Use of Transient Measurements for Real-Time Optimization via Modifier Adaptation

Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. Explicit RTO schemes, which are characterized by solving a static optimization problem repeatedly, typically require multiple iterations to steady state. In contrast, implicit RTO methods, which do not solve an optimization problem explicitly, can use transient measurements and gradient control to bring the plant to steady-state optimality in a single iteration, provided the set of active constraints is known. This paper investigates the explicit RTO scheme “modifier adaptation” (RTO-MA) and proposes a framework that uses transient measurements. Convergence to the true plant optimum can be achieved in a single iteration provided the plant gradients can be estimated appropriately, for which we propose a linearization-based method. The approach is illustrated through the simulated example of a continuous stirred-tank reactor. It is shown that the time needed for convergence is of the order of the plant settling time, while more than five iterations to steady state are required when MA is applied in its classical form. In other words, the explicit RTO-MA scheme is able to compete in performance with the implicit RTO schemes based on gradient control, with the additional ability to handle process constraints.