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Identification of hammerstein systems using subspace methods with applications to ankle joint stiffness

A Hammerstein system is a series connection of a static non-linearity followed by a linear dynamic system. The subspace method is an efficient alternate to the classic Prediction Error Method to identify linear time invariant systems, especially those with multiple inputs and/or outputs. Furthermore, the subspace method has been extended to identify block-structured, nonlinear systems including those with Wiener and Hammerstein structures. This paper reviews the extended subspace method for the identification of Hammerstein systems, and demonstrates how it can be used to estimate dynamic joint stiffness. Simulation results demonstrate that the algorithm estimates the linear and nonlinear components of the ankle joint stiffness accurately.