A Nyquist criterion for time-varying periodic systems, with application to a hydraulic test bench

In this paper, stability results dedicated to sampled periodic systems are applied to a mechanical system the stiffness of which exhibits quick variations: an hydraulic test bench used for mechanical testing of complex structures. To achieve this application, a time-varying w transformation representation of sampled periodic systems is introduced. An extension of the Nyquist criterion to sampled periodic systems is then given. Finally, this theorem is applied to evaluate the stability degree of the hydraulic test bench controlled using CRONE control methodology.