Joint operation-control design for a class of batch exothermic reactors

This paper addresses the joint design of the nominal state motion and feed-forward (FF) output-feedback (OF) tracking control for a class of exothermic batch reactors, using a hydrothermal carbonization (HTC) reactor as a case study. The objective is to design the nominal state motion to maximize profit while incorporating a control strategy that includes an event-based component to stop the batch. The reactor's sustained evolution and profit per unit time are modeled by the state motion of a nonlinear, non-autonomous ordinary differential equation (ODE) over a finite-time interval. The problem is solved within a constructive control framework, combining concepts from chemical reactor engineering and nonlinear control theory, tailored to the characteristics of batch reactors. First, the nominal optimal operation is designed with a balanced compromise between duration, robustness, and heat exchange load, through: (i) the identification of passivity and detectability solvability conditions for the OF tracking control, and (ii) a simple recursive numerical construction approach. Then, a nonlinear FF OF tracking-termination control is developed, ensuring closed-loop (CL) robust motion stability, along with a straightforward gain tuning scheme. The proposed methodology is demonstrated and validated through numerical simulation with a representative HTC reactor example.