Simplified predictive control of dynamical systems based on incremental type of cause-effect models

An incremental cause-effect type of dynamical model is proposed for use in a predictive control scheme. The model parameters comprise of a scaling factor, a memory length and the shape of a specially introduced membership function. This function represents the normalized degrees of the cause-effect relationships between the past time changes of the control input and the current change of the plant output. The model of the plant dynamics can be identified from the experimental data by the least mean squares (LMS) algorithm. A special algorithm for reduced size identification that uses tuning of a 1D Takagi-Sugeno fuzzy model by the LMS algorithm is shown. An improved version of the predictive control scheme is also introduced that leads to a reduction of the prediction errors caused by the inaccuracy of the plant model. Finally, numerical simulations are shown to illustrate the performance of proposed control algorithm that lead to a conclusion for applicability of the method.