Use of Transient Measurements for Static Real-Time Optimization

Modifier adaptation (MA) is a real-time optimization (RTO) method characterized by its ability to enforce plant optimality upon convergence despite the presence of model uncertainty. The approach is based on correcting the available model using gradient estimates computed at each iteration. MA uses steady-state measurements and solves a static optimization problem. Hence, after every input change, one typically waits for the plant to reach steady state before measurements are taken. With many iterations, this can make convergence to the plant optimum rather slow. Recently, an approach that uses transient measurements for steady-state MA has been proposed. This way, plant optimality can be reached in a single transient operation. This paper proposes to improve this approach by using a dynamic model to process transient measurements for gradient computations. The approach is illustrated through the simulated example of a CSTR. Furthermore, the proposed method is less dependent on the choice of the RTO period. The time needed to reach plant optimality is of the order of the plant settling time, whereas several transitions to steady state would have been necessary using the standard static MA scheme.