State Observer Based on an Accelerometer for an Elastic Joint with Nonlinear Friction

This paper presents a state observer for an elastic joint with nonlinear friction via the information from an acceleration sensor. In order to avoid discontinuities, the nonlinear friction of the motor, which includes static, coulomb, and viscous terms, is considered a smooth function. In addition, it uses an acceleration sensor to obtain the information about the link with high uncertainty. The proposed state observer guarantees that the estimation error for the position and velocity of the link connected via an elastic joint containing a nonlinear stiffness (elasticity) converges to zero. In addition, it is shown that the observer gain can be designed by LMI (linear matrix inequality) optimization. Finally, to verify the performance of the proposed observer, the method proposed in this paper is tested by experiments on a two-inertia system with an elastic shaft.