This work generalizes a preliminary investigation (Georgakis and Li, 2010) in which we examined the use of Response Surface Methodology (RSM) for the estimation of surrogate models as accurate approximations of high-dimensional knowledge-driven models. Three processes are examined with higher complexity than before, accounting for a much larger number of input and output variables. The surrogate models obtained are used to analyze several steady-state plant-wide characteristics. In all processes, the knowledge-driven model is a dynamic simulation with a plant-wide control structure of multiple SISO controllers. This type of controller proves to not be robust enough in its stability characteristics to enable substantial changes in the set-points. The net-elastic regularization is successfully used for the estimation of the metamodel parameters, avoiding overfitting and eliminating insignificant terms. Cross validation is used to compare and evaluate the relative accuracy of the quadratic and cubic models. (C) 2018 Elsevier Ltd. All rights reserved.