PID controller design for fractional-order systems with time delays

Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of sαsα, where 0<α<10<α<1, and ss is the Laplace transform variable. Effect of input–output time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants.