Output-constrained control of beam-swing dynamics of tower cranes with elastic jibs

Tower crane jibs are prone to vibration due to their lightweight structure. The complex dynamics of coupled vibrations pose significant challenges in designing effective damping control systems. This study addresses the vibration suppression problem for a nonlinear tower crane model with a flexible jib undergoing slewing motion. We derive the fully coupled differential equation for the crane system by utilizing Euler–Bernoulli beam theory and Lagrange’s equations. The effect of the parameters on the vibration characteristics is analyzed and verified by experiments. Furthermore, we propose a novel boundary control method to suppress distributed deformation as the jib approaches the desired angle. Applying the Barrier Lyapunov Function (BLF) can keep the output states within the designed range. Finally, we conduct numerical simulations to verify the effectiveness of the designed control strategy.