Lyapunov Based Adaptive Control for Varying Length Pendulum with Unknown Viscous Friction

Varying length pendulum is studied here to address its oscillations damping using conveniently generated Coriolis force. Lateral damping friction is assumed to be practically negligible and therefore it is not included in the model. Magnitude of the Coriolis force is equal to the product of the angular swing velocity and the velocity of the change of the string length. As a consequence, the problem is modelled by the nonlinear control system having non-controllable and non-stabilizable approximate linearization at the requested damped steady state. Lyapunov technique combined with backstepping design and control Lyapunov function selection is used to tackle this truly nonlinear problem. Furthermore, Lyapunov based adaptive estimation of the viscous friction at the string pivot is designed to improve the controller performance. Besides theoretical mathematical justification the simulations and the real-time experiments using laboratory test-bed are included to highlight the paper results.