Generation of LPV models and LFRs for a nonlinear aircraft model

In this chapter we present a general approach to generate a linear parameter varying (LPV) state-space model, which approximates a nonlinear system with high accuracy and is well suited for LFT-based robustness analysis. A Jacobian-based linearisation of the nonlinear parametric aircraft model is performed first to generate a set of linearised state-space models describing the local behaviour of the nonlinear aircraft for a representative set of parameter values and flight conditions. These models are then approximated by a unique LPV model, by using multivariable polynomial fitting techniques in combination with global optimisation. The objective is to find an LPV model which guarantees a specified approximation accuracy and simultaneously leads to a linear fractional representation (LFR) of least possible order. For this, a gap metric constraint on the input-output transfer-function error is included in the optimisation problem. The effectiveness of the proposed method is demonstrated by generating high accuracy LPV models and the corresponding LFRs for the COFCLUO nonlinear aircraft model.