Two fuzzy internal model control methods for nonlinear uncertain systems

The purpose of this paper is to use the internal model control to deal with nonlinear stable systems affected by parametric uncertainties.

The dynamics of a considered system are approximated by a Takagi-Sugeno fuzzy model. The parameters of the fuzzy rules premises are determined manually. However, the parameters of the fuzzy rules conclusions are updated using the descent gradient method under inequality constraints in order to ensure the stability of each local model. In fact, without making these constraints the training algorithm can procure one or several unstable local models even if the desired accuracy in the training step is achieved. The considered robust control approach is the internal model. It is synthesized based on the Takagi-Sugeno fuzzy model. Two control strategies are considered. The first one is based on the parallel distribution compensation principle. It consists in associating an internal model control for each local model. However, for the second strategy, the control law is computed based on the global Takagi-Sugeno fuzzy model.

According to the simulation results, the stability of all local models is obtained and the proposed fuzzy internal model control approaches ensure robustness against parametric uncertainties.

This paper introduces a method for the identification of fuzzy model parameters ensuring the stability of all local models. Using the resulting fuzzy model, two fuzzy internal model control designs are presented.