The aim of this paper is to present a finite element modeling of the dynamic motion of a turbine rotor and its controller design with the mass unbalance under a crack on a rotating shaft. This process is an advanced method to the mathematical description of a system including an influence of a mass unbalance and a crack on the rotor shaft. As the first step, the shaft is physically modeled with a finite element method and the dynamic mathematical model is derived by using the Hamilton principle; thus, the system is represented by various subsystems. The equation of motion of a shaft with a mass unbalance and a crack is established by adapting the local mass unbalance and stiffness change through breathing and gaping from the existence of a crack. This is a reference system for the given system. Based on a fictitious model for transient behavior induced from vibration phenomena measured at the bearings, an elementary estimator is designed for the safety control and detection of a mass unbalance on the shaft. Using the state estimator, a bank of an estimator is established to get the diagnosis and the system data for a controller.
 R. J. Patton and S. M. Kangetehe, “Robust Fault Diagnosis Using Eigen Structure Assignment of Observers,” In: R. Patton, P. Frank and R. Clark, Eds., Fault Diagnosis in Dynamic Systems, Prentice Hall, Herausgeber, 1984.