基于分数阶微积分的模糊分数阶控制器研究

Fuzzy Fractional Order Controller Based on Fractional Calculus

在分析分数阶微积分的基础上,提出了一种新型模糊分数阶比例积分微分控制器.分数阶微积分将传统控制器中的积分和微分的阶数扩展到任意实数,为控制器的设计提供了比传统整数阶更好的性能扩展.结合分数阶比例积分微分控制器和模糊控制逻辑,用分数阶比例积分微分单元代替传统的模糊比例积分微分控制器中的比例积分微分单元,构建了模糊分数阶比例积分微分控制器的结构,采用模糊逻辑推理和Tus-tin离散方法实现了模糊分数阶比例积分微分控制器的计算.最后,用数字仿真方法和不同条件下的对比分析验证了新型模糊分数阶比例积分微分控制器的优良控制特性.研究结果表明,设计的新型模糊分数阶比例积分微分控制器对非线性和参数不确定性具有较强的鲁棒性.

A novel fuzzy fractional order proportional integral derivative （FFPID） controller based on fractional calculus is presented. Fractional calculus performs more effectively for the controller design than integer order calculus with arbitrary integral and derivative orders of real number. Combined the fractional proportional integral derivative controller with fuzzy control logic, the unit of fractional proportional integral derivative replaces the unit of proportional integral derivative in conventional fuzzy PID controllers to establish the structure of FFPID. The operational process of FFPID controllers is realized with the method of Tustin discretization and fuzzy logic reasoning. To demonstrate better control characteristics of the FFPID controllers, a numerical simulation with a detailed comparative analysis under individual conditions is carried out. The results verify the fine robust performance for the nonlinearity and parameter uncertainty.