. It firstly shows tools developed for fine and coarse positioning: 4 DOF microgrippers, 2 DOF modules and smart surfaces. The paper then goes on the automation of tridimensional microassembly of objects measuring between 10 and 400 microns. We are especially focusing on several principles. Closed loop control based on micro-vision has been studied and applied on the fully automatic assembly of several 400 microns objects. Force control has been also analyzed and is proposed for optical Microsystems assembly. At least, open loop trajectories of 40 microns objects with a throughput of 1,800 unit per hour have been achieved. Scientific and technological aspects and industrial relevance will be presented.

https://hal.archives-ouvertes.fr/hal-00801873/document

Yassine Haddab

Papers

Quadrilateral Modelling and Robust Control of a Nonlinear Piezoelectric Cantilever

A microgripper using smart piezoelectric actuators

Development, Modeling, and Control of a Micro-/Nanopositioning 2-DOF Stick–Slip Device

Modeling and Optimal Force Control of a Nonlinear Electrostatic Microgripper

Robotic microassembly and micromanipulation at FEMTO-ST