Fractional-order systems and (PID mu)-D-lambda-controllers

Dynamic systems of an arbitrary real order (fractional-order systems) are c onsidered, A concept of a fractional-order PIlambda D-mu-controller, involv ing fractional-order integrator and fractional-order differentiator, is pro posed. The Laplace transform formula for a new function of the Mittag-Leffe r-type made it possible to obtain explicit analytical expressions for the u nit-step and unit-impulse response of a linear fractional-order system with fractional-order controller both for the open and closed leap. An example demonstrating the use of the obtained formulas and the advantages of the pr oposed PIlambda D-mu-controllers is given.