Sliding mode control with gain scheduled hyperplane for LPV plant

This study presents sliding mode hyperplane design for a class of linear parameter-varying (LPV) plants, the state-space matrices of which are an affine function of time-varying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertainties. We have designed a time-varying hyperplane for a rotor-magnetic bearing system with a gyroscopic effect, which can be considered an LPV plant due to parameter dependence on rotational speed. The obtained hyperplane is continuously scheduled with respect to rotational speed. We successfully carried out experiments using a commercially available turbomolecular pump system and results were reasonable and good.