Vojtěch Mlynář | Searcharxiv

arXiv2026

FPGA-based LQG controller and hardware-in-the-loop simulator implementation for nanomechanical systems

We present an open-source framework for real-time Linear Quadratic Gaussian (LQG) control and hardware-in-the-loop (HIL) simulation on the affordable Red Pitaya STEMlab FPGA platform. The controller implements a discrete-time Kalman filter and Linear Quadratic Regulator (LQR) for systems with up to three coupled oscillatory degrees of freedom, targeting applications in levitated optomechanics, MEMS/NEMS, and related experimental platforms. Complementing the controller, the HIL simulator provides a~configurable second-order stochastic plant with nonlinear input and output mappings, enabling realistic closed-loop testing under real-time and fixed-point constraints. A MATLAB-based workflow automates model configuration, controller synthesis, numerical scaling, and FPGA deployment without requiring specialized hardware expertise. As an end-to-end demonstration, we present the stabilization of a levitated nanoparticle in a two-dimensional double-well potential, illustrating the complete workflow from model definition and simulation to real-time feedback control.

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arXiv2025

Feedback stabilization of a nanoparticle at the intensity minimum of an optical double-well potential

In this work, we develop and analyze adaptive feedback control strategies to stabilize and confine a nanoparticle at the unstable intensity minimum of an optical double-well potential. The resulting stochastic optimal control problem for a noise-driven mechanical particle in a nonlinear optical potential must account for unavoidable experimental imperfections such as measurement nonlinearities and slow drifts of the optical setup. To address these issues, we simplify the model in the vicinity of the unstable equilibrium and employ indirect adaptive control techniques to dynamically follow changes in the potential landscape. Our approach leads to a simple and efficient Linear Quadratic Gaussian (LQG) controller that can be implemented on fast and cost-effective FPGAs, ensuring accessibility and reproducibility. We demonstrate that this strategy successfully tracks the intensity minimum and significantly reduces the nanoparticle's residual state variance, effectively lowering its center-of-mass temperature. While conventional optical traps rely on confining optical forces in the light field at the intensity maxima, trapping at intensity minima mitigates absorption heating, which is crucial for advanced quantum experiments. Since LQG control naturally extends into the quantum regime, our results provide a promising pathway for future experiments on quantum state preparation beyond the current absorption heating limitation, like matter-wave interference and tests of the quantum-gravity interface.

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