Reduced Dimension Control of Dynamic Systems

Reduced dimension control involves the indirect control of the entire output variable space through the judicious selection of a much smaller number of controlled and manipulated variables. A general framework for the selection of the subspace of manipulated and controlled variables, developed on the basis of minimum variance control theory, is presented. Given the disturbance directions and process gain matrix, expressions for the optimal directions for control are derived. The role of the number of independent disturbances in determining the number of controlled variables and the structure of the resulting reduced dimension controller are clearly shown. The framework is then applied to a simulated dynamic Kamyr digester. Two single-input, single-output reduced dimension controllers (RDCs) are proposed and compared to a 5 × 5 dynamic matrix controller (DMC) that controls all outputs and manipulates all inputs. The RDCs performed very well at the conditions for which they were designed and showed only modest degradation when the process operating point was changed. Despite their much simpler structure, their performance in terms of the full output space was very close to that of the DMC.