Simple Fractional Order Model Structures and their Applications in Control System Design

In this paper, firstly a four-parameter fractional order model structure is introduced to approximate processes having S-shaped step responses. Three different strategies are presented in order to determine the parameters of the proposed model. In a special case where the proposed model is not satisfactory, another fractional order model structure with five free parameters is introduced to improve the model approximation. Also in this case, a procedure is provided to estimate the parameters of the introduced five-parameter model. Then, some common classical integer order control design approaches are modified or extended to their fractional order counterparts in order to incorporate the proposed models in their design stage. Finally, some numerical examples are provided to show the applicability of the proposed procedures in estimating the parameters of the introduced models and evaluate the performance of the obtained models in the studied controllers.