基于改进Oustaloup滤波器的分数阶PID控制器简化设计

针对分数阶微积分算子的直接和间接近似化方法所表现出来的形式复杂、运算量大的问题，对Oustaloup滤波器的结构进行改进，对常规分数阶PID控制器进行了简化设计，并采用自适应遗传算法对控制器的参数进行整定.选取两种代表性分数阶系统，在模型处于两种典型状态下，对简化型分数阶PID控制器、常规分数阶PID控制器和整数阶PID控制器的控制性能进行仿真实验对比.结果表明，在控制器性能基本相同的情况下，通过该方法设计的简化型分数阶PID控制器性具有结构简单，耗时量小的优点，提高了工程可实现性.

Design of Simplified Fractional-order PID Controller Based on Improved Oustaloup Filter

The direct and indirect approximation methods for fractional calculus operators have complicated forms and a large amount of computation. A simplified fractional differential operator approximation method based on improved Oustaloup filter is proposed. A simplified fractional-order PID controller is designed, and the parameters of the controller are tuned by an adaptive genetic algorithm. Two representative fractional-order systems are selected, under the nominal and perturbation states of the model, and the simulation performances of the simplified fractional-order PID controller, conventional fractional-order PID controller, and integer-order PID controller are compared. The results show that the designed simplified fractional-order PID controller can achieve a control performance close to that of the conventional fractional-order PID controller, and it has the advantages of a simple structure, less time consumption, and improved project feasibility.