Guaranteed Closed Loop Precision in Multiple Model Based Control

Abstract

In this paper, gain scheduled controllers designed on the basis of multiple modelling are considered. Specifically, Local Controller Networks are designed by interpolation of a set of linear controllers. The local linear controllers are obtained by Minimum Variance design based on a Local Model Network, i.e., a model of a nonlinear plant obtained by interpolation of linear models that guarantee a good approximation of the plant, at least locally, in the operating regime space. In particular, robustness issues are considered, based on the consideration that it is well known that the characteristics of the interpolating functions play a crucial role. This paper shows necessary qualitative conditions for designing robust control systems based on the interpolating function shape and rate of change. Additionally, under certain flatness conditions for those functions (well fulfilled by the so called super-Gaussian family), the upper bound for closed loop error can be precisely estimated and strictly connected to the interpolating function family features.