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

Abstract

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. I. INTRODUCTIONControl of nonlinear systems based on a family of linear models has been studied widely for decades, and several theoretical frameworks have been developed. In these frameworks, it has been presumed that a mathematical model of the nonlinear system is available, and local models can be generated by linearization of the system. In practice, particularly for more complicated systems, a control engineer may not have access to such models and, alternatively, identification of linear models from input/output (I/O) data must be considered. A piecewise linear (PL) model can be constructed from a family of local linear models of the system, e.g. [1], or through a concurrent identification of linear models from global data, e.g. [2].In this paper Takagi-Sugeno (TS) control of the elevation channel of a twin-rotor system, as an unstable nonlinear SISO system, based on closed-loop I/O data is considered. Applications of different control schemes such as fuzzy sliding [3], model predictive [4], decoupling control [5], and evolutionary PID control [6] to twin-rotor systems have been reported in the literature. Herein, given a low quality controller with an integral action, provided by the manufacturer, a family of linear models are identified at various operating

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