<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A nonsmooth optimization control (NOC) based on a sandwich model with hysteresis is proposed to control a micropositioning system (MPS) with a piezoelectric actuator (PEA). In this control scheme, the hysteresis phenomenon inherent in the PEA is described by a Duhem submodel embedded between two linear dynamic submodels that describe the behavior of the drive amplifier and the flexible hinge with load, respectively, thus constituting a sandwich model with hysteresis. Based on this model, a nonsmooth predictor for sandwich systems with hysteresis is constructed. To avoid the complicated online search for the optimal value of the generalized gradient at a nonsmooth point, the method of the so-called weighted estimation of generalized gradient is proposed. In order to compensate for the model error caused by model uncertainty, a model error compensator (MEC) is integrated into the online optimization control strategy. Afterwards, the stability of the control system is analyzed based on Lyapunov’s theory. Finally, the proposed NOC-MEC method is verified on an MPS with a PEA, and the corresponding experimental results are presented.</p>
</abstract>

A nonsmooth optimization control (NOC) based on a sandwich model with hysteresis is proposed to control a micropositioning system (MPS) with a piezoelectric actuator (PEA). In this control scheme, the hysteresis phenomenon inherent in the PEA is described by a Duhem submodel embedded between two linear dynamic submodels that describe the behavior of the drive amplifier and the flexible hinge with load, respectively, thus constituting a sandwich model with hysteresis. Based on this model, a nonsmooth predictor for sandwich systems with hysteresis is constructed. To avoid the complicated online search for the optimal value of the generalized gradient at a nonsmooth point, the method of the so-called weighted estimation of generalized gradient is proposed. In order to compensate for the model error caused by model uncertainty, a model error compensator (MEC) is integrated into the online optimization control strategy. Afterwards, the stability of the control system is analyzed based on Lyapunov’s theory. Finally, the proposed NOC-MEC method is verified on an MPS with a PEA, and the corresponding experimental results are presented.

Nonsmooth Optimization Control Based on a Sandwich Model with Hysteresis for Piezo–Positioning Systems

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A nonsmooth optimization control (NOC) based on a sandwich model with hysteresis is proposed to control a micropositioning system (MPS) with a piezoelectric...

Nonsmooth Optimization Control Based on a Sandwich Model with Hysteresis for Piezo–Positioning Systems

Published Online: Sep 21, 2023

Page range: 449 - 461

Received: Dec 08, 2022

Accepted: Feb 14, 2023

DOI: https://doi.org/10.34768/amcs-2023-0033

Keywords
optimization control, hysteresis, compensation, piezoelectric actuator, sandwich system

© 2023 Sen Yang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Nonsmooth Optimization Control Based on a Sandwich Model with Hysteresis for Piezo–Positioning Systems

Published Online: Sep 21, 2023

Page range: 449 - 461

Received: Dec 08, 2022

Accepted: Feb 14, 2023

DOI: https://doi.org/10.34768/amcs-2023-0033

Keywordsoptimization control, hysteresis, compensation, piezoelectric actuator, sandwich system

© 2023 Sen Yang et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
optimization control, hysteresis, compensation, piezoelectric actuator, sandwich system