Robust Stability in IMC Framework using the Numerical Range Approach

Process control in the presence of modeling uncertainty depends critically on the manner in which the uncertainty is characterized. Depending on the information about the parameter variations and the modeling simplifications, the space spanned by the process transfer function can take various shapes. Representing this space solely by its maximum radius can lead to significant overestimation of the possible model/plant mismatch and can restrict the performance of the closed-loop process. In this paper, numerical range approach is used to study robust stability for multivariable systems in the Internal Model Control (IMC) framework. Results indicate that the additional phase information provided by the numerical range can reduce the conservatism of singular value based approaches. Strategies to decompose the process transfer function as well as to tune the IMC filter are discussed.