The Mellin transform to control system described by an implicit derivative transmittance

In the time domain, linear systems can be described by a differential equation of integer or noninteger order type. Using the Laplace transform, these systems are also represented by a transfer function corresponding to an implicit or explicit derivative transmittance. As a general rule, this approach corresponds to a wide range of systems studied in control theory. In this paper, the authors study the control system described by an implicit derivative transmittance with a PID controller of noninteger order type. A method based on the calculus of the Mellin transform of the system impulse response is developed to obtain the controller parameters. A comparison between controller of integer and noninteger order type is realized in the time domain