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研究了分数阶控制器的模拟和数字实现方法,其中数字实现是重点。数字实现是通过构造一个新的IIR型数字滤波器来对函数的分数阶微积分计算进行近似求解,然后对该滤波器进行连分式展开来完成的。以PID控制为例进行的数值仿真结果表明,用此方法设计的离散分数阶PID控制器比传统离散整数阶PID控制器具有更优的控制性能,同时也验证了该数字实现方法的正确性与可行性。
The simulation and digital realization methods of fractional order controllers are studied, of which digital implementation is the key point. The digital implementation is achieved by constructing a new IIR digital filter to approximate the fractional calculus calculation of the function, and then performing the fractional expansion of the filter. The numerical simulation with PID control as an example shows that the discrete fractional PID controller designed by this method has better control performance than the traditional discrete integer PID controller and the correctness of the method feasibility.