Controllability of Processes with Large Singular Values

Abstract

The singular-value decomposition has been used to analyze the robustness of closed-loop systems and to determine whether any controllability problems can be expected. Past controllability conditions have been derived in terms of the condition number and the minimum singular value of the process and the condition number of the controller transfer function matrix, in terms of potential sensitivities of the closed-loop system to model uncertainties or problems with saturation of the manipulated variables. This paper considers processes with a large maximum singular value. It is shown that the closed-loop control of such processes can result in poor transient performance as a result of valve accuracy considerations, even if the condition number is small and the minimum singular value is large, which would indicate no performance limitations according to existing controllability criteria. Further, processes with large singular values can be prone to sensor saturation. This indicates that the magnitude of all of the singular values should be considered when assessing the controllability of a process. A new interaction tool based on output correlation is introduced to help select measurements and manipulated variables that have a good range of singular values for practical application. The approach proposed is illustrated on two simple examples and on the Tennessee Eastman process.