A quadratic approximation of the back-off methodology for the control structure selection problem

For almost three decades, the back-off methodology has been extensively developed and refined for addressing the control structure selection problem. Previous work has been based on a linear and a non-linear formulation. The linear formulation ensures quick determination of the optimal solution but with a potentially significant loss of accuracy in complex non-linear processes. The non-linear formulation develops higher accuracy and offers the opportunity of simultaneous consideration of design and control. This improved accuracy usually comes with an increase in computational cost and complexity. A new methodology based on linear models and a quadratic approximation of economics is proposed which demonstrates improved accuracy when compared with the linear approximation and reasonable increase in computational effort than the non-linear counterpart. Three case studies are studied in detail to examine the advantages of the new formulation.