Hybrid vibration suppression in deep well hoisting systems: Series-connected variable stiffness and damping adaptive control

Time-varying hoisting ropes (HR) in deep well hoisting systems (DWHS) are prone to shock and vibration under multi-source excitations. This paper presents a variable stiffness and damping damper (VSDD) connected in series with the HR and conveyance, synergistically coordinating stiffness and damping to suppress both loading/unloading pulses and operational harmonic-acceleration step excitations. A coupled distributed-parameter dynamic model of the HR–VSDD–conveyance system is established via Hamilton’s principle. For the two distinct excitation types, an enhanced backstepping-energy method is adopted to design adaptive damping laws: a robust correction term suppresses pulse-induced parameter drift under loading/unloading, while a parametric estimator identifies harmonic disturbances during operation conditions. Concurrently, variable stiffness control is derived to maintain static tension equilibrium. Simulations show that the proposed control outperforms passive and PID schemes and drastically reduces vibration compared with the system without VSDD: under loading, RMS acceleration is reduced by 32.4% versus without VSDD and by 13.4% versus PID, with a settling time of 2.7 s; under braking, it is reduced by 87% versus without VSDD and by 68% versus PID, with a settling time of 3.7 s.