Identification and realization by state affine models

Representation of a “black-box” type, an alternative to the knowledge of the theoretical model, is well mastered in the cases of stationary linear systems. Indeed, by means of experiments carried out on the process, many identification procedures lead to state space equations or a transfer matrix representation. In the varylinear case, the model depends upon one or several influential parameters. It is interesting to obtain a global model, that is, a model which validly represents the system in the whole working range, whether for simulation or control law synthesis. Determining the exact dependence laws of model coefficients with respect to this or these influential parameters is tricky. The problem may be simplified if one is interested in regulation around a finite number of setting points. The procedure that is described in the next paragraphs shows how to get such a model by the use of state affine representation. After setting the retained hypothesis in section 4.2 and the mathematical background in section 4.3, two approaches to the identification problem are presented in section 4.4. One is a methodology for realization from a series of identification of the “linear tangent” around each setting point. The other is characterized by a direct identification. Both methods lead to obtaining a nonlinear discrete time global model (state affine model). Various applications of these techniques have been developed in close collaboration with the industrial world. Two examples are presented in section 4.5: The first concerns the modeling of a helicopter and the second deals with identification of a chemical neutralization process. These application results have justified the development of the AFFINE (software for Personal Computer), that uses Matlab facilities.