Synchronous Control of the Anti-Back-Slip Support System for Hard-Rock TBMs in Large-Inclination Shafts

The underground caverns of pumped-storage power stations generally feature large inclination angles. During the bottom-up oblique excavation by hard-rock Tunnel Boring Machines (TBMs), the Anti-Back-Slip (ABS) support system is the core device ensuring safe operations. Specifically, the synchronization of the multiple hydraulic cylinders within the ABS system is a critical factor determining the stability and safety of the TBM. Therefore, this paper designs a hydraulic control system for the ABS device and proposes an adjacent cross-coupling synergistic control strategy based on adaptive backstepping. This strategy innovatively integrates an adaptive backstepping control law into the adjacent cross-coupling topology to achieve high-precision multi-cylinder control. Utilizing the AMESim-Simulink platform, high-fidelity co-simulations are conducted under both uniform and eccentric load conditions. The results demonstrate that under nominal conditions, the proposed algorithm exhibits asymptotic convergence at the mathematical level. The system maintains robust stability under dynamic excitations. When subjected to sudden asymmetric eccentric loads of 1.0–2.0 times, the system prevents tracking divergence and limits the maximum multi-cylinder synchronization error to within 1.82 mm. This research satisfies the requirements for synchronous control and provides a theoretical and engineering reference for the disturbance-rejection synergy of inclined shaft TBM support systems.