Safety-Constrained Robust Backstepping Control with Dual-MRD Force Allocation for Double-Rope Mine Hoist

Payload eccentricity and time-varying rope length can cause excessive inter-rope tension imbalance in a double-rope mine hoist. This study develops a safety-constrained semi-active differential-tension control method using dual magnetorheological dampers (MRDs). A coupled longitudinal model with time-varying rope length separates eccentricity-induced static load sharing from vibration-induced dynamic tension. A barrier Lyapunov function (BLF)-based robust backstepping controller regulates the dynamic tension-imbalance deviation about the shifted equilibrium and incorporates the prescribed 10% tension-imbalance limit into the control design. To ensure actuator feasibility, the nominal differential-force command is processed through a physically constrained MRD realization layer involving force projection, force allocation, and current regulation. Numerical results under nominal conditions show that the proposed strategy reduces the maximum tension-imbalance ratio from 0.1380 to 0.0404, produces no numerical boundary violation, and decreases the peak inter-rope tension difference during deceleration from 19.51 to 1.89 kN. Sensitivity analyses further demonstrate that the proposed controller maintains positive safety margins across all investigated variations in payload eccentricity, payload mass, hoisting acceleration, maximum hoisting speed, and maximum allowable MRD current.