Takagi-Sugeno control of the elevation channel of a twin-rotor system using closed-loop empirical data

In this paper, design of Takagi-Sugeno controllers for a twin-rotor system from empirical data is addressed. First, identification of linear models using Prediction Error Method in the presence of nonlinear distortions and in feedback systems is revisited, and it is demonstrated that feedback nonlinear systems with an integral action can be locally represented by linear models rather than affine models. Moreover, it is demonstrated that how the consistency and unbiasedness of the identified models can be improved by proper design of the experiments. In order to ensure that the unmodeled contributions in the resulting piecewise linear model are sufficiently small, a criterion is proposed based on the small-gain theorem that can be used for unfalsification of the piecewise linear model. Finally, by taking advantage of the separation principle, design of fuzzy Takag-Sugeno state feedback and observer is formulated in terms of Linear Matrix Inequalities (LMIs). The implementation results on the actual system demonstrate significant improvements with respect to the initial controller and previous work on similar systems.