Combining Analytic and Experimental Information for Linear Parameter-Varying Model Identification: Application to a Flexible Robotic Manipulator

Identifying a linear parameter-varying (LPV) model of a non-linear system from local experimental data is still a problem which deserves attention. Many difficulties related to the determination of the local models with respect to coherent bases have been recently pointed out and must be solved in order to ensure a good behavior of the interpolated LPV model. Rather than building a model either from the law of physics or from experimental data independently, the combination of an analytic and an experimental approach is used in this paper to identify an LPV model of a flexible robotic manipulator. This technique focuses on the interpolation step by combining local re-structured linear time-invariant (LTI) state-space models satisfying a state-space parameterization deduced from the non-linear equations governing the dynamic behavior of the system. A dedicated H∞-norm technique is introduced to solve the underlying re-structuring problem. This contribution shows that prior information can be really helpful when the problem of coherent basis selection arises. As a sample, the case of the identification of a 2-DoF non-linear flexible manipulator is addressed.