Augmented TP model transformation-based parallel distributed compensation control design

The usual sampled hyper grid points of uniform sampling method are distributed equally in the TP model transformation, thus, the sampling results often omit the local extrema when the sampling step is not fine-tuned. Then the resultant tensor which is used for controller design can not fully cover the state space, although the gain which is the feasible solution of the linear matrix inequalities. In this paper, we proposed a non-uniform sampling method for tensor product model transformation, local extrema are considered in the sampling step, while the sampling step can vary dynamically for different function entries. In this paper, TP model transformation-based parallel distributed compensation (PDC) controller is extended in three folds: (i) The existing TP model transformation-based PDC controller with uniform sampling method is extended to TP model transformation-based PDC tracking controller with the uniform sampling method and an extended signal. (ii) A new TP model transformation-based PDC tracking controller is proposed based on a new sampling method, that is, the Hammersley sampling method. (iii) TP model transformation-based PDC tracking controller is also proposed based on the non-uniform sampling method. The proposed adaptive TP model transformation-based PDC tracking controller is able to enhance the performance of the TP model transformation-based PDC controller, and the adaptive TP model transformation-based PDC controller obtains the best results due to the nearly exact sampling of the system.

Automated summary

In this paper, a non-uniform sampling method is introduced for tensor product model transformation to consider local extrema, allowing for nearly exact sampling of the system. This adaptive approach improves the performance of the PDC controller and achieves the best results.