Digital realization and characteristics of fractional order controllers
分数阶控制器的数字实现及其特性

In order to overcome the difficulty of the discretization and application of fractional order controllers (FOC), the digital realization and control characteristic of FOC are studied in this paper. The limited memory method (LMM) is derived from the direct discretization of the truncated Grunwald-Letnikov formula. After Z transform with Tustin generating function, the fractional order calculus can be approximated by continued fraction expansion (CFE), which is called the Tustin CFE method. The comparative frequency analysis between them verifies that the Tustin CFE method dominates LMM in the sense that the Tustin CFE method is close to the real fractional order system. Applying the proposed approximation, the control performance simulation is carried out to compare FOC with conventional PID controllers. The results show that FOC possesses more robust performance for the nonlinearity.