Virtual non-linear disturbance observer by dual inverse dynamic modelling

Abstract

A method to predict unknown external disturbances and modelling errors for trajectory tracking of non-linear systems is presented. The technique involves dual inverse non-linear dynamics modelling based on Lagrangian dynamics and the use of redundant coordinates incorporating Lagrange multipliers. The first inverse dynamics model is a conventional formulation where the desired trajectory is used to calculate the required control inputs. The second inverse dynamics model treats the measured response as the desired motion, and calculates the inputs that would be required to achieve the measured motion. The method is applicable to cases where the acceleration signal is available. It can be used either to measure actual disturbances or to estimate virtual disturbances, which effectively represent all the disturbances and modelling errors on the control input coordinates. It is also suitable to be used in conjunction with or in addition to existing controllers. A numerical simulation of a two-link manipulator is used to demonstrate the effectiveness of the controller under various external disturbances, modelling errors, and unmodelled substructures.