Virtual Sensing of Unmeasured Supply–Return Disturbances for Predictive Control in Cooperative Hydraulic Support Pushing

Cooperative pushing of hydraulic supports is affected by pressure-boundary fluctuations and neighboring-branch actions transmitted through shared supply–return circuits. In longwall mining systems, common-node pressures and neighboring-branch flow disturbances are difficult to measure continuously, which limits their use in feedback predictive control. This study proposes a virtual-sensing-based output -feedback predictive control method for cooperative hydraulic support pushing under limited sensing conditions. A control-oriented coupled model is established by retaining the two-chamber pressure dynamics of the target cylinder, supply-main impedance, common return-main dynamics, and equivalent neighboring supply-side and return-side disturbance flows. The equivalent disturbance flows are introduced as nodal disturbance inputs in the supply and return pressure dynamics. A linear extended state observer reconstructs the common supply-node pressure, common return-node pressure, and equivalent neighboring-disturbance flows from target-cylinder measurements, including displacement, velocity, cap-end pressure, and rod-end pressure. The reconstructed variables are incorporated into an output-feedback model predictive controller to coordinate displacement tracking, velocity stabilization, pressure-boundary regulation, and valve-input smoothing under input-amplitude, input-increment, and output constraints. The method is validated using AMESim–MATLAB/Simulink co-simulation and a dual-branch hydraulic experimental platform. Co-simulation results show that the proposed controller gives a maximum velocity deviation of 1.7484 mm/s, a recovery time of 0.112 s within the 1% velocity error band, and an input total variation of 2.3383. Experimental results show that controller intervention reduces the maximum velocity fluctuation from 1.0041 mm/s to 0.3011 mm/s and shortens the recovery time from 0.505 s to 0.038 s. The results demonstrate that virtual sensing of supply–return pressure boundaries and equivalent neighboring-disturbance flows improves motion continuity and driving-pressure stability in cooperative hydraulic actuation under limited sensing conditions.