Experimental Platform for Boundary Control of Mechanical Frenkel-Kontorova Model

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 the 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.