A Structure-Inspired Disturbance Observer for Finite-Dimensional Mechanical Systems

This article describes a disturbance observer (DO) design for systems whose dynamics are piecewise differentiable and satisfy certain structural conditions. Provided a Lipschitz continuity condition holds with a sufficiently small Lipschitz constant—a condition that is implied by “sufficiently slow” dynamics—the observer ensures local ultimate boundedness of the disturbance estimate error, which converges exponentially to a positively invariant set whose size can be made arbitrarily small. This observer is appropriate for finite-dimensional mechanical systems. We demonstrate the design in two examples—a tutorial example of a nonlinear mass-damper-spring system and a practical example of an experimental underwater vehicle.