A new modifier adaptation methodology for real-time optimization

The traditional modifier adaptation can be used to deal with the optimization problem of mismatched model, and it shows good performance in most cases. However, the method cannot be used directly, when the gradients of the model outputs, with respect to the decision variables, are difficult to calculate directly. Also, the simulation results show that the method cannot achieve the optimum in theory when the gradient estimation is particularly inaccurate. Therefore, a new modifier adaptation methodology for real-time optimization is proposed in this paper. A method similar to Proportion integration differentiation is used to deal with the deviation between the actual gradient and the model gradient and to improve the method of modifier terms computation. In addition, we find that the appropriate relaxation of certain constraints can expand the search area and improve the effectiveness of the optimization. The validation of the method is demonstrated by the solution of an artificial example and the optimal setting problem of the converter entrance temperatures in flue gas acid-making.