Research Initiation: Robustness Properties of Multiple Loop Feedback Systems

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Linear multivariable feedback systems possess many properties not present in single-loop systems which pose great difficulty in design. One such difficulty is that multivariable systems can have radically different stability margins depending on where the loop is broken. An even greater difficulty is that a multivariable feedback system may possess good stability margins against uncertainty appearing at only one loop breaking point, yet may be destabilized by small perturbations appearing simultaneously at more than one point. The goal of this research is to understand how feedback properties, e.g. performance and robustness, at one point of a multivariable system are related to those properties at other loop breaking points and to investigate how properties of the plant and compensator affect this relation. The techniques used in the research include a method for approximating closed loop from open loop properties. This research should prove useful in developing methods for solving multivariable control system design problems.