Nanopositioning with piezoelectric actuators: Modeling, control, and applications

Xie, Shengwen
Major Professor
Juan Ren
Committee Member
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Mechanical Engineering
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Mechanical Engineering

Nanopositioning is critical for applications in microscale or nanoscale, such as investigation and manipulation of biological, chemical or physical processes/materials, and usually realized with piezoelectric actuators (PEA). However, due to the nonlinearities, it is challenging to achieve high-accuracy and broad-bandwidth control of PEAs. In this dissertation, we investigate how to improve the control accuracy and bandwidth. In addition, we apply the proposed controllers on two applications based on atomic force microscopes (AFMs).

In Chapter 2, we combine iterative learning control (ILC) with predictive control (MPC) forming IL-MPC. It avoids the inversion model compared to inversion-based ILC and also has low tracking errors in the first iteration. The convergence condition of IL-MPC is derived. In particular, we studied the performance of IL-MPC when the reference trajectory is varying both theoretically and experimentally.

Although IL-MPC can be used for high-accuracy and broad-bandwidth control of PEAs, it is not a real-time controller, the design of which is the focus of Chapters 3-6. The key idea is to accurately model the PEA dynamics over a broad bandwidth with recurrent neural networks (RNNs) and design predictive controllers based on the resulted models.

In Chapter 3, RNN is used to model the PEA dynamics and combined with a linear model to improve the modeling accuracy. Then a nonlinear predictive controller is designed with the augmented RNN model. To improve the computation efficiency of the controller, the gradient is computed analytically for the optimization problem. Nevertheless, the computation efficiency hinders the usage of large sampling frequency which is necessary for many applications. This issue is alleviated in Chapter 4 in which the nonlinear model is linearized with Koopman operators.

However, as the RNN becomes more complex, the computation efficiency is still a problem even with linearization. An alternative is to model the inversion dynamics with RNNs, which leads to the control approach in Chapter 5. The inversion model based on RNNs can compensate for most of the nonlinearities; then, a linear model was used to capture the residual dynamics. Furthermore, how to reduce the modeling errors when incorporating the linear model with the RNN inversion model is investigated in Chapter 6.

Finally, with regard to the applications, we applied IL-MPC for high-speed AFM imaging and the proposed real-time controller for polymer indentation control, which further validate the proposed methods.