Generation of Optimal Linear Parametric Models for LFT-Based Robust Stability Analysis and Control Design

Abstract

We present a general approach to generate a linear parametric state-space model, which approximates a nonlinear system with high accuracy and is optimally suited for linear fractional transformation (LFT) based robust stability analysis and control design. At the beginning a Jacobian-based linearization is applied to generate a set of linearized state-space systems describing the local behavior of the nonlinear plant about the corresponding equilibrium points. These models are then approximated using multivariable polynomial fitting techniques in combination with global optimization. The objective is to find a linear parametric model, which allows the transformation into a linear fractional representation (LFR) of least possible order. A gap metric constraint is included during the optimization in order to guarantee a specified accuracy of the transfer function of the linear parametric model. The effectiveness of the proposed method is demonstrated by applying it to a simple benchmark problem as well as to two industrial applications, one being a nonlinear missile model the other a nonlinear transport aircraft model.