Controlled synchronization of coupled pendulums by Koopman Model Predictive Control

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00367542" target="_blank" >RIV/68407700:21230/23:00367542 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.conengprac.2023.105629" target="_blank" >https://doi.org/10.1016/j.conengprac.2023.105629</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.conengprac.2023.105629" target="_blank" >10.1016/j.conengprac.2023.105629</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Controlled synchronization of coupled pendulums by Koopman Model Predictive Control

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Controlled synchronization of coupled pendulums by Koopman Model Predictive Control

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20205 - Automation and control systems

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Control Engineering Practice

ISSN

0967-0661

e-ISSN

1873-6939

Svazek periodika

139

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

—

Kód UT WoS článku

001054626400001

EID výsledku v databázi Scopus

2-s2.0-85166195931