分数阶控制器的数字实现及其特性

针对分数阶控制器数值计算和应用难的问题,研究了分数阶控制器的数字实现方法和控制特性．取Grunwald-Letnikov定义有限项,并直接离散化,得到有限记忆数字实现法;利用Tustin算子生成函数把分数阶微分由复频域变换到Z域,然后用连分式展开式CFE(continued fraction expansion)近似展开,可得到Tustin CFE数字实现法．两种方法的频域对比分析表明Tustin CFE法优于有限记忆法．采用设计的分数阶控制器的数字实现方法,对分数阶控制器和传统PID控制器的控制性能进行了对比实验分析．研究结果表明:分数阶控制器对非线性具有较强的控制能力．

Digital realization and characteristics of fractional order controllers

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.