Generation of Self-oscillation in a Flexible Rope using Boundary Two-Relay Controller

Self-oscillations on a rope may help to release it when stuck inside a surface or rubbish. Here, we introduced the two-relay boundary controller to induce self-oscillations in a flexible rope or cable, governed as a hyperbolic partial differential equation. The two-relay controller has been used to induce periodic motion systems governed by nonlinear ordinary differential equations. As a contribution, the two-relay controller was extended to a class of partial differential equations. The asymptotic stability, without self-oscillator, was proved by means of a Lyapunov functional. Finally, we presented simulation results validating the proposed methodology.