A real-time parametric stiffness observer for VSA devices

We consider the problem of estimating non-linear time-varying stiffness of a mechanical system based only on force and position measurements. A recent work presented a non-parametric stiffness observer, which converges to within an Uniformly Ultimately Bounded neighborhood of the real stiffness value. The method provides excellent results for applications where the system is persistently excited. In this paper, we provide a parametric identification method that complements the previous solution in that it can provide, after a sufficiently long learning period, a complete model of the nonlinear stiffness, which can be applied henceforth even in the absence of excitation. Convergence conditions for the proposed method are discussed. Simulation and experimental results are provided, illustrating the performance of the proposed algorithm.