Determination of all stability region of unstable fractional order system in case of bearing system

In this paper, we propose and investigate the optimal tuning PID controller of unstable fractional order system by desired transient characteristics using the real interpolation method (RIM). The research shows that the main advantages of this method are drawn as the followings: 1) Carrying out an investigation of the stable region of coefficients of a PID controller using D-decomposition method; 2) Applying the method to investigate an unstable fractional order system.