Structural Identification of Dynamic Systems with Hysteresis

The method of structural identificat ion dynam- ic systems with a hysteresis in the conditions of uncer- tainty is developed. The method is based on selection of the special set containing the information on properties of a nonlinear part system. The virtual structure (VS) wh ich allo ws the make the decision about hysteresis structure is offered. The concept of structural identifiability of non- linear dynamic systems is introduced. Structural identifi- ability is a necessary condition of obtaining the original form of hysteresis. The criterion of structural identifiabil- ity is proposed. The solution of a problem selection the class of the functions belonging to hysteresis to nonlin e- arities is given. The procedure of structural identification of hysteresis functions is developed. Procedure realization is based on the phenomenological analysis of structure VS. Defin i- tion of features and properties of the VS is the goal of phenomenological analysis. Each non-linearity introduces the features in the behavior of the system. Therefore, their detection gives only the concrete analysis of VS. Algorith ms of estimation structural parameters the hys- teresis in the conditions of uncertainty are offered. They analyze the data in special structural space and are based on the application of secant method VS. Such approach gives adequate estimations of parameters hysteresis. The method of the structurally -frequency analysis is offered for check of the obtained results and estimations. It is based on the analysis of frag ments VS in t wo planes. Such analysis allows the ma ke a decision about hysteresis structure. We show that the offered methodology is appli- cable to unstable dynamic systems. Results of the com- puter simulation are given.