Observer Design and Parameter Estimation for Linear Systems with Nonlinearly Parameterized Perturbations

We introduce a method of observer design for systems described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. The design is modular, and consists of a modified high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator. The parameter estimator is constructed by the designer to identify the unknown parameters, by dynamically inverting a nonlinear equation. We apply the method to observer design for a DC motor with friction modeled by the dynamic LuGre friction model, estimating the internal state in the friction model and an unknown parameter representing Coloumb friction.