System identification in the presence of completely unknown periodic disturbances

A system identification method to extract the disturbance-free dynamics and the disturbance effect correctly despite the presence of unknown periodic disturbances is presented. The disturbance frequencies and waveforms can be completely unknown and arbitrary Only measurements of the excitation input and the disturbance-contaminated response are used for identification. Initially, the disturbances are modeled implicitly. When the order of an assumed input-output model exceeds a certain minimum value, the disturbance information is completely absorbed in the identified model coefficients. A special interaction matrix explains the mechanism by which information about the system and the disturbances are intertwined and more importantly, how they can be separated uniquely and exactly for later use in identification and control. From the identified information a feedforward controller can be developed to reject the unwanted disturbances without requiring the measurement of a separate disturbance-correlated signal. The multi-input multi-output formulation is first derived in the deterministic setting for which the system and disturbance identification is exact. Extensions to handle noise-contaminated data are also provided. Experimental results illustrate the method on a flexible structure. A companion paper addresses the problem where the disturbance effect is modeled explicitly.