Use of transient measurements for the optimization of steady-state performance via modifier adaptation

Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. RTO schemes differ in the way measurements are incorporated in the optimization framework. Explicit RTO schemes solve a static optimization problem repeatedly, with each iteration requiring transient operation of the plant to steady state. In contrast, implicit RTO methods use transient measurements to bring the plant to steady-state optimality in a single iteration, provided the set of active constraints is known. This paper considers the explicit RTO scheme "modifier adaptation" (MA) and proposes a framework that allows using transient measurements for the purpose of steady-state optimization. It is shown that convergence to the plant optimum can be achieved in a single transient operation provided the plant gradients can be estimated accurately. The approach is illustrated through the simulated example of a continuous stirred-tank reactor. The time needed for convergence is of the order of the plant settling time, while more than five iterations to steady state are required with conventional static MA. In other words, MA using transient information is able to compete in performance with RTO schemes based on gradient control, with the additional ability to handle plant constraints.