Cause-effect Relations Based Dynamic Modeling and Its Application to Control∗

In this paper a special incremental type of cause-effect dynamic model is proposed for use in different control schemes. The model parameters are integrated into the shape of the specially introduced cause-effect relation function. This function represents the degrees of relationship between the past time changes of the control input and the change of the current plant output. The model of the plant dynamics is identified from experimental data by three different algorithms. The first one is a Direct Identification by use of the Least Mean Squares (LMS) algorithm. The second one is the Indirect (reduced size) Identification, which identifies the parameters of an one-dimensional Takagi-Sugeno fuzzy model that is further used to approximate the cause-effect relation function of the dynamic model. Thus a significant reduction in the size of the identification problem is achieved. The third algorithm is called “Soft Guided” Identification that is able to use preliminary human knowledge about the possible or expected type of the plant dynamics. It is able to produce a more plausible dynamic model especially in the presence of highly noised input-output data. Several versions of predictive control schemes based on the proposed dynamic model are described and investigated in the paper. They use different horizon lengths and horizon widths. Finally, a special version of a feed-forward reference model control, based on the proposed type of incremental cause-effect relation model is described and analyzed in the paper by numerical simulations. All the simulation results are a kind of numerical proof for the real applicability of the proposed dynamic modeling method and the respective control schemes.