Fractional Order PID Controller and Its Digital Implementation

A new kind of PID controller, fractional order PID (Proportional, Integral and Derivative) controller (involving fractional order integrator and differentiator), was proposed which is the generalization of classical integer order PID controller. It is useful not only for fractional order systems but also for some integer order systems, and may have some superior performances compared with the classical integer order PID controller. A digital implementation of fractional order PID controller was given. Some limited terms of the definition of Grunwald-Letnicov fractional calculus are taken such that Z-transform method can be used to compute fractional order PID controller directly in the time domain. The simulation outcomes verify the effectiveness of the method proposed.