SINGULAR VALUE ANALYSIS AND SCALING: APPLICATIONS FOR MULTIVARIABLE PROCESS DESIGN AND CONTROL

Singular Value Analysis (SVA), an analysis structure formalized on Singular Value Decomposition (SVD), has become an important new tool in the areas of process design and control. Application has been mainly to the process steady state gain matrix. The SVA literature notes that the properties of the decomposition matrices are scale dependent; thus a shortcoming of SVA is its scale dependence. The present research aims to capitalize on the "problem of scaling" and use it as a source of information.; SVA is based on the 1(,2)-norm of the process gain matrix and SVD matrices. An important aspect in design and control is process matrix conditioning which is represented by matrix condition number. Analytical expressions for optimal scaling for the 1(,2)-norm condition number cannot be obtained. Utilization of Tomlin's scaling procedures to obtain "well-conditioned" matrices and a numerical search routine have been employed successfully to minimize condition number of a matrix.; Interaction is another major concern in multivariable process control. Interaction and process conditioning are two distinct problems. However, it is shown that scaling can alleviate a conditioning problem for low interaction and that numerical analysis may be needed to determine scaling effects when the interaction is high.; Scaling can be related to a process via sensitivity of transmitters and range of final control elements. The units of SVD are logically distributed on the three SVD matrices: singular values are dimensionless, the principle output directions (U) have output units and the principle input directions (V) have input units.; Other areas addressed include structure of U and V, uniqueness of SVD, analytical expressions for SVD based on Givens reflections versus rotations, and rules to match the results of analytical SVD and the QR algorithm. The concept of "controller conditioning" versus " process conditioning" has been introduced.; New definitions have been introduced and several theorems were developed to provide research direction and help explain the numerical results. Largely on the basis of these new theorems, additional avenues for SVA, as a formal interaction measure, are suggested.