On the stability of ADRC for manipulators with modelling uncertainties

The Active Disturbance Rejection Control (ADRC) is an object of the ever growing interest in the latest years due to its limited requirements concerning knowledge of a plant's mathematical model. In this paper, a problem of system stability in presence of modelling uncertainties is investigated. Precisely, imperfect knowledge of the manipulator dynamics and an inertia matrix is considered by the means of the Lyapunov analysis and conditions are formulated which guarantees convergence of the errors in the system to some finite boundary. Influence of the unknown inertia matrix is thoroughly investigated. It is shown, that if the third derivative of the desired trajectory is small enough then an intentional increase of the input matrix estimation error may lead to a reduction of the tracking error boundary. Obtained results are supported by presented simulations and experiments.