Tuning of a new class of robust fractional-order proportional–integral–derivative controllers

A new class of fractional proportional–integral (PI) and PI–derivative (PID) controllers is defined, based on a closed-loop reference model expressing the dynamical and robust performances. Moreover, the filtering of the derivative action is explicitly formulated using a generalized second-order reference model. Numerical simulations with simple systems illustrate some general principles that can be used as guidelines for the tuning of fractional PID controllers. For more complex or delayed systems, a tuning method based on the time moments approach is also proposed. Numerical examples illustrate the capabilities of this tuning technique.