A parametrization of All stabilizing repetitive controllers for linear minimum phase systems

摘要

In the present paper, we give an exact parametrization of all causal stabilizing repetitive controllers for the single-input/single-output continuous time minimum phase systems. The past studies on the parametrization of repetitive controller is to obtain the parametrization of all stabilizing controllers for the system such that the plant is connected to 1/(1 - q(s)e{sup}(-sL)) in series, where q(s) is strictly proper asymptotically stable rational function. Since 1/(1 - q(s)e {sup}(-sL)) has no zeroes in the closed right half plane, in the case that the plant is of minimum phase, the system such that the phase plant is connected to 1/(1 - q(s)e{sup}(-sL)) in series is also of minimum phase. This implies that the exact paremetrization of all repetitive controllers for the minimum phase plant is obtained using the parametrization of all controllers for the minimum phase plant described by Glaria and Goodwin. Using above mentioned idea, the simple parametrization of all stabilizing repetitive controllers for the strictly proper system is given. Finally, numerical example to show the advantage of this parametrization is indicated.