Modeling and Control of Irrational Fractional-Order System and Its Block Diagram Simulation

The use of fractional-order to describe an actual system can better reveal its essential characteristics and its behavior. The description and analysis of an irrational fractional-order system are more complicated than that of a rational fractional-order system. To solve this difficulty, this paper studies its system identification and controller design for the characteristics of such systems. Firstly, based on the frequency domain response data of these systems, combined with the optimization algorithm to realize the rationalization of them, the curves fitting are used to illustrate the correctness and effectiveness of the identification algorithm. Then, based on the identified rational models, the optimum controllers are designed. Step response comparison shows that the performance of fractional-order controllers is superior to that of traditional integer-order controllers. Finally, through the block diagram implementation, the effectiveness and correctness of the fractional-order controller design are explained.