Constrained Data-Driven Optimal Control for Scrubber Systems Under Non-Stationary Compositional Drifts

In scrubbing tower (ST) systems, outlet vapor temperature regulation is subject to strict thermal constraints, requiring the bottom temperature to remain below a critical safety threshold. Transient overshoots can rapidly trigger pyrolytic coking, foul mass-transfer packed beds and spray nozzles, and ultimately force complete production shutdowns. Due to feedstock compositional drifts, high thermal inertia, and significant transport delays, high-fidelity predictive identification is essential for proactive early warning and for overcoming the limitations of reactive feedback control. To address these bottlenecks, this paper introduces an offset-free, hard-constrained, data-driven adaptive optimal control paradigm, designated as the improved GRU-coupled conjugate gradient linear quadratic regulator (IGRUCG-LQR). First, by constructing an augmented state space embedded with integral error, the proposed paradigm eliminates permanent tracking offsets induced by long-term nonstationary drifts. Second, automatic differentiation is used to extract the time-varying Jacobian matrix of a gated recurrent unit (GRU) online, thereby tracking the nonlinear evolution of the underlying thermodynamic baseline with high fidelity. To manage the critical trade-off between strict actuator saturation and short real-time sampling intervals, the conjugate gradient (CG) method is fused with a hard-boundary projection operator, enforcing physical constraints with high computational efficiency and without complex matrix inversions. Experimental validation on a real-world industrial dataset demonstrates that the proposed paradigm secures the safety baseline while achieving high-resolution transient tracking. Furthermore, it significantly suppresses high-frequency valve chattering to mitigate mechanical fatigue, establishing a solid theoretical and engineering foundation for the prolonged stable operation of safety-critical processes. The proposed framework achieves an Integral Absolute Error (IAE) of 86.66 and an Integral Time Absolute Error (ITAE) of 4064.49.