Direct and indirect gradient control for static optimisation

Static “self-optimising” control is an important concept, which provides a link between static optimisation and control (Skogestad, 2000). According to the concept, a dynamic control system could be configured in such a way that when a set of certain variables are maintained at their setpoints, the overall process operation is automatically optimal or near optimal at steady-state in the presence of disturbances. A novel approach using constrained gradient control to achieve “self-optimisation” has been proposed by Cao (2004). However, for most process plants, the information required to get the gradient measure may not be available in real-time. In such cases, controlled variable selection has to be carried out based on measurable candidates. In this work, the idea of direct gradient control has been extended to controlled variable selection based on gradient sensitivity analysis (indirect gradient control). New criteria, which indicate the sensitivity of the gradient function to disturbances and implementation errors, have been derived for selection. The particular case study shows that the controlled variables selected by gradient sensitivity measures are able to achieve near optimal perf