A Structured Singular Value Test for Variable Selection and Pairing

The proper selection and pairing of manipulated and controlled variables is crucial for successful control system design. A test for such a purpose is developed in this paper. The criteria for which a set of variables is deemed adequate for control purposes are 1) robustness to model uncertainty, 2) stability despite decentralized control, and 3) constraints (on manipulated and associated variables) satisfied at steady-state. The basis for this test is the Structured Singular Value, which provides a generalized framework for simultaneously addressing the performance and robustness aspects of control systems. This test, which is independent of a specific controller design methodology, is a definitive test - alternatives can be evaluated precisely on whether they satisfy requirements, without requiring the user to specify a scaling or some arbitrary "cut-off" point for acceptable configurations. The effectiveness of the test is illustrated with a case study involving the control of a Heavy Oil Fractionator, which forms part of the Shell Standard Control Problem.