Stiffness estimation of a lumped mass-spring system using sliding DFT

Obtaining an accurate parametric model of a mechanism enables optimised control. System identification through noise injection is a common method for obtaining frequency responses which are suited for control design, but not for feedforward control and motion profile optimisation as the response is non-parametric. Especially when the mechanism consists of multiple sources of flexibility, extracting parameters from frequency responses is challenging and often requires model order reduction. Moreover, if the parameters are either time or position-dependent, an on-line estimator is required for enabling adaptive control and optimisation. This paper therefore presents a computationally efficient approach, based on the sliding Discrete Fourier Transform, for tracking stiffness during operation. A lumped mass-spring system with 4 degrees of freedom is used as a proof of concept. Through simulations, the expected accuracy of the developed estimator is analysed and its ability to deal with noise is demonstrated.