Evaluating estimation of gain directionality: Part 1: Methodology

For multivariable systems the input-output gain depends on the directionality of the inputs. This is denoted gain directionality, and explicit bounds on the possible gain of a system are obtained from singular value decomposition. In order to obtain high performance of multivariable control schemes it is mandatory that the dynamic model describes the gain directionality with sufficient accuracy. Based on this we pose the questions: with what accuracy can the gain directionality be estimated for a given system? Given an identified model what is the quality of the estimate of the gain directionality? This leads to an analysis in which a model set is defined based on a linear reference model, a relative output uncertainty description and the experimental design. The experimental design may include feedback, i.e. closed-loop identification. The error in the estimate of the gain in a given direction is then formulated as an H∞-norm problem. Given this representation the uncertainty on the estimated gain can be obtained by the structured singular value.