The techniques of dynamic systems identification are algorithms of most importance for generating mathematical and computational models capable to represent the dynamic of systems and processes present in many fields of society, such as: industrial processes; automobiles; food production; aerospace vehicles; biological systems and etc. The identification of these systems, which generally have more than one variable of input and output (multivariable systems) and also are nonlinear, it is very important for science and engineering in relation to the development of new control techniques, fault monitoring and prediction of operating state of these mechanisms. Nonetheless, the identification of nonlinear MIMO (Multiple Input Multiple Output) systems is a hard task, as much due the difficulty of implementing the classic algorithms for solve this problem, as the fact that nonlinear systems require complex models for represent their dynamics in satisfactory way. In order to contribute with the solution of this problem, this work proposes a framework capable of performing as much the identification of nonlinear dynamic MIMO systems in multivariable fuzzy TSK model, which can represent in simple way the coupling among the variables involved in identification, as the selection of regressor vector used in model. To perform fuzzy TSK multivariable model parameterization, the proposed framework uses the algorithms Least Square (LS) and Particle Swarm Optimization (PSO), which are responsible to estimate the matrix of parameters and the set of standard deviation of the Gaussians in model inputs, respectively. The proposed methodology is tested and compared with RNA and a Hammerstein-Wiener (WH) model in identification of two nonlinear MIMO industrial plants: Continuous Stirred Tank Reactor (CSTR); Industrial Dryer. The comparison of these three techniques is made with base in indices of Mean Squared Error (𝑀𝑆𝐸) and Variance Accounted For (𝑉𝐴𝐹), further the analysis of residues between the observed and estimated data. The results show that the proposed framework got the best performance, based in the two indices, in 80% of outputs estimation of the two multivariable plants, and also reached the best performance in 60% of residual analysis of plants identification.
|
