Ing. Loi Do

LAMMPS, an acronym for Large-scale Atomic and Molecular Massively Parallel Simulator, is a widely used open-source tool for high-fidelity molecular dynamics (MD) simulations. In this paper, we take the initial steps towards using LAMMPS for synthesis and validation of feedback control in nanoscale manipulation. We begin by introducing the field of MD itself, discussing the specific challenges related to control synthesis, applications of nanoscale manipulation, and the intricacies of high-fidelity MD simulations. Then, we explain the main steps in modeling a molecular system in LAMMPS and provide an illustrative example. In the example, we consider a nanoscale flake of molybdenum disulfide manipulated with the tip of an atomic force microscope over an atomic surface. We designed a simple PID controller to slide the flake with the microscope tip into a desired position. To run LAMMPS simulations with closed-loop control, we utilized the official Python wrapper for LAMMPS, upon which we implemented additional functionalities. We share the code of the simulations freely with the research community through a public repository.

We propose a method to solve a class of control problems arising from a system of coupled pendulums. The system considered in this work is a one-dimensional array of pendulums pivoting around a single axis with adjacent pendulums coupled through torsion springs. Only a single torque motor attached to one of the two boundary pendulums actuates the system. This setup of coupled pendulums is a mechanical realization of the Frenkel–Kontorova (FK) model – a spatially discrete version of the sine-Gordon equation describing (nonlinear) waves. The main challenges of controlling this system are high order (the number of pendulums can be high), nonlinear and oscillatory dynamics, and only one actuator. The proposed class of problems can be characterized as controlled synchronization – designing a closed-loop controller that synchronizes the motion of the pendulums. Controlled synchronization is a special case of reference tracking, where all pendulums reach a common point or a trajectory. One can formulate many practically motivated problems within this class; here, we identify three problems: a vibration control of a flexible structure, swing-up control of all pendulums in the array, and low-friction sliding of an atomic-scale structure. We show that the presented problems can be dealt with by the Koopman Model Predictive Control (KMPC). The KMPC allows for controlling nonlinear systems by combining the classical linear model predictive control (MPC) with the Koopman operator approach for nonlinear dynamical systems. The main idea of the method is to construct a linear predictor of a nonlinear system in a higher-dimensional, lifted space and use the predictor within the linear MPC. The optimization problem formulation within the KMPC can then be tailored to a specific problem in the class. Simulations and experiments on a hardware platform realizing the FK model show the effectiveness of the method.

In this paper, we present a laboratory mechatronic platform for experimental demonstration and verification of various dynamical and control system phenomena exhibited by the Frenkel-Kontorova (FK) model – a spatially discretized version of the sine-Gordon equation. The platform consists of an array of spring-coupled pendulums pivoting around a single axis with the first and the last pendulums controlled by motors and all pendulums’ angles measured electronically. We first introduce and describe the platform, providing details of its mechatronic design and software architecture. All the design files are freely shared with the research community under an open-source license through a public repository. The platform can be used as a testbed for various control algorithms, e.g., for distributed control or control of flexible structures. In the second part of the paper, we showcase the platform using two control problem formulations tailored to the FK model. We discuss the practical motivation for studying these problems, propose methods for solving them, and experimentally demonstrate their functionality. In particular, the first control formulation deals with non-collocated stabilization of a single pendulum through one boundary of the array in the presence of a disturbance sent from the other boundary; the second control problem consists in synchronizing pendulums’ angular speeds. Other problems can certainly be formulated, solved, and demonstrated using the proposed platform whether for research or education purposes.

This paper tailors synchronization of multi-agent systems to motion control of the Frenkel-Kontorova (FK) model, a one-dimensional chain of harmonically coupled identical particles in a spatially periodic potential field. In particular, the goal is to drive all particles in the FK model to the desired trajectory by controlling only a single—boundary—particle. The proposed solution augments harmonic coupling in the FK model with dissipative inter-particle interactions, allowing all particles in the chain to synchronize to a particular reference trajectory. The boundary control represents a special case of pinning control. Moreover, as the FK model describes the frictional dynamics of a nanosheet sliding over a surface, we use its synchronization for controlling the nanoscale sliding friction. The key idea is to introduce a sliding reference trajectory that allows particles to move near synchrony. Synchronization effectively increases the system’s stiffness, so less energy ends up dissipated through inter-particle relative motion, thus reducing the frictional force. We validate the proposed solution through numerical simulations.

In this paper, we document a design of a computational method for an onboard prediction of a breaking distance for a city rail vehicle|a tram. The method is based on an onboard simulation of tram braking dynamics. Inputs to this simulation are the data from a digital map and the estimated (current) position and speed, which are, in turn, estimated by combining a mathematical model of dynamics of a tram with the measurements from a GNSS/GPS receiver, an accelerometer and the data from a digital map. Experiments with real trams verify the functionality, but reliable identification of the key physical parameters turns out critically important. The proposed method provides the core functionality for a collision avoidance system based on vehicle-to-vehicle (V2V) communication.