Modeling of a plant with variable operating conditions: an interpolation of coprime factorization models

Modeling of a multi-input multi-output plant with variable operating conditions is considered. The plant model is described as a linear interpolation of proper stable coprime factorizations of the transfer functions of two models defined at two representative operating points. The coprime factorizations are not unique and the interpolated model is dependent on the choice of them. To choose the coprime factorizations of the representative models appropriately so that the interpolated model well approximates the real plant, we formulate a norm-minimization problem for the difference of coprime factorizations between the real plant and the interpolated model at a specified operating point. To compute the solution of this problem, a BMI (bilinear matrix inequality) approach in state space is proposed.