Experimental Platform for Boundary Control of Mechanical Frenkel-Kontorova Model

Abstract: In this paper, we present a laboratory mechatronic platform for experimental verification and demonstration 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 torsionally coupled pendulums pivoting around a single shaft that can be controlled through the motors at boundaries while all angles are read electronically. We first introduce and describe the platform, providing details of its mechatronic design and software architecture. All the files are freely shared with the research community under an open-source license through a public repository. The motivation for this sharing is to help reproducibility or research -- the platform can be useful for others as a testbed for control algorithms for this class of dynamical systems, for instance, distributed control or control of flexible structures. In the second part of the paper, we then showcase the platform using two control problem formulations tailored to the FK model -- we discuss the practical motivation for studying these problems, propose (some) methods for solving them and demonstrate the functionality using experiments. In particular, the first control formulation deals with non-collocated control/regulation 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. Some other motivated problems can certainly be formulated, solved, and demonstrated using the proposed platform.