TP transformation based dynamic system modeling for nonlinear control

The aim of this paper is to propose a numerical controller design methodology. This methodology is based on two steps. In the first step, the tensor product (TP) model transformation is applied, which is capable of transforming a given nonlinear state-space dynamic model into TP model form. Then, in the second step, the linear matrix inequality (LMI) theorems are used within the parallel distributed compensation (PDC) controller design frameworks. The main novelty of this paper is the TP model transformation of the first step. It is also capable of dealing with the tradeoff between complexity and accuracy of the resulting TP model. The TP model transformation is a numerical method that leads to the following advantages: it is capable of functioning with models given either by analytic explicit forms or by various soft-computing based identification techniques; it does not need problem dependent analytic derivations, but can be executed "automatically" by computers. Numerical simulations are used to provide empirical validation of the proposed control design methodology. In order to demonstrate the effectiveness of the TP model transformation a controller is derived for the prototypical aeroelastic wing section that exhibits limit cycle oscillation and chaotic behavior.