M. A. Vasquez-Beltran

Bio: M. A. Vasquez-Beltran is an academic researcher from University of Groningen. The author has contributed to research in topics: Deformable mirror & Hysteresis. The author has an hindex of 3, co-authored 6 publications receiving 23 citations.

Recursive Algorithm for the Control of Output Remnant of Preisach Hysteresis Operator

Abstract: We study in this letter the control of hysteresis-based actuator systems where its remanence behavior (e.g., the remaining memory when the actuation signal is set to zero) must follow a desired reference point. We present a recursive algorithm for the output regulation of the hysteresis remnant behavior described by Preisach operators. Under some mild conditions, we prove that our proposed algorithm guarantees that the output remnant converges to a desired value. Simulation result shows the efficacy of our proposed algorithm.

Influence functions for a hysteretic deformable mirror with a high-density 2D array of actuators

Abstract: We present modeling and analysis of a hysteretic deformable mirror where the facesheet interacts with a continuous layer of piezoelectric material that can be actuated distributively by a matrix of electrodes through multiplexing. Moreover, a method to calculate the actuator influence functions is described considering the particular arrangement of electrodes. The results are presented in a semi-analytical model to describe the facesheet's deformation caused by a high-density array of actuators, and validated in a simulation. The proposed modeling of an interconnection layout of electrodes is used to determine the optimal pressures the actuators must exert to achieve a desired surface deformation.

High pixel number deformable mirror concept utilizing piezoelectric hysteresis for stable shape configurations

Abstract: We present the conceptual design and initial development of the hysteretic deformable mirror (HDM). The HDM is a completely new approach to the design and operation of deformable mirrors (DMs) for wavefront correction in advanced imaging systems. The key technology breakthrough is the application of highly hysteretic piezoelectric material in combination with a simple electrode layout to efficiently define single actuator pixels. The set-and-forget nature of the HDM, which is based on the large remnant deformation of the newly developed piezomaterial, facilitates the use of time division multiplexing to address the single pixels without the need for high update frequencies to avoid pixel drift. This, in combination with the simple electrode layout, paves the way for upscaling to extremely high pixel numbers (≥128 × 128) and pixel density (100 / mm2) DMs, which is of great importance for high spatial frequency wavefront correction in some of the most advanced imaging systems in the world.

Influence functions for a hysteretic deformable mirror with a high density 2D array of actuators.

Abstract: We present modeling and analysis of a hysteretic deformable mirror where the facesheet interacts with a continuous layer of piezoelectric material that can be actuated distributively by a matrix of electrodes through multiplexing. Moreover, a method for calculating the actuator influence functions is described considering the particular arrangement of electrodes. The results are presented in a semi-analytical model to describe the facesheet's deformation caused by a high density array of actuators, and validated in a simulation. The proposed modeling of an interconnection layout of electrodes is used to determine the optimal pressures the actuators have to exert for achieving a desired surface deformation.

High pixel number deformable mirror concept utilizing piezoelectric hysteresis for stable shape configurations

Abstract: We present the conceptual design and initial development of the Hysteretic Deformable Mirror (HDM). The HDM is a completely new approach to the design and operation of deformable mirrors for wavefront correction in advanced imaging systems. The key technology breakthrough is the application of highly hysteretic piezoelectric material in combination with a simple electrode layout to efficiently define single actuator pixels. The set-and-forget nature of the HDM, which is based on the large remnant deformation of the newly developed piezo material, facilitates the use of time division multiplexing (TDM) to address the single pixels without the need for high update frequencies to avoid pixel drift. This, in combination with the simple electrode layout, paves the way for upscaling to extremely high pixel numbers ($\geq 128\times 128$) and pixel density ($100/mm^2$) deformable mirrors (DMs), which is of great importance for high spatial frequency wavefront correction in some of the most advanced imaging systems in the world.

Differential Models Of Hysteresis

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Modeling and Analysis of Butterfly Loops via Preisach Operators and its Application in a Piezoelectric Material

Abstract: We present modeling and analysis of the so-called butterfly hysteresis behavior, based on the use of the Preisach operator. The desired butterfly loop properties can be obtained under some mild conditions on the weighting function that defines the Preisach operator. The proposed framework is used to model the electric-field dependence of the strain in a piezoelectric material purposely designed to exhibit asymmetric butterfly loops with remnant deformation.

Asymptotic Stability Analysis of Lur’e Systems with Butterfly Hysteresis Nonlinearities

Abstract: We study the asymptotic stability of Lur'e systems with butterfly hysteresis nonlinearities modeled by the Preisach operators with respect to a set of equilibrium points. We present the input-output rate property of the Preisach operators that exhibit butterfly hysteresis behavior. Based on this characterization, we present sufficient conditions on the linear systems that guarantee the asymptotic stability of the closed-loop system to a set of equilibrium points via circle criterion. Finally numerical simulations are presented to demonstrate these results.

Recursive Algorithm for the Control of Output Remnant of Preisach Hysteresis Operator

Abstract: We study in this letter the control of hysteresis-based actuator systems where its remanence behavior (e.g., the remaining memory when the actuation signal is set to zero) must follow a desired reference point. We present a recursive algorithm for the output regulation of the hysteresis remnant behavior described by Preisach operators. Under some mild conditions, we prove that our proposed algorithm guarantees that the output remnant converges to a desired value. Simulation result shows the efficacy of our proposed algorithm.

Modeling and Compensation for Asymmetrical and Dynamic Hysteresis of Piezoelectric Actuators Using a Dynamic Delay Prandtl-Ishlinskii Model.

Abstract: Piezoelectric actuators are widely used in micro- and nano-manufacturing and precision machining due to their superior performance. However, there are complex hysteresis nonlinear phenomena in piezoelectric actuators. In particular, the inherent hysteresis can be affected by the input frequency, and it sometimes exhibits asymmetrical characteristic. The existing dynamic hysteresis model is inaccurate in describing hysteresis of piezoelectric actuators at high frequency. In this paper, a Dynamic Delay Prandtl–Ishlinskii (DDPI) model is proposed to describe the asymmetrical and dynamic characteristics of piezoelectric actuators. First, the shape of the Delay Play operator is discussed under two delay coefficients. Then, the accuracy of the DDPI model is verified by experiments. Next, to compensate the asymmetrical and dynamic hysteresis, the compensator is designed based on the Inverse Dynamic Delay Prandtl–Ishlinskii (IDDPI) model. The effectiveness of the inverse compensator was verified by experiments. The results show that the DDPI model can accurately describe the asymmetrical and dynamic hysteresis, and the compensator can effectively suppress the hysteresis of the piezoelectric actuator. This research will be beneficial to extend the application of piezoelectric actuators.